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Francesco PELLICANO

Professore Ordinario
Dipartimento di Ingegneria "Enzo Ferrari"

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Pubblicazioni

2023 - Fluid–Structure Interaction of a thin cylindrical shell filled with a non-Newtonian fluid [Articolo su rivista]
Zippo, A.; Iarriccio, G.; Bergamini, L.; Colombini, E.; Veronesi, P.; Pellicano, F.
abstract

This paper presents the results of an extensive experimental campaign on the dynamic interactions between an elastic structure and a non-Newtonian fluid. The structure consists of a thin circular cylindrical shell, with the bottom end clamped to a shaking table, and the top end carrying a heavy mass. The fluid is a mixture of water and cornstarch, also known as oobleck. The system dynamics has been analyzed in the presence of different fluid levels (i.e., empty, partially, and full-filled). The experimental modal analysis has been carried out to identify the modal properties of the system. High energy tests have been performed by means of a seismic excitation consisting in a stepped sine sweep, spanning the forcing frequency within the neighborhoods where strong resonance phenomena take place. Different excitation amplitudes have been considered in order to induce phase transitions in the fluid, and the onset of complex dynamics has been detected using Fourier spectra and bifurcation diagrams of the Poincaré maps: when the fluid–solid​ transition occurs, the entangled non-Newtonian fluid rheology results in a complex dynamic scenario where period-doubling cascades, quasiperiodic and chaotic responses can be observed.

2023 - Spiral Bevel Gears: nonlinear dynamic model based on accurate static stiffness evaluation [Articolo su rivista]
Molaie, Moslem; Samani, Farhad S.; Zippo, Antonio; Pellicano, Francesco
abstract

In the present paper non-linear dynamics of a spiral bevel gear pair with backlash are investigated in order to clarify the internal excitations of major importance from the vibration point of view: manufacturing errors in the teeth profile, teeth spacing errors, and elastic deformation of the teeth. In some conditions, like in the case of backside contact, the destructive effect of internal excitations can be intensified leading to complex dynamics; for such reasons here backside contacts and reverse rotation are investigated in detail using a nonlinear time-varying model. The effect of damping is investigated as well. A one-DOF model is developed in order to study the dynamic behavior; the resulting a nonlinear differential equation with time-varying mesh stiffness is solved via numerical integration based on an adaptive step-size implicit Runge-Kutta scheme. The dynamic response of the system is analyzed through time histories, phase portraits, bifurcation diagrams, and Poincaré maps. Results show that for small backlash values, the possibility of backside contact increases. Meanwhile, by increasing the backlash value, the amplitude vibration of the gear rotation rises as well. By comparing the dynamic response of the system with different damping ratios, the results show that higher damping effectively reduces gear vibration resonance, although the probability of unsteady response still exists.

2023 - Vibration reduction of footbridges subjected to walking, running, and jumping pedestrian [Articolo su rivista]
Saber, H.; Samani, F. S.; Pellicano, F.
abstract

In this paper, the performance of vibration absorbers in reducing the vertical deflections of the footbridges subjected to human activities is studied. The vertical component of the pedestrian force during walking, running, and jumping is simulated as a moving time-dependent force model. The optimal parameters for the attached vibration absorbers are defined to minimize the deflection of the footbridge. The effectiveness of each vibration absorber is reviewed for different types of excitations. Results show reductions of 91%, 95%, and 96% in terms of the amplitude of vibration for the footbridge with the optimized tuned mass damper subjected to walking, running, and jumping, respectively, in comparison with a bare footbridge. The performance of the tuned mass dampers optimized numerically in the present study is compared with the tuned mass dampers possessing parameters achieved analytically. The damped footbridge with the numerically optimized tuned mass damper under walking, running, and jumping pedestrian experienced a deflection reduction of 9%, 34%, and 37%, respectively, concerning the tuned mass damperwith analytical parameters.

2022 - A novel nonlinear variable damping device and its application for the systems with uncertain parameters [Articolo su rivista]
Saber, H.; Samani, F. S.; Pellicano, F.
abstract

This paper deals with the performance of a novel nonlinear viscous dashpot with variable damping. The new proposed dashpot can be utilized in devices for instance dynamic vibration absorbers (DVAs). When the vibration absorber is tuned to the bridge's fundamental frequency, it represents a robust effect in controlling the vibrations of the bridge; however, a DVA is very sensitive to frequency detuning. The proposed nonlinear dashpot can be applied in a passive vibration absorber and upgrades it to a nonlinear variable damping one. Since the parameter of such DVA can be adjusted, it is the so-called nonlinear adjustable DVA. The mentioned dashpot, provides a quadratic nonlinearity for the damping element. The proposed dashpot in this study possesses a simple mechanism, which can handle large range of flow rates of fluid, smoothly without turbulence, in the oil channel. To investigate the effectiveness of an adjustable vibration absorber, a semi-active DVA with variable damping, and stiffness elements is applied on a footbridge; where, the footbridge is experienced variations of the fundamental frequency over time, and is subjected to a walking pedestrian. For the case study in the present study, a vibration reduction of 31% in comparison with the attached traditional passive DVA with constant parameters was achieved. The results show that, by using the proposed nonlinear dashpot, presented in this study, into an attached DVA, the footbridge will experience about 10% more deflection reduction concerning a classical linear DVA.

2022 - Asymmetric vibrations and chaos in spherical caps under uniform time-varying pressure fields [Articolo su rivista]
Iarriccio, G.; Zippo, A.; Pellicano, F.
abstract

This paper presents a study on nonlinear asymmetric vibrations in shallow spherical caps under pressure loading. The Novozhilov’s nonlinear shell theory is used for modeling the structural strains. A reduced-order model is developed through the Rayleigh–Ritz method and Lagrange equations. The equations of motion are numerically integrated using an implicit solver. The bifurcation scenario is addressed by varying the external excitation frequency. The occurrence of asymmetric vibrations related to quasiperiodic and chaotic motion is shown through the analysis of time histories, spectra, Poincaré maps, and phase planes.

2022 - Correction to: Asymmetric vibrations and chaos in spherical caps under uniform time-varying pressure fields (Nonlinear Dynamics, (2022), 107, 1, (313-329), 10.1007/s11071-021-07033-7) [Articolo su rivista]
Iarriccio, G.; Zippo, A.; Pellicano, F.
abstract

The original article was published with erroneous author information. The correct authorship is as it stands in this correction. The original article has been corrected.

2022 - Digital Twins: Neural-Networks for the implementation of digital twins of gearboxes [Relazione in Atti di Convegno]
Zippo, A.; Bergamini, L.; D'Elia, G.; Pellicano, F.; Dalpiaz, G.; Iarriccio, G.; Molaie, M.
abstract

2022 - Effects of laser surface texturing on the dynamic performance of spur gears [Relazione in Atti di Convegno]
Iarriccio, G.; Zippo, A.; Molaie, M.; Bergamini, L.; Pellicano, F.
abstract

Laser Surface Texturing (LST) has been successfully applied to improve the tribological performance of reciprocating surfaces. In this context, although the relative motion between the meshing teeth is a combination of sliding and rolling, gears provided with LST could further reduce losses and vibrations in power transmissions. In this study, experimental results on the efficiency and the vibrations of gears are reported. The tests were carried out through a test bench that allows for evaluating the power losses of the transmission and the dynamic transmission error thanks to a set of torquemeters and accelerometers. Different load and speed conditions were investigated, and a comparison of the results between textured gears and standard carburized gears is provided.

2022 - Experimental and numerical investigation of a vertical vibration isolator for seismic applications [Articolo su rivista]
Eskandary-Malayery, F.; Ilanko, S.; Mace, B.; Mochida, Y.; Pellicano, F.
abstract

In near-fault seismic zones, the vertical acceleration experienced during a strong event can be greater than horizontal acceleration. Methods to reduce horizontal acceleration are applied in various forms and are in common use. However, methods to reduce vertical acceleration, and practical protection systems for these applications, remain elusive. One strategy to protect structures, which has been demonstrated to be effective in situations where the excitation is horizontal, is to isolate the structure. For vertical excitations, this is difficult due to the need to maintain sufficient stiffness and strength in the direction of gravitational loads. The need to maintain high stiffness for gravity loading while allowing flexibility for isolation during earthquakes has led to research on the use of High-Static-Low-Dynamic Stiffness Systems (HSLDSS) and in particular Quasi-Zero Stiffness Systems (QZSS), which have zero equivalent stiffness in the equilibrium position. Although effective, the QZSS is sensitive to mistuning and prone to large deformations for relatively small increments in static load for building applications. This paper presents the results of an analytical and experimental study in which a HSLDSS isolation system carrying a payload is subject to vertical base excitation using sinusoidal as well as actual, scaled earthquake signals. Static loading tests are also presented. This isolation system consists of rigid rotating arms, horizontal and vertical springs and a vertical damper. By a suitable selection of parameters this could also serve as a QZSS. Results show that both the QZSS and HSLDSS can significantly reduce the magnification of the force as well as the transmission of the acceleration and that the HSLDSS retains stiffness at the equilibrium position. The numerical model includes friction and is solved using direct integration of the equation of motion. Experimental results from a scale model agree well theoretical predictions.

2022 - Experiments on a Quasi-zero Stiffness Suspension for Passive Vibration Control [Relazione in Atti di Convegno]
Iarriccio, G.; Molaie, M.; Zippo, A.; Pellicano, F.
abstract

Experimental measurements on a quasi-zero stiffness (QZS) isolator under base excitations are reported. The setup is described and the QZS isolator is compared to a standard mass-spring system. The role of the geometric nonlinearities on the dynamic behavior is clear: the QZS isolator transmissibility shows a natural frequency reduction, and the system effectively suppresses the ground vibration about the fundamental frequency of the standard system. The QZS isolator performance has been tested also under real earthquake signals, showing satisfactory acceleration mitigation.

2022 - Loaded and unloaded tooth contact analysis of spiral bevel gears in consideration of misalignments [Articolo su rivista]
Moslem, M.; Zippo, A.; Iarriccio, G.; Bergamini, L.; Pellicano, F.
abstract

Bevel gear pairs are employed extensively in transmission systems, such as vehicle transmissions (rear axle drive), aircraft engines/turbines and helicopter gears, to transfer power between non-parallel shafts at high speed or high torque. The most complex form of bevel gear is the spiral bevel gear (SBG). SBG pairs are commonly used in applications that require high load capacity at higher operating speeds than are typically possible with other types of bevel gear. When manufactured in a metal-cutting process, spiral bevel gears can either be produced using single indexing (a face-milling method, which is considered in this study) or continuous indexing (a face-hobbing method). Due to manufacturing imperfections and the flexibility of components, the system might experience misalignments that intensify or exert a destructive effect on the gear vibration, which causes disruption in the stress distribution, thereby decreasing the lifetime of the gearbox. The main purpose of this study is to carry out loaded tooth contact analysis (LTCA) and unloaded tooth contact analysis (UTCA) for an SBG pair in the presence of two types of misalignment, axial and radial misalignment, and represent their effects on the mesh stiffness (MS). To calculate the MS, it is essential to determine the geometrical mismatch between two mating tooth profiles by means of UTCA. To conduct LTCA, three main approaches can be utilised: the finite element method (FEM) and experimental and analytical approaches. Due to the development of software packages during the last decade, Transmission3D-Calyx, an FEM-based software, is used in this study to carry out LTCA and UTCA. Finally, the MS for different misalignment cases is compared to represent the effect of misalignment on the SBG pair.

2022 - Modal localization in vibrations of circular cylindrical shells with geometric imperfections [Articolo su rivista]
Hemmatnezhad, M.; Iarriccio, G.; Zippo, A.; Pellicano, F.
abstract

The present study aims to investigate the effect of geometric imperfections in circular cylindrical shells on the vibration characteristics. Perfect circular shells are characterized by the presence of double shell-like modes, i.e., modes having the same frequency with modal shape shifted of a quarter of wave-length in the circumferential direction. However, in the presence of geometric imperfections, the double natural frequencies split into a pair of distinct frequencies, the splitting is proportional to the level of imperfection. In some cases, the imperfections cause an interesting phenomenon on the modal shapes, which present a strong localization in the circumferential direction. The present study has been carried out by means of a semi-analytical approach. Theoretical formulation were derived based on Sanders–Koiter thin shell theory. The analytical results have been compared with those of standard finite element analyses. The results corresponding to the analysis of modal localization are novel and can be used as a benchmark for further studies.

2022 - Nonlocal anisotropic elastic shell model for vibrations of double-walled carbon nanotubes under nonlinear van der Waals interaction forces [Articolo su rivista]
Strozzi, M.; Smirnov, V. V.; Pellicano, F.; Kovaleva, M.
abstract

In this paper, a novel nonlocal anisotropic elastic shell model is developed to investigate the nonlinear vibrations of double-walled carbon nanotubes (DWCNTs) in the framework of Sanders–Koiter shell theory. Van der Waals interaction forces between the two concentric single-walled carbon nanotubes (SWCNTs) composing a DWCNT are modelled via Lennard-Jones potential and He's formulation. In the linear vibration analysis, the displacement field of each SWCNT is expanded by means of a double mixed series in terms of Chebyshev orthogonal polynomials along the longitudinal direction and harmonic functions along the circumferential direction, and Rayleigh–Ritz method is considered to get approximate natural frequencies and modal shapes. In the nonlinear vibration analysis, the three displacements of each SWCNT are re-expanded by means of the approximate eigenfunctions derived in the linear analysis, and an energy approach based on Lagrange equations is adopted to obtain a set of nonlinear ordinary differential equations of motion, which is then solved numerically. Molecular dynamics simulations are performed in order to calibrate the proper value of nonlocal parameter to be inserted in the constitutive equations of the proposed elastic continuum model. A simplified linear distribution of van der Waals interaction forces is initially adopted to analyse the nonlinear vibrations of DWCNTs, obtaining a hardening nonlinear behaviour. By considering a more realistic nonlinear distribution of van der Waals interaction forces, a stronger hardening nonlinear behaviour is found.

2022 - On the buckling load estimation of grid-stiffened composite conical shells using vibration correlation technique [Articolo su rivista]
Zarei, M.; Rahimi, G. H.; Hemmatnezhad, M.; Pellicano, F.
abstract

In this paper, the vibration correlation technique (VCT) has been used as a nondestructive method for predicting the buckling load of grid-stiffened composite conical shells. This technique is capable of predicting the buckling load of structures without reaching failure point through modal testing. The grid-stiffened composite conical shell has been fabricated using the filament winding process. To perform the experiment, the fundamental natural frequency of the specimen is measured under stepped axial compression loading. The procedure is followed up without actually reaching the instability point when the structure collapses and is no longer usable. A finite element model has been built using ABAQUS software considering the effect of geometric imperfection in order to determine the correlation between natural frequency and applied compressive load. A comparison of the experimental and numerical approaches indicated that the difference between numerical buckling loads and those obtained via the VCT is negligible. Moreover, the VCT has provided a reliable estimate of the buckling load, especially when the maximum applied load is greater than 67% of the experimental buckling load.

2022 - Planet Load-Sharing and Phasing [Articolo su rivista]
Molaie, M.; Deylaghian, S.; Iarriccio, G.; Samani, F. S.; Zippo, A.; Pellicano, F.
abstract

2021 - Applicability and Limitations of Simplified Elastic Shell Theories for Vibration Modelling of Double-Walled Carbon Nanotubes [Articolo su rivista]
Strozzi, Matteo; Gendelman, Oleg V.; Elishakoff, Isaac E.; Pellicano, Francesco
abstract

The applicability and limitations of simplifiedmodels of thin elastic circular cylindrical shells for linear vibrations of double-walled carbon nanotubes (DWCNTs) are considered. The simplified models, which are based on the assumptions of membrane and moment approximate thin-shell theories, are compared with the extended Sanders–Koiter shell theory. Actual discrete DWCNTs are modelled by means of couples of concentric equivalent continuous thin, circular cylindrical shells. Van der Waals interaction forces between the layers are taken into account by adopting He’s model. Simply supported and free–free boundary conditions are applied. The Rayleigh–Ritz method is considered to obtain approximate natural frequencies and mode shapes. Different aspect and thickness ratios, and numbers of waves along longitudinal and circumferential directions, are analysed. In the cases of axisymmetric and beam-like modes, it is proven that membrane shell theory, differently from moment shell theory, provides results with excellent agreement with the extended Sanders–Koiter shell theory. On the other hand, in the case of shell-like modes, it is found that both membrane and moment shell theories provide results reporting acceptable agreement with the extended Sanders–Koiter shell theory only for very limited ranges of geometries and wavenumbers. Conversely, for shell-like modes it is found that a newly developed, simplified shell model, based on the combination of membrane and semi-moment theories, provides results in satisfactory agreement with the extended Sanders–Koiter shell theory in all ranges.

2021 - Efficiency and Durability of Spur Gears with Surface Coatings and Surface Texturing [Relazione in Atti di Convegno]
Iarriccio, G.; Zippo, A.; Barbieri, M.; Pellicano, F.
abstract

Experimental results on mechanical efficiency and durability of spur gears are presented. Reducing the power losses and increasing the reliability of gears are fundamnetal aspects of the design of transmissions. In order to analyze the tribological performance of innovative coatings and laser texturing, three different types of spur gears were tested: standard carburized gears, WC/C-coated carburized gears, and carburized gears with laser texture pattern. Tests have been carried out through a power recirculating test rig equipped with a single-stage transmission; power losses were evaluated by analyzing the torque-meters signals; several pictures of the teeth were taken at scheduled times to monitor the wear progression. In conclusion, results are presented and discussed.

2021 - Gear diagnostic: Experimental data comparison of radial accelerometers, tangential accelerometers and torquemeter [Abstract in Atti di Convegno]
Zippo, A.; Pellicano, F.; Iarriccio, G.; Bergamini, L.; D'Elia, G.; Dal Piaz, G.
abstract

Industry 4.0 is the next step of the evolution of future companies in order to improve efficiency sustainability and performances. With a view to industry 4.0 and to improve the efficiency of gear transmission a measurement campaign has been performed comparing four gear pair with different surface treatment, damages and coating The experimental results on the measurement of radial accelerometers, tangential accelerometers and torque-meter measurement of spur gears rig with surface coatings, advanced pitting with a crack and damaged gears are presented and analysed with Time Synchronous Averaged (TSA) method and results are explained, comparing the effectiveness of the different sensors used to monitor the system under investigation.

2021 - Gear prognostics: A predictive algorithm for lifetime estimation of operating gearboxes [Abstract in Atti di Convegno]
Bergamini, L.; Zippo, A.; Pellicano, F.; Iarriccio, G.; Molaie, M.
abstract

For the realization of optimized, effective gearboxes, both the set of design rules and the study of operation conditions, interconnected to each other, have to be taken into account. Condition monitoring is an essential tool when study of gearbox operation is tackled, and many techniques have been developed to detect the onset and the development of wear. However, these techniques fall short when prediction of gearbox conditions is concerned, as in the case of tracking the useful lifetime during operation. Within this framework, a prognostic software is developed and presented. This software is able to estimate the useful lifetime of a gearbox on the base of design features (safety factors and parameters), standards and codes (ISO) and realistic/measured load spectra, representative of the operation condition of the gearbox. This tool opens up the possibility of combining condition monitoring and prediction for a wider, comprehensive study of gearbox operation. Moreover, it potentially allows to detect machinery misuse and plan accurate usage-dependent maintenance in industrial environment.

2021 - Nonlinear dynamics and stability of shallow spherical caps under pressure loading [Articolo su rivista]
Iarriccio, G.; Pellicano, F.
abstract

The post-buckling and nonlinear dynamic response of shallow spherical caps subjected to external pressure is analyzed. The Novozhilov's nonlinear thin shell theory is used to express the strain-displacement relations. Following the Rayleigh-Ritz method, the displacement fields are expanded using a mixed series: Legendre polynomials in the meridional direction, harmonic functions in the circumferential direction. Once the linear analysis is completed, the displacement fields are re-expanded and the nonlinear dynamic model is obtained by using the Lagrange equations. The response of clamped caps, made of isotropic and homogeneous material, is investigated. The bifurcation analyses of equilibrium points and periodic orbits are presented by using continuation techniques. Benchmark results are provided in terms of natural frequencies and critical buckling loads. The dynamic effects due to the interaction between static and dynamic pressure are investigated. Numerical results pointed out that, under particular load conditions, dynamic bifurcation results in nonnegligible asymmetric states activation in the response of the structure.

2021 - Nonlinear vibration absorbers applied on footbridges [Articolo su rivista]
Saber, H.; Samani, F. S.; Pellicano, F.
abstract

This paper deals with the performance of linear and nonlinear dynamic vibration absorbers (DVAs) to suppress footbridges vertical vibrations. The walking pedestrian vertical force is modeled as a moving time-dependent force and mass. The partial differential equations govern the dynamics of the system; such equations are reduced to a set of ordinary differential equations by means of the Bubnov–Galerkin method with an accurate multimode expansion of the displacement field. The optimal vibration absorber parameters are determined using two objective functions: maximum footbridge deflection and the transferred energy from the footbridge to the DVA. The most suitable nonlinear DVA is proposed for the investigated footbridge. The results show that the DVAs with quadratic nonlinearity are the most performant DVAs.

2021 - Resonances and nonlinear vibrations of circular cylindrical shells, effects of thermal gradients [Articolo su rivista]
Iarriccio, G.; Zippo, A.; Pellicano, F.; Barbieri, M.
abstract

In this paper, the results of an experimental campaign focused on the vibrations of shells are presented. More specifically, the goal is to investigate the effect of thermal gradients across the shell thickness on the nonlinear dynamics. The shell is made of polymeric material and an aluminum mass is clamped on one end of the shell; the other shell end is clamped to an electrodynamic shaker, which provides a base harmonic excitation. Tests are performed in a controlled environment where a thermal gradient on the shell thickness is generated by means of a climatic chamber and an internal cartridge heater. Different temperature gradients and base excitation levels have been considered. The nonlinear dynamic scenario is analyzed through amplitude–frequency diagrams, bifurcation diagrams, waterfall diagrams, time histories, Fourier spectra, phase portraits, and Poincaré maps. Results show a strong effect of the temperature on the dynamic response of the shell: subharmonic, quasi-periodic, and chaotic vibrations take place as well as large amplitude vibrations, high sound levels are detected.

2021 - Seismic vibration of shells with non-Newtonian fluid interaction: Experiments [Abstract in Atti di Convegno]
Pellicano, F.; Zippo, A.; Iarriccio, G.
abstract

In the presented study the nonlinear vibrations of a fluid-filled circular cylindrical shell under seismic excitation is investigated. A PET thin shell with an aluminum top mass is harmonically excited from the base through an electrodynamic shaker in the neighborhood of the natural frequency of the first axisymmetric mode. The dilatant fluid is composed of a cornstarch-water mixture with 60% cornstarch and 40% water of total weight. The preliminary results show a strong non-linear response due to the coupling between the fluid and structure and the shaker-structure interaction that leads to a very interesting dynamic response of the system. The specimen is a polymeric circular cylindrical shell: an aluminum cylindrical mass is glued on the shell top edge; conversely, the bottom edge of the shell is clamped to a shaking table. The following sensors have been adopted: three triaxial accelerometers placed on the top mass at 120°, a monoaxial accelerometer at the base of the shell, a laser vibrometer to measure the lateral velocity on the mid-height of the shell. The test article has been excited in the axial direction through a harmonic load, with a step-sweep controlled output, the voltage signal sent to the shaker amplifier is closed-loop controlled; to avoid interaction between the control system and the specimen under study, no controls have been used for controlling the shaker base motion. The harmonic forcing load consists of a stepped-sine sweep of frequency band 100-500 Hz with a step of 2.5 Hz. All the tests have been performed with the shell full filled with quiescent fluid. The dynamic scenario is carefully analyzed by means of time histories, spectra, phase portraits and Poincaré maps. The experiments show the onset of complex dynamics: subharmonic and quasiperiodic responses, Chaos.

2021 - Synchronicity Phenomena in Circular Cylindrical Shells Under Random Excitation [Capitolo/Saggio]
Zippo, A.; Iarriccio, G.; Pellicano, F.
abstract

In many engineering areas, the structures are subjected to external forcing with a prevalent harmonic component in conjunction with significant likely non-deterministic contribution; moreover, the coupling between loading conditions and extreme environmental temperatures can lead to complex dynamic phenomena. In this paper, an experimental study on the nonlinear dynamics of a thin polymeric circular cylindrical shell, carrying a top mass, subjected to thermal gradients and random excitation is presented. Tests have been performed in controlled temperature conditions and the shell has been excited through an electrodynamic shaker. The experimental results pointed out that a broadband random excitation at the base of the shell can give rise to the synchronicity of the response to the resonance corresponding to the first axisymmetric mode of the shell; the vibration energy is conveyed to specific harmonics, some of which are outside and far from the excitation band.

2021 - Time series analysis of arm and forearm measurement for functional electrical stimulation control [Abstract in Atti di Convegno]
Zippo, A.; Pellicano, F.; Iarriccio, G.
abstract

Identify the dynamics of the muscular group of arm and forearm related to accelerometric and surface electromyographic signals is not an easy task especially in persons affected by pathological tremor, in which irregular tremor is not voluntary. The vibrational phenomena studied in this work regards the arm and forearm vibration that are monitored by means of SEMG (surface electro-myographic) sensor and accelerometer sensor with the purpose to detect and recognize the dynamic properties and correlations of onset of pathological tremor in patients affected by Parkinson disease and essential tremor. These pathologies that affect skeletal muscles present a typical characteristic vibration frequency between 1Hz and 12Hz, this property is monitored in out-patient tests. A condition monitoring system has been developed to monitor the tremor and produce an electrical stimulation to reduce the tremor: the system allows data monitoring with a portable microcontroller board powered with low voltage batteries and is based on a cDAQ9191 data acquisition system with a chassis controller module designed for data input, controlling and output generation. The algorithm generates functional electrical stimulation signals for control purpose. Experimental measurement data on parkinsonian patient are presented. Data are analyzed, and the results are presented.

2020 - Dynamic Modelling of Mechanical System for the Packaging Industry [Relazione in Atti di Convegno]
Di Canosa, R.; Pellicano, F.
abstract

The development of robust and reliable systems in the packaging industry requires the creation and the validation of physical models that can estimate both the mission profile of the components and the sub-assemblies and to provide data related to the status of the system when operating out of the nominal working condition. The work relies on the creation of a multibody model of a complex mechanism covering multiple phases of the production process in each operating cycle. The model has been developed with the commercial software MSC Adams® and validated on a test rig specifically manufactured for the purpose. Some components of the system were redesigned in order to behave as sensing elements and to provide data about the forces exchanged in the system, which were correlated with the virtual results. The dynamic model will be used in further activities for integrating the response of the system when interacting with the other assemblies of the equipment, for simulating operating conditions that are out of the design ranges and collecting data from a system that is approaching failure.

2020 - Dynamic characterization of polymeric vibration dampers [Relazione in Atti di Convegno]
Barbieri, Marco; DE FELICE, Alessandro; Pellicano, Francesco; Sorrentino, Silvio; Zippo, Antonio
abstract

Polymeric dampers are used in many fields for vibration isolation. These devices are based upon a low stiffness and high damping connection between a vibrating support and the item to be fastened. Whenever the connection is assured by a polymeric element, it is mandatory to be aware that stiffness and damping change with the excitation frequency. The characterization of stiffness and damping of the polymeric element in terms of storage modulus and loss modulus is commonly carried out at low frequency by means of a Dynamic Mechanical Analysis (DMA), nonetheless this approach cannot be applied at higher frequency. In the present study, a novel experimental approach for estimating the frequency dependent storage modulus and loss modulus in a polymeric vibration damper is presented. The proposed method is based on a direct measurement of the energy loss in hysteretic cycles and it is suitable for simple implementation using common instruments for vibration measurement.

2020 - Efficiency and Durability of DLC-Coated Gears [Relazione in Atti di Convegno]
Barbieri, M.; Iarriccio, G.; Pellicano, F.; Strozzi, M.; Zippo, A.
abstract

This paper presents an experimental study on spur gears. Gears with and without tungsten-carbide coatings (WC/C) are compared in terms of efficiency, durability and vibration performance. In order to carry out the experiments, a test rig including two electric motors/brakes is described. Gears are designed for this specific experimental campaign, so that the number of teeth, the selected materials and thermochemical treatments are optimal to investigate gear efficiency and durability. The experimental procedure allows for a simultaneous evaluation of efficiency and dynamic transmission error by varying the rotational velocity of the gear pair. An additional investigation has been performed for varying load, so that a complete characterization of the effect of WC/C coating on gear performance is presented.

2020 - Experimental Study on Nonlinear Random Excitation [Relazione in Atti di Convegno]
Pellicano, F.; Zippo, A.; Iarriccio, G.; Barbieri, M.
abstract

Experimental design methods are instruments for directing useful, time-effective and efficient experiments and an accurate strategy in experimental activities lead to successful results. In the present paper is explained an experimental campaign focused on the random vibrations of circular cylindrical shells under thermal gradients across the shell thickness and broadband random loading to identify a particular phenomenon called synchronicity: the investigation is fully experimental. Nuclear, aerospace and automotive are some of the engineering fields involved in this subject, and in these real environments non-deterministic excitations can be coupled with a thermal load; extreme thermal conditions can cause differences of the temperature inside and outside the shell, e.g. thermal ex-changers. Due to the importance of the subject, the literature on shell vibration is extremely wide, it is not analyzed here for the sake of brevity; however, it is to note that the number of papers containing experimental results is not large. Under a random forcing, a system generally expects a random response, the statistical properties of the random response are correlated with the forcing through the transfer function in the case of linear systems, or more complicated relationships in the case of nonlinear systems. However, in some particular conditions (e.g. internal resonances, parametric resonances, ...) the presence of nonlinearity in the systems can give rise to a surprising phenomenon, said synchronicity or entrainment. In this work a shell subjected to a random base excitation is analyzed experimentally, the excitation is random (flat or limited frequency band), and takes advantage of previous setup and experimental techniques [3–5] developed by the present research team. The phenomenon of synchronicity is clearly observed for some particular thermal conditions: a strong transfer of energy from a broadband excitation signal to an almost harmonic response is experimentally observed, confirming the general findings of refs. [1, 2].

2020 - Experimental study on large amplitude vibrations of a circular cylindrical shell subjected to thermal gradients [Relazione in Atti di Convegno]
Iarriccio, G.; Zippo, A.; Barbieri, M.; Pellicano, F.
abstract

In this paper, an experimental study on large amplitude vibrations of a thin-walled shell, subjected to thermal gradient across the thickness, is presented. The temperature gradient effects on the shell dynamic behavior are investigated. The vibration tests are performed on a polymeric cylindrical shell that carries a top mass. The structure is harmonically excited in the longitudinal direction by means of an electrodynamic shaker. The results of the experimental study are here reported and discussed.

2020 - Nonlinear Vibration of Continuous Systems 2020 [Articolo su rivista]
Pellicano, Francesco; Strozzi, Matteo; Avramov, Konstantin V.; Sinniah, Ilanko
abstract

2020 - Nonlinear dynamics and stability of pressure-loaded shallow spherical caps [Relazione in Atti di Convegno]
Iarriccio, G.; Pellicano, F.
abstract

In this work, the nonlinear dynamic response of a shallow spherical cap subjected to a time-dependent pressure load is analyzed. The Novozhilov s nonlinear thin shell theory is used to express the strain-displacement relations, geometric imperfections are considered. Using the Rayleigh-Ritz method, the displacement fields are expanded using a mixed series: Legendre polynomials are considered in the azimuthal direction and harmonic functions in the circumferential one. The dynamic model is derived by using the Lagrange equations. The response of a homogeneous shell, made of isotropic material, clamped at its ends, and subjected to an external pressure load is investigated: using the continuation software AUTO, the bifurcation analysis of equilibrium points and periodic responses has been performed. The model is validated by means of comparison with the existing results in literature for spherical shells having a circular base, in particular with models developed through the Marguerre s theory.

2020 - Nonlinear normal modes, resonances and energy exchange in single-walled carbon nanotubes [Articolo su rivista]
Strozzi, M.; Smirnov, V. V.; Manevitch, L. I.; Pellicano, F.
abstract

The nonlinear resonance interaction and energy exchange between bending and circumferential flexure modes in single-walled carbon nanotubes is studied. First, the results of an analytical model of the resonance interaction between the considered nonlinear normal modes previously developed are reported. This approach was based on a reduced form of the Sanders–Koiter thin shell theory obtained by using simplifying hypotheses on the shell deformations. The analytical model predicted that the nonlinear resonance interaction leads to energy localization in a certain coherence domain over the carbon nanotube surface within a specific range of the initial oscillation amplitude. Then, a numerical model of the resonance interaction between the analysed nonlinear normal modes in the framework of the complete Sanders–Koiter thin shell theory is reported. Numerical simulations are performed to verify the energy localization phenomenon over the carbon nanotube surface and to compute the threshold values of the initial oscillation amplitude giving rise to energy localization. Finally, from the comparison between the two different approaches, it is obtained that the results of the numerical model for the threshold values of the nonlinear energy localization confirm with very good accuracy the predictions of the analytical model.

2020 - Nonlinear vibrations of circular cylindrical shells with thermal effects: an experimental study [Articolo su rivista]
Zippo, Antonio; Barbieri, Marco; Iarriccio, Giovanni; Pellicano, Francesco
abstract

The nonlinear dynamics of a polymeric cylindrical shell carrying a top mass under axial harmonic excitation are experimentally investigated; the tests have been carried out in a controlled environment under several conditions of homogeneous temperature and excitation amplitude. The thermal effects on shells dynamics have been studied. The purpose of this paper is to fill an important gap in the literature regarding the effect of the temperature on the complex dynamics of shells. The cylindrical shell is excited in the axial direction by means of a seismic excitation provided by an electrodynamic shaker. The analysis is focused on the range of frequencies of excitation close to the first axisymmetric mode resonance; the base motion induces a parametric excitation. A saturation phenomenon of the top mass vibration is observed; the vibrating energy directly transferred from the shaker to the first axisymmetric mode is transferred to radial motion of the shell. The experimental data are examined and discussed in detail; a complete dynamic scenario is analyzed by means of: amplitude–frequency curves, bifurcation diagrams, spectrograms, Poincaré maps, phase portraits, Fourier spectra and time histories. Results show that: (i) the temperature strongly affects the instability regions and the magnitude of the measured kinematic quantity, (ii) high environmental temperature leads to a more complex shell dynamics.

2020 - Vibrations of circular cylindrical shells under random excitation and thermal gradients [Relazione in Atti di Convegno]
Zippo, A.; Pellicano, F.; Iarriccio, G.; Barbieri, M.
abstract

The present paper is focused on the random vibrations of circular cylindrical shells subjected to thermal gradients across the shell thickness; the investigation is fully experimental. The topic is of practical interest in many engineering fields such as: Aerospace, Automotive, Civil, Nuclear. Indeed, in real environments the excitations are likely non deterministic, moreover, extreme thermal conditions can cause differences of temperature inside and outside the shell, e.g. thermal exchangers. Due to the importance of the subject the literature on shell vibration is extremely wide, it is not analyzed here for the sake of brevity; however, it is to note that the number of papers containing experimental results is not large. When a system is excited with random forcing one generally expects a random response of the system, the statistical properties of the random response are correlated with the forcing through the transfer function in the case of linear systems, or more complicated relationships in the case of nonlinear systems. However, in some particular conditions (e.g. internal resonances, parametric resonances,…) the presence of a nonlinearity in the systems can give rise to a surprising phenomenon, said synchronicity or entrainment (see [1, 2]), which consists in a response made of a combination of random and harmonic signals. In this work a shell subjected to a random base excitation is analyzed experimentally, the excitation is random (flat or limited frequency band). The work take advantage from previous setup and experimental techniques [3–5] developed by the present research team. The phenomenon of synchronicity is clearly observed for some particular thermal conditions: a strong transfer of energy from a broad band excitation signal to an almost harmonic response is experimentally observed, confirming the general findings of refs. [1, 2].

2020 - Vibrations of plates with complex shape: Experimental modal analysis, finite element method, and R-functions method [Articolo su rivista]
Zippo, A.; Iarriccio, G.; Pellicano, F.; Shmatko, T.
abstract

In this paper, the dynamic behavior of 3D-printed plates with different shapes and boundary conditions is investigated. The natural frequencies and mode shapes were determined using three different methods: the experimental analysis, the finite element method, using Nastran, and the R-functions method. The experimental and theoretical results are compared. Thespecimens tested included four cases. The test procedure is deeply described, and the material properties of the plates are given. The fixed-fixed configuration shows a better agreement both in the rectangular plate and in the plate with rectangular cuts, and the R-functions method gives better convergence with respect to the experimental and finite element analysis. The simply supported arrangement indicates some uncertainty in the boundary realization of the specimen.

2019 - Condition monitoring of parkinson pathological tremor for functional electrical stimulation control [Relazione in Atti di Convegno]
Zippo, A.; Pellicano, F.; Iarriccio, G.; Valzania, F.; Cavallieri, F.
abstract

The aim of this work is to identify the correlation of accelerometric and electromyographic signals and the difference between healthy patients (control group) and patients affected by Parkinson disease (PD) and essential tremor (ET). The vibrational phenomena studied in this work regards the forearm and hand vibration that are monitored by means of SEMG (surface electro-myographic) sensor and accelerometer sensor with the purpose to detect and recognize the dynamic properties of onset of pathological tremor in patients affected by (PD) and (ET). PD and ET present a typical characteristic vibration frequency between 3Hz and 12Hz, this property is monitored in out-patient tests. Two condition monitoring systems have been developed and deep described to monitor the tremor: the former system allows data monitoring with a portable lightweight microcontroller board powered with low voltage batteries (5Volt); and the latter is based on a CompactRio data acquisition system with a chassis controller module designed for data input, controlling and output generation, powered by 12 Volt battery. The CRio System provide an algorithm to generate functional electrical stimulation signals for control purpose. Experimental measurement data on healthy control subjects are presented. Data are analyzed, and results are presented.

2019 - Experimental durability test for condition monitoring of carburized spur gears [Relazione in Atti di Convegno]
Iarriccio, G.; Zippo, A.; Barbieri, M.; Pellicano, F.
abstract

An experimental study on the durability of spur gears has been carried out. Tests have been performed through a power re-circulating test rig at a fixed speed and torque load. For condition monitoring purpose, vibrations have been measured through a triaxial accelerometer mounted on the shaft frame. Acquired data have been post-processed and preliminary results are shown. The aim of the present work is to analyze the changes in the vibrations signal in order to depict a clear view on the onset and progression of the wear and damages in gear transmissions.

2019 - Experimental investigation on spur gears with novel coatings and surface micro texturing [Relazione in Atti di Convegno]
Zippo, A.; Pellicano, F.; Iarriccio, G.; Barbieri, M.
abstract

Gears fault diagnostic and prognostic techniques have been the significant subjects of the condition-based monitoring systems in recent time due to the potential advantages that could be gained from. The present work is part of a more extensive study regarding efficiency and durability of novel tungsten carbide coatings and surfaces laser micro-texturing applied on carburized and nitride gears for several industrial application. In this paper, the effect of the different gear coatings and texturing on the vibration level is investigated experimentally. The durability and the pitting arising have been examined. The test rig consists of two electric motors with an electric power recirculating layout and is equipped with a temperature monitoring of the oil-jet type lubrication system. Vibrations phenomena are measured through triaxial accelerometer mounted on the shaft frame, close to the bearings, in order to detect spectral characteristics of vibration signals due to gear fault. Tests have been conducted far from the resonances of the system at a fixed speed and torque load; Vibration measurements have been performed at planned intervals. Results are presented and discussed

2019 - Experimental study on the nonlinear vibrations of a circular cylindrical shells: Effects of thermal gradients [Relazione in Atti di Convegno]
Iarriccio, G.; Zippo, A.; Barbieri, M.; Pellicano, F.
abstract

In this paper, an experimental study on the large amplitude vibrations of a thin polymeric cylindrical shell subjected to a thermal gradient across the thickness is presented. The effects of the temperature gradient on the shell dynamic behavior are investigated. The present study has the aim of providing a deeper contribution to the experimental literature on the shell structures. Test have been carried out in controlled environment condition thanks to a climatic chamber and a heater cartridge placed inside the shell. The shell carries a top mass and an electro-dynamic shaker has been used in order to excite, with a harmonic load, the test specimen in the longitudinal direction. The harmonic forcing load consists of a stepped-sine sweep with frequency band limits containing the resonance frequency of the first axisymmetric vibration mode. Four different excitation amplitude levels and two different thermal gradients have been considered. The experimental results are presented and discussed in detail by means of frequency response analysis and bifurcation analysis

2019 - Identification of dynamic behaviour of forearm for active control of pathological tremor [Relazione in Atti di Convegno]
Zippo, A.; Pellicano, F.; Iarriccio, G.; Franco, V.; Francesco, C.
abstract

Pathological tremor is defined as an oscillatory and rhythmic movement of a segment of the body caused by the alternating activation of muscle groups in antagonism between them; a typical pathological condition known as essential tremor, which is the most common form of tremor also having a family character (2-5% of the population) have a characteristic frequency between 5 Hz and 7 Hz, such as Parkinsonian tremor that arises at frequencies higher than 8 Hz. The purpose of this study is to investigate the dynamic behavior of the forearm induced by the hand movements, measured due to the electromyographic sensors and accelerometers. The relationships of accelerometric and electromyographic signals are compared between a control group of healthy subjects and patients affected by Parkinson disease (PD) and essential tremor (ET). The vibrational phenomena analyzed in this experimental investigation are observed by means of SEMG (surface electro-myographic) sensors placed on flexor and extensor muscle compartment of forearm and accelerometer sensors for the hand vibration with the aim to detect and recognize the dynamic properties of onset of pathological tremor in patients affected by (PD) and (ET). A real-time monitoring and data logger system have been developed and deep described to monitor the tremor: the system allows data monitoring with a portable lightweight microcontroller board based on a CompactRio data acquisition system with a chassis controller module designed for data input, controlling and output generation, powered by 12 Volt battery. The CRio System provides an algorithm to generate functional electrical stimulation signals with different waveforms for control purpose. Experimental measurement data on healthy control subjects are presented. Data are analyzed, and the results are discussed

2019 - Interazioni di risonanza e localizzazioni di energia in nanotubi di carbonio [Abstract in Atti di Convegno]
Andrisano, A. O.; Manevitch, L. I.; Pellicano, Francesco; Strozzi, Matteo
abstract

2019 - Nonlinear Resonance Interaction between Conjugate Circumferential Flexural Modes in Single-Walled Carbon Nanotubes [Articolo su rivista]
Strozzi, M.; Pellicano, F.
abstract

This paper presents an investigation on the dynamical properties of single-walled carbon nanotubes (SWCNTs), and nonlinear modal interaction and energy exchange are analysed in detail. Resonance interactions between two conjugate circumferential flexural modes (CFMs) are investigated. The nanotubes are analysed through a continuous shell model, and a thin shell theory is used to model the dynamics of the system; free-free boundary conditions are considered. The Rayleigh-Ritz method is applied to approximate linear eigenfunctions of the partial differential equations that govern the shell dynamics. An energy approach, based on Lagrange equations and series expansion of the displacements, is considered to reduce the initial partial differential equations to a set of nonlinear ordinary differential equations of motion. The model is validated in linear field (natural frequencies) by means of comparisons with literature. A convergence analysis is carried out in order to obtain the smallest modal expansion able to simulate the nonlinear regimes. The time evolution of the nonlinear energy distribution over the SWCNT surface is studied. The nonlinear dynamics of the system is analysed by means of phase portraits. The resonance interaction and energy transfer between the conjugate CFMs are investigated. A travelling wave moving along the circumferential direction of the SWCNT is observed.

2019 - Nonlinear dynamic stability of cylindrical shells under pulsating axial loading via Finite Element analysis using numerical time integration [Articolo su rivista]
Rizzetto, Fabio; Jansen, Eelco; Strozzi, Matteo; Pellicano, Francesco
abstract

Nonlinear dynamic stability investigations for isotropic and composite cylindrical shells under pulsating axial loading are carried out through Finite Element analysis using numerical time integration. In particular, im- portant characteristics of the geometrically nonlinear behaviour are systematically studied through Finite Element analysis. The results of the Finite Element analysis are compared with results obtained in earlier studies using semi-analytical procedures. In order to facilitate the evaluation and the comparison of these two com- plementary approaches, a modal projection procedure has been developed for the Finite Element analysis. Critical dynamic loads and frequency-response curves for isotropic and composite shells under pulsating loading obtained with the Finite Element analysis using numerical time integration are shown to be generally in good qualitative agreement with the results of earlier semi-analytical work. The analysis of the modal amplitude achieved via the modal projection procedure also makes it possible to study the interactions between con- tributing modes and to observe and interpret interesting phenomena such as the occurrence of travelling waves in the circumferential direction of the shell.

2019 - Nonlinear strain gradient analysis of nanoplates embedded in an elastic medium incorporating surface stress effects [Articolo su rivista]
Allahyari, Ehsan; Asgari, Masoud; Pellicano, Francesco
abstract

Nonlinear vibration of nano graphene plates with considering surface effects is studied in this paper based on the nonlocal strain gradient theory and von K ́arm ́an geometric nonlinearity. The isotropic nanoplate is assumed to lie on an elastic foundation with the simply supported boundary conditions. Both Winkler-type and Pasternak-type models are utilized to simulate the interaction of the nano graphene with a surrounding elastic medium. Due to the increase in the surface-to-volume ratios at smaller scales, the surface elasticity theory of Gurtin and Murdoch is developed to study the effects of surface properties which are the basis for size-dependent behaviors. The governing equation of motion can be obtained by von K ́arm ́an nonlinear strain-displacement relationship and the nonlinear frequency is obtained analyti- cally using the perturbation approach. Moreover, two moveable and immoveable in-plane conditions are analyzed. The presented method is verified by comparing the results with their counterparts reported in the open literature and a good agreement is observed for two different boundary conditions. Finally, the effects of various parameters such as nonlocal parameter, material characteristic parameter, residual sur- face tension, mode number, temperature change and elastic medium coefficients for two kinds of in-plane conditions are discussed.

2019 - Nonlinear vibration of continuous systems [Articolo su rivista]
Pellicano, F.; Strozzi, M.; Avramov, K. V.
abstract

Continuous systems, such as beams, membranes, plates, shells, and other structural/mechanical components, represent fundamental elements of mechanical systems in any field of engineering: Aerospace, Aeronautics, Automation, Automotive, Civil, Nuclear, Petroleum, and Railways. The modern designer is required to optimize structural elements to improve the performance-to-cost ratio, produce lightweight machines, and improve the efficiency. Such optimizations easily lead to a magnification of vibration/dynamic problems such as resonances, instabilities, and nonlinear behaviors. Therefore, the development of new methods of analysis, testing, and monitoring is greatly welcome. This special issue focuses on sharing recent advances and developments of theories, algorithms, and applications that involve the dynamics and vibrations of continuous systems. The contributions to this special issue include innovative theoretical studies, advanced numerical simulations, and new experimental approaches to investigate and better understand complex dynamic phenomena; more specifically, methods and theories for beams, membranes, plates, and shells; numerical approaches for structural elements; fluid-structure interaction; nonlinear acoustics; identification, diagnosis, friction models, and vehicle dynamics. Seventeen contributions have been received from all over the world: Canada, China, Kazakhstan, Italy, Macau, Spain, and USA. This shows the generalized interest on the topic. The following short description of the special issue content is organized by grouping the contributions in coherent subtopics.

2019 - Nonlinear vibration of the spiral bevel gear with a novel tooth surface modification method [Articolo su rivista]
S. Samani, Farhad; Molaie, Moslem; Pellicano, Francesco
abstract

The issue of gear noise is fairly common in power transmission systems. This noise largely stems from the gear pairs vibration triggered by transmission error excitation. This is mainly caused by tooth profile errors, misalignment and tooth deflections. This research endeavors to examine nonlinear spiral bevel gears vibration with the innovative method of tooth surface modification. To design spiral bevel gears with the higher-order transmission error (HTE), the non- linear vibration of a novel method is investigated. The meshing quality of the HTE spiral bevel gears, as the results demonstrate, sounds more suitable than of the meshing quality gears. Their design was made by means of the parabolic transmission error (PTE). The maximum time response root mean square of the HTE method decreases by 44% concerning the PTE method. The peak-to-peak of the transmission error is decreased by 35% via HTE overall frequency range. However, HTE method is not able to decrease the vibration level on all frequency ratios.

2019 - Temperature gradient effect on dynamic properties of a polymeric circular cylindrical shell [Articolo su rivista]
Zippo, Antonio; Barbieri, Marco; Pellicano, Francesco
abstract

In this paper, an experimental study on the dynamic of cylindrical shells made of Polyethylene terephthalate (PET) is presented; a thermic gradient has been applied on a specimen of the present work to obtain a functionally gradient material (FGM) equivalent properties: the PET shell had been exposed at a thermal temperature gradient in the range of its glass transition temperature of 79 °C. A complex setup has been specifically designed and built to characterise, with dynamic tests, the structural properties of the specimen on temperature change from −10 °C up to about 90 °C and under thermic gradient with different forcing load. Predicting the mechanical properties of shells, panels and plates is one of the main concerns of structural engineers; since shell elements present complicated stability behaviours, rich linear vibration spectra (high modal density), high sensitivity to perturbations and strong interactions with surrounding elements. The linear and dynamic behaviour have been investigated. The shell behaviour is also investigated by means of a finite element model, in order to enhance the comprehension of experimental results.

2018 - Active isolation of structures under seismic vibrations [Relazione in Atti di Convegno]
Barbieri, M.; Ilanko, S.; Pellicano, F.
abstract

Seismic isolation of structures is very important to prevent serious damage in buildings due to earthquake, and to protect equipment during transportation. Several passive or semi-active devices exist for protecting structures from secondary seismic waves, but few solutions are present to avoid damage due to primary waves. Usually, primary waves are considered less dangerous than secondary waves, nonetheless they can produce serious damage close to the epicentre. In order to protect structures from vertical oscillations, in this paper an active vibration control system is proposed. In the present formulation, active vibration control is based upon varying foundation stiffness during the seismic movement. In the paper, it will be shown how such kind of vibration control is effective in suppressing vibrations for the case of a measured earthquake signal.

2018 - Active vibration control of seismic excitation [Articolo su rivista]
Barbieri, Marco; Ilanko, Sinniah; Pellicano, Francesco
abstract

Seismic wave control is very important both in civil and mechanical engineering. Common passive methods for isolating a building or a device include base isolators and tuned mass dampers. In the present paper, a time-varying controllable spring is considered as a vibration isolator for a linear mechanical system. The controller works as follows: When the seismic movement is active, the velocity of the moving mass is monitored as the reference velocity. When such reference velocity is positive, the stiffness is reduced; when it is negative, the stiffness is increased. Numerical investigations show that the controller is capable of filtering seismic excitation close to the natural frequency of the controlled system and reducing the total seismic energy transfer up to 5 times. The role played by the gravity in the active vibration filtering is pointed out by showing that no filtering action can be observed in gravity-free simulations. Moreover, control effectiveness has been proven for a measured seismic signal, showing its robustness in presence of noise.

2018 - Experimental identification of static and dynamic stiffness of polymeric vibration dampers [Relazione in Atti di Convegno]
Barbieri, Marco; DE FELICE, Alessandro; Pellicano, Francesco; Sorrentino, Silvio; Zippo, Antonio
abstract

Polymeric dampers are frequently used in the automotive field in order to filter engine produced vibrations and thus protecting electronic devices. An accurate knowledge of damper stiffness is therefore important for a proper design of such mechanical filters. Since viscoelastic materials exhibit a significant stiffness–frequency dependency, characterization of dynamic stiffness is required for automotive vibration dampers. In the present paper, a method for broadband identification of the dynamic complex stiffness is described; since the proposed method is reliable at medium and high frequency only (500–1500 Hz), an additional static measurement has been performed. Therefore, the resulting method is a combination of static and dynamic measurements and it does not require specific DMA equipment: all experiments have been carried out using typical vibration testing equipment.

2018 - Linear vibrations of triple-walled carbon nanotubes [Articolo su rivista]
Strozzi, Matteo; Pellicano, Francesco
abstract

In this paper, the linear vibrations of triple-walled carbon nanotubes (TWNTs) are investigated. A multiple elastic thin shell model is applied. The TWNT dynamics is studied in the framework of the Sanders–Koiter shell theory. The van der Waals interaction between any two layers of the TWNT is modelled by a radius-dependent function. The shell deformation is described in terms of longitudinal, tangential and radial displacements. Simply supported, clamped and free boundary conditions are applied. The three displacement fields are expanded by means of a double mixed series based on Chebyshev polynomials for the longitudinal variable and harmonic functions for the tangential variable. The Rayleigh–Ritz method is applied to obtain approximate natural frequencies and mode shapes. The present model is validated in the linear field by means of comparisons with data from the literature. This study is focused on determining the effect of geometry and boundary conditions on the natural frequencies of TWNTs.

2018 - Modelling and simulation of rack-pinion steering systems with manufacturing errors for performance prediction [Articolo su rivista]
Marano, Davide; Pellicano, Francesco; Pallara, Emanuele; Piantoni, Angelo; Tabaglio, Luca; Lucchi, Marco; Orlandi, Stefano
abstract

In the present paper, the modelling and simulation of a mechanical rack-and-pinion steering gear are presented. The study is performed using multibody simulations that include a reverse geometry rack to predict the functional measurements of the gear. A novel test for the characterisation of the functional performances of a mechanical steering gear is introduced and experimental data are used to validate prediction models.

2018 - Nonlinear vibrations and energy exchange of single-walled carbon nanotubes. Radial breathing modes [Articolo su rivista]
Strozzi, Matteo; Smirnov, Valeri V.; Manevitch, Leonid I.; Pellicano, Francesco
abstract

In this paper, the nonlinear vibrations and energy exchange of single-walled carbon nanotubes (SWNTs) are analysed. The Sanders-Koiter shell theory is used to model the nonlinear dynamics of the system in the case of finite amplitude of vibration. The SWNT deformation is described in terms of longitudinal, circumferential and radial displacement fields. Simply supported, clamped and free boundary conditions are applied. The resonant interaction between radial breathing (axisymmetric) modes (RBMs) is analysed. An energy method, based on the Lagrange equations, is considered in order to reduce the nonlinear partial differential equations of motion to a set of nonlinear ordinary differential equations, which is then solved applying the implicit Runge-Kutta numerical method. The present model is validated in linear field comparing the RBM natural frequencies numerically predicted with data reported in the literature from experiments and molecular dynamics simulations. The nonlinear energy exchange between the two halves along the SWNT axis in the time is studied for different amplitudes of initial excitation applied to the two lowest frequency resonant RBMs. The influence of the SWNT aspect ratio on the numerical value of the nonlinear energy beating period under different boundary conditions is analysed.

2018 - Preface [Articolo su rivista]
Mikhlin, Y. V.; Pellicano, F.; Gendelman, O. V.
abstract

2018 - Thermal effects on dynamics of circular cylindrical shell [Relazione in Atti di Convegno]
Zippo, A.; Pellicano, F.
abstract

In this paper, an experimental study on the dynamic of cylindrical shells made of Polyethylene terephthalate (PET) is presented; a thermic gradient has been applied on a specimen of the present work to obtain a functionally gradient material (FGM) equivalent properties: the PET shell had been exposed at a thermal temperature gradient in the range of its glass transition temperature of 79°C. A complex setup has been specifically designed and built to characterise, with dynamic tests, the structural properties of the specimen on temperature change from -10°C up to about 90°C and under thermic gradient with different forcing load. Predicting the mechanical properties of shells, panels and plates is one of the main concern of structural engineers; since shell elements present complicated stability behaviours, rich linear vibration spectra (high modal density), high sensitivity to perturbations and strong interactions with surrounding elements. The linear and dynamic behaviour have been investigated. The shell behaviour is also investigated by means of a finite element model, in order to enhance the comprehension of experimental results.

2017 - A novel method for dynamic characterization of polymeric vibration dampers [Relazione in Atti di Convegno]
Barbieri, Marco; DE FELICE, Alessandro; Pellicano, Francesco; Sorrentino, Silvio; Zippo, Antonio
abstract

Polymeric vibration dampers are very important devices used in many fields for vibration isolation and damping. These devices are based upon a low stiffness and high damping connection between a vibrating support and the item to be fastened. Whenever the connection is assured by a polymeric element, it is mandatory to be aware that stiffness and damping change with the excitation frequency as well as with temperature. Characterization of stiffness and damping of the polymeric element in terms of storage modulus and loss modulus is commonly carried out at low frequency by means of a Dynamic Mechanical Analysis (DMA), nonetheless this approach cannot be applied at higher frequency. In the present paper, a novel experimental approach for estimating the frequency dependent storage modulus and loss modulus in a polymeric vibration damper is presented. The proposed method is based on a direct measurement of the energy loss in hysteretic cycles, and it is suitable for simple implementation using common instruments for vibration measurement.

2017 - Dynamic imbalance of high-speed planetary gears [Articolo su rivista]
Masoumi, Asma; Barbieri, M; Pellicano, F; Zippo, A; Strozzi, M
abstract

A non-linear 2D lumped mass model of a single-stage spur planetary gear system with time-varying mesh stiffness, bearing compliance and non-smooth non-linearity due to backlash is taken into account. The time-varying meshing stiffness is evaluated by means of a non-linear finite element model, through an accurate evaluation of global and local tooth deformation. The non-linear dynamic behaviour of the system is analysed over a reasonable range of rotation speed and torque. The possibility of occurrences of different dynamic phenomena and instability of the system with respect to the bearing compliance and operating parameters are also evaluated. The possibility of dynamic imbalance of equally-spaced planetary gears in the presence of chaotic regimes is discussed. Such imbalance may lead to unexpected high-level stresses on bearings and gears.The effect of tooth profile modification at the sun-planet and ring-planet meshes on the vibration behaviour of the planetary gear system is also investigated in this paper. In order to avoid modification on the ring gear, both tip and root reliefs are considered for sun and planet gears.

2017 - Effects of gear manufacturing errors on rack and pinion steering meshing [Relazione in Atti di Convegno]
Marano, D.; Piantoni, A.; Tabaglio, L.; Lucchi, M.; Barbieri, M.; Pellicano, F.
abstract

In the present paper the effects of rack manufacturing errors on the meshing of crossed helical rack and pinion are analyzed. The study is performed using multibody simulations that include the effects of the forces acting at the gear mesh to determine the influence of rack geometrical errors on operating center distance; results are in good agreement with a simplified analytical formulation.

2017 - Experimental analysis of pre-compressed circular cylindrical shell under axial harmonic load [Articolo su rivista]
Zippo, Antonio; Barbieri, Marco; Pellicano, Francesco
abstract

In this paper the nonlinear dynamics of circular cylindrical shells under axial static (compressive) and periodic resonant loads have been experimentally investigated, the goal is to study the dynamic scenario and to analyze nonlinear regimes. A special test rig has been developed for the experiment in order to apply a static axial load combined with a dynamic axial load. The setup allows for investigating the linear behavior under static preload by means of the usual modal testing techniques; moreover, it allows for analyzing the nonlinear response which occurs when the dynamic axial load is periodic and gives rise to complex resonances. The complex dynamics, arising when a periodic axial load excites the asymmetric (shell like) modes, are analyzed by means of amplitude frequency diagrams, waterfall spectrum diagrams, bifurcation diagrams of Poincaré maps; a deep analysis of time histories, spectra, phase portraits and Poincaré maps completes the study of the complex dynamic scenario.

2017 - Experimental identification of FGM shell properties (aimeta 2017) [Relazione in Atti di Convegno]
Zippo, A.; Pellicano, F.; Barbieri, M.; Strozzi, M.; Masoumi, A.
abstract

Functionally gradient materials (FGMs) have attracted a growing interest as advanced structural materials because of their heat-resistance properties. In this paper, an experimental study on the vibration of cylindrical shells made of a functionally gradient material (FGM) composed of Polyethylene terephthalate (PET) is presented: to obtain functional gradient proprieties the PET shell had been exposed at a thermal temperature gradient in the range of its glass transition temperature of 79°C. The setting up of the experiment is explained and deeply described along with the thermal characterisation of the specimen. The linear and the nonlinear dynamic behaviour have been investigated. The shell behaviour is also investigated by means of a finite element model, in order to enhance the comprehension of experimental results.

2017 - Modal localization in vibrating circular cylindrical shells [Relazione in Atti di Convegno]
Pellicano, F.; Zippo, A.; Barbieri, M.; Strozzi, M.
abstract

The goal of the present paper is the analysis of the effect of geometric imperfections in circular cylindrical shells. Perfect circular shells are characterized by the presence of double shell-like modes, i.e., modes having the same frequency with modal shape shifted of a quarter of wavelength in the circumferential direction. In presence of geometric imperfections, the double natural frequencies split into a pair of distinct frequencies, the splitting is proportional to the level of imperfection. In some cases, the imperfections cause an interesting phenomenon on the modal shapes, which present a strong localization in the circumferential direction. This study is carried out by means of a semi-analytical approach compared with standard finite element analyses.

2017 - Nonlinear optical vibrations of single-walled carbon nanotubes [Articolo su rivista]
Manevitch, L. I.; Smirnov, V. V.; Strozzi, M.; Pellicano, F.
abstract

We demonstrate the new specific phenomenon of the long-time resonant energy exchange in the carbon nanotubes (CNTs) in the two optical branches - the Circumferential Flexure Mode (CFM) and Radial Btreathing Mode (RBM). It is shown that the modified nonlinear Schrödinger equation, obtained in the framework of nonlinear elastic thin shell theory, allows to describe the CNT nonlinear dynamics connected with considered frequency bands. Comparative analysis of the oscillations of the CFM and RBM branches shows the principal difference between nonlinearity effects. If the nonlinear resonant interaction of the low-frequency modes in the CFM branch leads to the energy capture in the some domain of the CNT, the same interaction in the RBM branch does not appear any tendency to the energy localization. The reason of such a distinction is the difference of the non-linear terms in the equations of motion. If the CFMs are specified by the soft power nonlinearity, the RBM dynamics is determined by the hard gradient nonlinearity. Moreover, in contrast to CFM the importance of nonlinearity in the case of RBM oscillations decreases with increasing of the length to radius ratio. The numerical integration of the thin shell theory equations confirms the results of the analytical study.

2017 - Nonlinear optical vibrations of single-walled carbon nanotubes. [Relazione in Atti di Convegno]
Manevitch, L. I.; Smirnov, V. V.; Strozzi, M.; Pellicano, F.
abstract

We demonstrate a new specific phenomenon of the long-time resonant energy exchange in carbon nanotubes (CNTs), which is realized by two types of optical vibrations, the Circumferential Flexure Mode (CFM) and the Radial Breathing Mode (RBM). We show that the modified nonlinear Schrdinger equation, obtained in the framework of the nonlinear theory of elastic thin shells, allows us to describe the nonlinear dynamics of CNTs for specified frequency bands. Comparative analysis of the oscillations of the CFM and RBM branches shows the qualitative difference of nonlinear effects for these branches. While the nonlinear resonant interaction of the low-frequency modes in the CFM branch leads to energy capture in some domains of the CNT, the same interaction in the RBM branch does not demonstrate any tendency for energy localization. The reason lies in the distinction in the nonlinear terms in the equations of motion. While CFMs are characterized by soft polynomial nonlinearity, RBM dynamics is characterized by hard gradient nonlinearity. Moreover, in contrast to the CFM, the importance of nonlinearity in the case of RBM oscillations decreases as the length to radius ratio increases. Numerical integration of the equations of thin shell theory confirms the results of the analytical study.

2017 - Numerical simulation and experimental validation of normal strain distribution and pitting phenomenon in industrial gears [Relazione in Atti di Convegno]
Strozzi, M.; Barbieri, M.; Zippo, A.; Pellicano, F.
abstract

In this paper, the normal strain distribution and pitting phenomenon on gears are investigated by means of numerical finite element analyses and experimental activities. In the first part of the paper, results of experimental tests for the investigation of the pitting phenomenon on gears are reported. These durability tests are made at a specific nominal load and far from the resonance. The experimental data are collected periodically from two tri-axial accelerometers placed on the gear shafts. After a short time, a visible pitting phenomenon arises on the gear teeth, where the contact pattern is perfectly centered (due to the high lead crown imposed on the teeth) and the wear pattern is consistent with FE simulations. In the second part of the paper, numerical finite element studies on the normal strain distribution at the base of the gear teeth during the contact are reported. These analyses are made at the same nominal load of the previous pitting analyses and at very low rotational speed (static analyses). A peak of normal strain at the base of the contact tooth is found around the contact time, preceded and followed by a low constant value of normal strain. The numerical results are validated by comparisons with experimental tests carried out in the same operating conditions and placing strain gauges at the tooth base of the gears.

2017 - Numerical study on nonlinear vibrations, energy exchange and resonant interactions in single walled carbon nanotubes [Relazione in Atti di Convegno]
Strozzi, M.; Barbieri, M.; Zippo, A.; Pellicano, F.
abstract

In this paper, the nonlinear vibrations, energy exchange and resonant interactions of singlewalled carbon nanotubes (SWNTs) are investigated. The Sanders-Koiter theory is applied to model the nonlinear dynamics of the system in the case of finite amplitude of vibration. The SWNT deformation is described in terms of longitudinal, circumferential and radial displacement fields. Simply supported boundary conditions are considered. The circumferential flexural modes (CFMs), radial breathing modes (RBMs) and beam-like modes (BLMs) are studied. A numerical model of the SWNT dynamics is proposed. The three displacement fields are expanded in the nonlinear field by using approximate linear eigenfunctions. An energy method based on the Lagrange equations is used to reduce the nonlinear partial differential equations of motion to a set of nonlinear ordinary differential equations, which is solved using the implicit Runge-Kutta numerical method. The nonlinear energy exchange along the SWNT axis is analysed for different initial excitation amplitudes. The resonant interactions between CFMs, RBMs and BLMs are investigated. The transition from energy beating to energy localization in the nonlinear field is studied.

2017 - Optimization of planetary gear systems by means of genetic algorithm [Relazione in Atti di Convegno]
Masoumi, A.; Barbieri, M.; Pellicano, F.
abstract

Effect of tooth profile modifications on dynamic behaviour of the planetary gear systems is analysed in this study. A nonlinear 2D lumped mass model of planetary gear system with time varying mesh stiffness, bearing compliance and non-smooth nonlinearity due to the backlash is taken into account. Genetic Algorithm (GA) is used to find the optimum profile shape of each element of the planetary gear system and the goal is to optimize the total static transmission error of the gearbox. The comparison between vibrations of the optimized and pure involute gear sets is performed in order to evaluate the effectiveness of the proposed method for optimization of the planetary gear systems.

2017 - Optimization of planetary gearboxes [Relazione in Atti di Convegno]
Masoumi, A.; Barbieri, M.; Pellicano, F.
abstract

This study investigates the effect of tooth profile modification on the vibrations of a single stage spur planetary gearbox. A lumped mass nonlinear dynamic model of the gearbox is used [1] to study the effect of tooth profile modifications applied on the sun-planet and ring-planet meshes on vibration behavior. In order to avoid modification on ring gear, both tip and root reliefs are considered for sun and planet wheels. The static model for planetary gear system with tooth profile modification is validated through comparisons with a static finite element analysis of the whole system, performed using commercial software. In the present study, an optimization approach based on Genetic Algorithms (GA) is proposed to improve planetary gear dynamic performances toward vibration reduction. As proven by dynamic analyses, a genetic algorithm is an effective optimization tool to design reliable profile modifications for reducing the planetary gears vibration amplitude over a wide frequency range.

2017 - Vibration Localization of Imperfect Circular Cylindrical Shells [Relazione in Atti di Convegno]
Pellicano, Francesco; Zippo, Antonio; Barbieri, Marco; Strozzi, Matteo
abstract

2017 - Vibration of functionally graded cylindrical shells [Relazione in Atti di Convegno]
Zippo, A.; Pellicano, F.; Barbieri, M.; Strozzi, M.
abstract

Functionally gradient materials (FGMs) have attracted a growing interest as advanced structural materials because of their heat-resistance properties. In this paper, an experimental study on the vibration of cylindrical shells made of a functionally gradient material (FGM) composed of Polyethylene terephthalate (PET) is presented: to obtain functional gradient proprieties the PET shell had been exposed at a thermal temperature gradient in the range of its glass transition temperature of 79°C. The setting up of the experiment is explained and deeply described along with the thermal characterisation of the specimen. The linear and the nonlinear dynamic behaviour have been investigated. The shell behaviour is also investigated by means of a finite element model, in order to enhance the comprehension of experimental results.

2016 - Active vibration control of a composite plate [Relazione in Atti di Convegno]
Zippo, A.; Barbieri, M.; Pellicano, F.; Strozzi, M.
abstract

A new active vibration control methodology is proposed and experimentally tested. The technique is applied to a honeycomb panel having a carbon-fiber reinforced polymer (CFRP) outer skins and a polymer-paper core, subjected to an orthogonal disturbance, due to an electrodynamics exciter. The control is carried out by means of Macro Fibre Composite (MFC) actuators and sensors. MFC parches consist of rectangular piezoceramic rods sandwiched between layers of adhesive, electrodes and polyamide film. The MFC actuators and sensors are controlled by a programmable digital dSPACER controller board. The control algorithm proposed in this paper is based on the Positive Position Feedback (PPF) technique, Single Input - Single Output, MultiSISO and Multi Input Multi Output controls are applied in order to control the first four normal modes. The control appears to be robust and efficient in reducing vibration in linear (small am- plitude) and nonlinear (large amplitude) vibrations regimes, although the structure under investigation exhibits a relativity high modal density, i.e. four resonances in a range of about 100Hz. The control strategy allows to effectively control each resonance both individually or simultaneously.

2016 - Dynamic imbalance of high speed planetary gears [Relazione in Atti di Convegno]
Masoumi, A.; Barbieri, M.; Pellicano, F.; Zippo, A.; Strozzi, M.
abstract

A nonlinear 2D lumped mass model of planetary gear system with time varying mesh stiffness, bearing compliance and nonsmooth nonlinearity due to the backlash is taken into account. The time varying meshing stiffness is evaluated by means of a nonlinear finite element model, through an accurate evaluation of global and local tooth deformation. Nonlinear dynamic behaviour of the system is analyzed over a reasonable range of rotation speed and torque. Possibility of occurrences of different dynamic phenomena and instability of the system with respect to bearing compliance and operating parameters is evaluated as well. Bifurcation diagrams are extracted as well and for specific regimes, the nonlinear scenario of system is discussed using the spectra, phase portraits and Poincare maps. Periodic, quasiperiodic and chaotic regimes are found and discussed with respect to system parameters. The possibility of dynamic imbalance of equally spaced planetary gears in presence of chaotic regimes is discussed. Such imbalance may lead to unexpected high level stresses on bearings and gears.

2016 - Experimental investigation of dynamic behaviour of pre-compressed circular cylindrical shell [Relazione in Atti di Convegno]
Zippo, Antonio; Pellicano, Francesco; Barbieri, Marco; Strozzi, Matteo
abstract

Circular cylindrical shells are very efficient structures that have many applications and plays as key elements in several engineering fields. Shells usually exhibit a complicated dynamic behaviours because the curvature will effectively couple the flexural and in-plane deformations together as the three displacement fields simultaneously appear in each of the governing partial differential equations and boundary conditions. Therefore, it is understandable that the axial constraints can have direct effects on a predominantly radial modes. For instance, it has been shown that the natural frequencies for the circumferential modes of a simply supported shell can be noticeably modified by the constraints applied in the axial direction. In this paper the results of experimental tests on pre-compressed circular cylindrical shell will be presented: different combinations of preload and harmonic external axial load have been tested but for brevity only few results are shown.

2016 - Experiments on shells under base excitation [Articolo su rivista]
Pellicano, Francesco; Barbieri, Marco; Zippo, Antonio; Strozzi, Matteo
abstract

The aim of the present paper is a deep experimental investigation of the nonlinear dynamics of circular cylindrical shells. The specific problem regards the response of circular cylindrical shells subjected to base excitation. The shells are mounted on a shaking table that furnishes a vertical vibration parallel to the cylinder axis; a heavy rigid disk is mounted on the top of the shells. The base vibration induces a rigid body motion, which mainly causes huge inertia forces exerted by the top disk to the shell. In-plane stresses due to the aforementioned inertias give rise to impressively large vibration on the shell. An extremely violent dynamic phenomenon suddenly appears as the excitation frequency varies up and down close to the linear resonant frequency of the first axisymmetric mode. The dynamics are deeply investigated by varying excitation level and frequency. Moreover, in order to generalise the investigation, two different geometries are analysed. The paper furnishes a complete dynamic scenario by means of: (i) amplitude frequency diagrams, (ii) bifurcation diagrams, (iii) time histories and spectra, (iv) phase portraits and Poincaré maps. It is to be stressed that all the results presented here are experimental.

2016 - Linear vibrations of multi-walled carbon nanotubes [Relazione in Atti di Convegno]
Strozzi, Matteo; Pellicano, Francesco; Barbieri, Marco; Zippo, Antonio
abstract

In this paper, the linear vibrations of Multi-Walled Carbon Nanotubes (MWNTs) are analysed. A multiple elastic shell model is considered. The shell dynamics is studied in the framework of the Sanders-Koiter shell theory. The van der Waals (vdW) interaction between two layers of the MWNT is modelled by a radius-dependent function. The shell deformation is described in terms of longitudinal, circumferential and radial displacements. Simply supported, clamped and free boundary conditions are considered. The three displacement fields are expanded by means of a double mixed series based on Chebyshev orthogonal polynomials for the longitudinal variable and harmonic functions for the circumferential variable. The Rayleigh-Ritz method is applied to obtain approximate natural frequencies and mode shapes. The present model is validated in linear field by means of data derived from the literature. This study is focused on determining the effect of the geometry and boundary conditions on the natural frequencies of the MWNTs.

2016 - Modelling and Testing Techniques for Gear- boxes Analysis and Optimization [Relazione in Atti di Convegno]
Andrisano, A. O.; Pellicano, Francesco; Barbieri, Marco; Zippo, Antonio; Strozzi, Matteo
abstract

2016 - Natural Frequencies of Triple-Walled Carbon Nanotubes [Relazione in Atti di Convegno]
Andrisano, A. O.; Pellicano, Francesco; Strozzi, Matteo
abstract

2016 - Nonlinear Dynamics of Pre-Compressed Circular Cylindrical Shell Under Axial Harmonic Load: Experiments [Relazione in Atti di Convegno]
Pellicano, Francesco; Zippo, Antonio; Barbieri, Marco; Strozzi, Matteo
abstract

2016 - Nonlinear dynamics of SWNTs. Energy beating and localization [Abstract in Atti di Convegno]
Strozzi, Matteo; Manevitch, L. I.; Smirnov, V. V.; Pellicano, Francesco
abstract

2016 - Nonlinear optical vibrations of single-walled carbon nanotubes. 1. Energy exchange and localization of low-frequency oscillations [Articolo su rivista]
Smirnov, V. V.; Manevitch, L. I.; Strozzi, M.; Pellicano, F.
abstract

We present the results of analytical study and molecular dynamics simulation of low energy nonlinear non-stationary dynamics of single-walled carbon nanotubes (CNTs). New phenomena of intense energy exchange between different parts of CNT and weak energy localization in the excited part of CNT are analytically predicted in the framework of the continuum shell theory. Their origin is clarified by means of the concept of Limiting Phase Trajectory, and the analytical results are confirmed by the molecular dynamics simulation of simply supported CNTs.

2016 - Nonlinear vibrations and energy exchange of single-walled carbon nanotubes. Circumferential flexural modes [Articolo su rivista]
Strozzi, Matteo; Smirnov, Valeri V.; Manevitch, Leonid I.; Milani, Massimo; Pellicano, Francesco
abstract

In this paper, the nonlinear vibrations and energy exchange of single-walled carbon nanotubes (SWNTs) are studied. The Sanders–Koiter theory is applied to model the nonlinear dynamics of the system in the case of finite amplitude of vibration. The SWNT deformation is described in terms of longitudinal, circumferential and radial displacement fields. Simply supported, clamped and free boundary conditions are considered. The circumferential flexural modes (CFMs) are investigated. Two different approaches based on numerical and analytical models are compared. In the numerical model, an energy method based on the Lagrange equations is used to reduce the nonlinear partial differential equations of motion to a set of nonlinear ordinary differential equations, which is solved by using the implicit Runge–Kutta numerical method. In the analytical model, a reduced form of the Sanders–Koiter theory assuming small circumferential and tangential shear deformations is used to get the nonlinear ordinary differential equations of motion, which are solved by using the multiple scales analytical method. The transition from energy beating to energy localization in the nonlinear field is studied. The effect of the aspect ratio on the analytical and numerical values of the nonlinear energy localization threshold for different boundary conditions is investigated.

2016 - Novel spectral kurtosis technology for adaptive vibration condition monitoring of multi-stage gearboxes [Articolo su rivista]
Gelman, L; Harish Chandra, N.; Kurosz, R.; Pellicano, Francesco; Barbieri, Marco; Zippo, Antonio
abstract

In this paper, the novel wavelet spectral kurtosis (WSK) technique is applied for the early diagnosis of gear tooth faults. Two variants of the wavelet spectral kurtosis technique, called variable resolution WSK and constant resolution WSK, are considered for the diagnosis of pitting gear faults. The gear residual signal, obtained by filtering the gear mesh frequencies, is used as the input to the SK algorithm. The advantages of using the wavelet-based SK techniques when compared to classical Fourier transform (FT)-based SK is confirmed by estimating the toothwise Fisher's criterion of diagnostic features. The final diagnosis decision is made by a three-stage decision-making technique based on the weighted majority rule. The probability of the correct diagnosis is estimated for each SK technique for comparison. An experimental study is presented in detail to test the performance of the wavelet spectral kurtosis techniques and the decision-making technique.

2016 - Pitting and stress analysis of gears: A numerical and experimental study [Relazione in Atti di Convegno]
Strozzi, M.; Barbieri, M.; Pellicano, F.; Zippo, A.
abstract

In this paper, the pitting phenomenon and stress distribution of gears are investigated by means of experimental activities and numerical finite element analyses. In the first part, results of experimental accelerated endurance tests for the investigation of the pitting phenomenon of gears are reported. These durability tests are made at a specific nominal load and far from the resonance. After a short time, a visible pitting phenomenon arises. In the second part, finite element numerical analyses for the evaluation of gear stresses are listed. The numerical analyses start from stress-vibration correlations and dynamic factors obtained by a 2-dof dynamic model; these results are used in the dynamic FEM simulations in order to calculate the maximum normal stress and the contact pressure on the contact tooth of the pinion vs. vibration amplitude for different dynamic factors.

2015 - Active vibration control of a composite sandwich plate [Articolo su rivista]
Zippo, Antonio; Ferrari, Giovanni; Amabili, Marco; Barbieri, Marco; Pellicano, Francesco
abstract

Active vibration control of a free-edge rectangular sandwich plate is proposed and tested. The experimental setup consists of a honeycomb panel having a carbon-fiber reinforced polymer (CFRP) outer skins and a polymer-paper core, subjected to an orthogonal disturbance, due to an electrodynamics exciter and controlled by Macro Fibre Composite (MFC) actuators and sensors. MFC parches consist of rectangular piezoceramic rods sandwiched between layers of adhesive, electrodes and polyamide film. The MFC actuators and sensors are controlled by a programmable digital dSPACE (R) controller board. The control algorithm proposed in this paper is based on the Positive Position Feedback (PPF) technique and is successfully applied with different combinations of inputs/outputs (Single Input Single Output, MultiSISO, Multi Input Multi Output) in order to control the first four normal modes. The control appears to be robust and efficient in reducing vibration in linear (small amplitude) and nonlinear (large amplitude) vibrations regimes, although the structure under investigation exhibits a relativity high modal density, i.e., four resonances in a range of about 100 Hz. The control strategy allows to effectively control each resonance both individually or simultaneously.

2015 - Beating phenomenon and energy localization in Single-Walled Carbon Nanotubes [Abstract in Atti di Convegno]
Strozzi, Matteo; Manevitch, Leonid I.; Pellicano, Francesco; Barbieri, Marco; Zippo, Antonio
abstract

In this paper, the low-frequency nonlinear oscillations and energy localization of Single-Walled Carbon Nanotubes (SWNTs) are analysed. The SWNTs dynamics is studied in the framework of the Sanders-Koiter nonlinear shell theory. The circumferential flexure vibration modes (CFMs) are considered. Simply supported, clamped and free boundary conditions are analysed. Two different approaches are compared, based on numerical and analytical models. The numerical model uses a double mixed series expansion for the displacement fields based on the Chebyshev polynomials and harmonic functions. The Lagrange equations are considered to obtain a set of nonlinear ordinary differential equations of motion which are solved using the implicit Runge-Kutta numerical method. The analytical model considers a reduced form of the shell theory assuming small circumferential and tangential shear deformations. The Galerkin procedure is used to get the nonlinear ordinary differential equations of motion, which are then solved using the multiple scales analytical method. The natural frequencies of SWNTs obtained by considering the analytical and numerical approaches are compared for different boundary conditions. A convergence analysis in the nonlinear field is carried out for the numerical method in order to select the correct number of the axisymmetric and asymmetric modes providing the actual localization threshold. The effect of the aspect ratio on the analytical and numerical values of the localization threshold for SWNTs with different boundary conditions is investigated in the nonlinear field.

2015 - Dynamic modelling of gear pairs [Relazione in Atti di Convegno]
Barbieri, Marco; Zippo, Antonio; Strozzi, Matteo; Serafini, Lorenzo; Pellicano, Francesco; Bonori, Giorgio
abstract

A clear understanding of the dynamics of gear pairs is important for many reasons. First of all, gear vibration is a main source of noise in gearboxes and vehicle trasmissions, secondly the torsional elasticity of the gear trasmission can produce relevant amplification of the contact force, and thus of the gear stress. Furthermore, gear vibrations are a useful parameter for gear monitoring and prognostics. In the present work, an overview of the models used to describe the dynamic behaviour of gear pairs will be presented, along with a comparison between a dynamic finite element model and different lumped parameter approaches. A correlation between the vibration transmitted to the gearbox, and thus easily measurable in a real application, and the local stresses in the gear pair will be drawn. The proposed approach is suitable to describe the effect of localized defects on the gear pair, such as tooth root cracks and pitted profiles, on the signal measured on a gearbox.

2015 - Dynamics and Stability of Carbon Nanotubes [Abstract in Atti di Convegno]
Strozzi, Matteo; Barbieri, Marco; Zippo, Antonio; Pellicano, Francesco
abstract

The low-frequency oscillations and energy localization of Single-Walled Carbon Nanotubes (SWNTs) are studied in the framework of the Sanders-Koiter shell theory. The circumferential flexure modes (CFMs) are analysed. Simply supported, clamped and free boundary conditions are considered. Two different approaches are proposed, based on numerical and analytical models. The numerical model uses in the linear analysis a double mixed series expansion for the displacement fields based on Chebyshev polynomials and harmonic functions. The Rayleigh-Ritz method is applied to obtain approximate natural frequencies and mode shapes. In the nonlinear analysis, the three displacement fields are re-expanded by using approximate eigenfunctions. An energy approach based on Lagrange equations is considered in order to obtain a set of nonlinear ordinary differential equations, which is solved by the Runge-Kutta numerical method. The analytical model considers a reduced version of the Sanders-Koiter shell theory obtained by assuming small circumferential and tangential shear deformations. These two assumptions allow to condense the longitudinal and circumferential displacement fields into the radial one. A nonlinear fourth-order partial differential equation for the radial displacement field is derived, which allows to calculate the natural frequencies and to estimate the nonlinearity effect. An analytical solution of this equation is obtained by the multiple scales method. The previous models are validated in linear field by means of comparisons with experiments, molecular dynamics simulations and finite element analyses retrieved from the literature. The concept of energy localization in SWNTs is introduced, which is a strongly nonlinear phenomenon. The low-frequency nonlinear oscillations of the SWNTs become localized ones if the intensity of the initial excitation exceeds some threshold which depends on the SWNTs length. This localization results from the resonant interaction of the zone-boundary and nearest nonlinear normal modes leading to the confinement of the vibration energy in one part of the system. The value of the initial excitation corresponding to this energy confinement is referred to as energy localization threshold. The effect of the aspect ratio on the analytical and numerical values of the energy localization threshold is investigated; different boundary conditions are considered.

2015 - EHL lubrication in spur and helical gear pairs [Relazione in Atti di Convegno]
Barbieri, Marco; Pellicano, Francesco
abstract

Gear efficiency is highly relying on elasto-hydrodynamic lubrication (EHL), and gear lubrication is significantly dependent upon non stationary conditions in gear pairs. Furthermore, the presence of lubricant is the main responsible of the damping effect in gear pair vibration. For these reasons, gear vibration and gear lubrication are to be considered as coupled problems. In the present work, a dynamic model of gear pairs taking into account for EHL lubrication is presented. The multilevel technique is used to solve the EHD lubrication problem, together with the equation describing the relative motion of the mating gears. Gear lubrication conditions at different gear rotation speed are investigated, in order to point out the effect of coupling between a thin lubricant film and elastic deformations in contacting bodies; a comparison between a dry contact and a lubricated contact is drawn, in order to clarify the amount of damping introduced by the lubricant film.

2015 - Energy localization in carbon nanotubes [Relazione in Atti di Convegno]
Strozzi, Matteo; Smirnov, Valeri V.; Manevitch, Leonid I.; Pellicano, Francesco; Shepelev, Denis S.
abstract

In this paper, the energy localization phenomena in low-frequency nonlinear oscillations of single-walled carbon nanotubes (SWNTs) are analysed. The SWNTs dynamics is studied in the framework of the Sanders-Koiter shell theory. Simply supported and free boundary conditions are considered. The effect of the aspect ratio on the analytical and numerical values of the localization threshold is investigated in nonlinear field.

2015 - Experimental and numerical study of MIMO active vibration control [Relazione in Atti di Convegno]
Zippo, Antonio; Pellicano, Francesco; Barbieri, Marco; Amabili, Marco
abstract

In this paper the finite element method is used for choosing the best position of nearby collocated pairs of actuator-sensor couples, an experimental investigation of active vibration control validates the theory; the application regards a rectangular sandwich laminated plate (carbon-epoxy outer skins and Nomex paper honeycomb core) with free boundary conditions. The piezoelectric unidirectional patches are used as strain sensors and strain actuators, respectively. The collocation of the patches is led by the results of a finite element modal analysis and allows the design of a modal control strategy, the efficiency of which is targeted to single vibration modes. The control configurations presented in this paper is a MIMO configuration in linear field. The identification activity and the extraction of stabilised transfer functions are performed by means of a dedicated Matlab algorithm. The stability and the robustness of the algorithm are briefly studied. A substantial reduction of the vibration amplitude is obtained both at specific frequencies and in a broadband random excitation-disturbance. It is also possible to control disturbances that would otherwise trigger geometrically nonlinear vibrations. The modal character of the resulting control is guaranteed by means of the MAC. An experimental setup has been developed, two to four Macro Fiber Composite (MFC) actuators and two MFC sensors are used in conjunction with a DSPACE controller system. The control appears robust and efficient in reducing vibration levels in linear and nonlinear field, even though the structure under investigation exhibits a high modal density, four resonances in a range of about 100Hz, and allows controlling each resonance separately or together.

2015 - Experimental, numerical and analytical investigation of free vibrational behavior of GFRP-stiffened composite cylindrical shells [Articolo su rivista]
Hemmatnezhad, M; Rahimi, G. H.; Tajik, M.; Pellicano, Francesco
abstract

The present research aims to investigate the vibration characteristics of stiffened composite cylindrical shells using experimental, numerical and analytical techniques. The specimens are fabricated from continuous glass fiber (GFRP) using a specially-designed filament winding setup. The theoretical formulation is established based on Sanders' thin shell theory. In the analytical approach, a smeared method is employed to superimpose the stiffness contribution of the stiffeners with those of shell in order to obtain the equivalent stiffness parameters of the whole panel. Using the Ritz method, the governing eigenvalue equations are obtained and will then be solved for evaluating the natural frequencies of the GFRP-stiffened composite shells. In order to validate the analytical achievements, experimental modal analysis is conducted on a stiffened cylinder. A 3-D finite element model is built for a further validation. This model takes into account the exact geometric configuration of the stiffeners and the shell. Results confirm the accuracy of the analytical method. Furthermore, the influences of changes in the skin thickness and boundary condition are analyzed.

2015 - Nonlinear dynamics of carbon nanotubes [Relazione in Atti di Convegno]
Andrisano, A. O.; Pellicano, F.; Strozzi, M.
abstract

2015 - Nonlinear oscillations of carbon nanotubes [Relazione in Atti di Convegno]
Strozzi, Matteo; Pellicano, Francesco; Barbieri, Marco; Zippo, Antonio; Manevitch, Leonid I.
abstract

In this paper, the low-frequency nonlinear oscillations and energy localizations of Single-Walled Carbon Nanotubes (SWNTs) are analysed. The SWNTs dynamics is studied within the framework of the Sanders-Koiter thin shell theory. The circumferential flexure vibration modes (CFMs) are considered. Simply supported boundary conditions are investigated. Two different approaches are compared, based on numerical and analytical models. The numerical model uses a double series expansion for the displacement fields based on the Chebyshev polynomials and harmonic functions. The Lagrange equations are considered to obtain a set of nonlinear ordinary differential equations of motion which are solved using the implicit Runge-Kutta numerical method. The analytical model considers a reduced form of the shell theory assuming small circumferential and tangential shear deformations. The Galerkin procedure is used to get the nonlinear ordinary differential equations of motion which are solved using the multiple scales analytical method. The natural frequencies obtained by considering the two approaches are compared in linear field. The effect of the aspect ratio on the analytical and numerical values of the localization threshold is investigated in nonlinear field.

2015 - Symmetry breaking and chaos-induced imbalance in planetary gears [Articolo su rivista]
Masoumi, Asma; Pellicano, Francesco; Samani, Farhad S.; Barbieri, Marco
abstract

The goal of the present paper was a com- plete analysis of the dynamic scenario of planetary gears. A lumped mass two-dimensional model is adopted; the model takes into account: time-varying stiffness; nonsmooth nonlinearity due to the backlash, i.e., teeth contact loosing; and bearing compliance. The time-varying meshing stiffness is evaluated by means of a nonlinear finite element model, which allows an accurate evaluation of global and local teeth defor- mation. The dynamic model is validated by compar- isons with the most authoritative literature: linear nat- ural frequencies and nonlinear response. The dynamic scenario is analyzed over a reasonable engineering range in terms of rotation speed and torque. The clas- sical amplitude–frequency diagrams are accompanied by bifurcation diagrams, and for specific regimes, the spectral and topological properties of the response are discussed. Periodic, quasiperiodic and chaotic regimes are found; nonsmooth bifurcations lead period one to period two trajectories. It is found that the bearing com- pliance can influence the natural frequencies combina- tion magnifying the modal interactions due to internal resonances and greatly enlarging the chaotic regions. It is evidenced that the chaotic response indices a sym- metry breaking in the dynamical systems. The physical consequence is that the planetary gearbox under inves- tigation, which is perfectly balanced for each position, can suffer of a big dynamic imbalance when chaotic regimes take place; such imbalance gives rise to alter- nate and unexpected high-level stresses on bearings.

2014 - Adaptive grid-size finite element modeling of helical gear pairs [Articolo su rivista]
Barbieri, Marco; Zippo, Antonio; Pellicano, Francesco
abstract

A method for solving the contact problem for generic helical gear pairs (either external or inter- nal) is described. Gear profiles are obtained by means of numerical simulation of the cutting pro- cess and an accurate description is provided in terms of NURBS curves or surfaces. A new method for finding the enveloping profiles for a generic tool (e.g. from a measured topography) is pro- posed. The minimum number of parameters needed to describe the profile in the presence of tip and root reliefs, helix modification and crowning is discussed. A reference structured grid is de- fined on the tooth, then refinement criteria are applied in order to obtain accurate solutions in terms of tooth deflection, contact pressure and fillet stress. The method allows to automatically perform a Loaded Tooth Contact Analysis (LTCA) starting from the design data of a gear pair. Re- sults from the LTCA include contact pressure and contact pattern maps, as well as maximum fillet stress and fatigue strength. Combining several analyses within a mesh cycle, information about the Static Transmission Error (STE) and mesh stiffness is provided. The whole procedure has been implemented in a software called helical pair. A comparison with other approaches is given.

2014 - Complex dynamics of circular cylindrical shells [Articolo su rivista]
Pellicano, Francesco; Barbieri, Marco
abstract

Complex dynamics of circular cylindrical shells subjected to inertial axial loads are investigated. The shell is vertically mounted on a shaker, i.e. its base is clamped to the shaker fixture, which induces a vertical motion along the shell axis. On the top of the shell a rigid disk is mounted, the vertical motion induced by the shaker induces huge inertial forces due to the rigid body motion. A complicating effect is due to the base actuator, which is an electro-dynamic shaking table; the interaction between the shell and shaker dynamics changes dramatically the system behaviour. The non-linear Sanders–Koiter theory is considered for the structural dynamics: the resulting set of non-linear partial differential equations is coupled with the linear ordinary differential equations that govern the shaker dynamics. A deep analysis of the non-stationary response of the shell is carried out in order to clarify the transition from stationary to non-stationary response. The model is validated by means of experimental results.

2014 - Complex dynamics of planetary gear systems [Relazione in Atti di Convegno]
Masoumi, Asma; Pellicano, Francesco; Barbieri, Marco
abstract

A full 2D dynamic model of a single-stage planetary gear system with backlash and time varying stiffness is considered here. This dynamic model is time variant and non-smooth, due to the presence of time varying meshing stiffness and backlash for all sun- planets and ring-planets meshes; moreover, bearing compliance is accounted for. The linear averaged equations of motion are solved to obtain the natural frequencies; conversely, the fully nonlinear equations of motion are analyzed numerically to study the effect of time varying stiffness and backlash and to point out the nonlinear dynamics of the system. The complex dynamics is deeply investigated over the meaningful mesh frequency ranges. The dynamic scenario is obtained by means of bifurcation analysis and completed with time spectral and topological properties of the response.

2014 - Eigenfrequencies and vibration modes of carbon nanotubes [Relazione in Atti di Convegno]
Strozzi, Matteo; Manevitch, Leonid I.; Smirnov, Valeri V.; Shepelev, Denis S.; Pellicano, Francesco
abstract

In 1991 Iijima discovered Carbon Nanotubes, he synthesised molecular carbon structures in the form of fullerenes and then reported the preparation of a new type of finite carbon structure consisting of needle-like tubes, the carbon nanotubes, described as helical microtubules of graphitic carbon. Examples of applications of Carbon Nanotubes (CNTs) can be found in ultrahigh frequency nanomechanical resonators, in a large number of nanoelectromechanical devices such as sensors, oscillators, charge detectors and field emission devices. The reduction of the size and the increment of the stiffness of a resonator magnify its resonant frequencies and reduce its energy consumption, improving its sensitivity. The modal analysis of carbon nanotubes is important because it allows to obtain the resonant frequencies and mode shapes, which influence the mechanical and electronic properties of the nanotube resonators. A large number of experiments and atomistic simulations were conducted both on single-walled (SWNTs) and multi-walled carbon nanotubes (MWNTs). The present work is concerned with the analysis of low-frequency linear vibrations of SWNTs: two approaches are presented: a fully analytical method based on a simplified theory and a semi-analytical method based on the theory of thin walled shells. The semi-analytical approach (shortly called “numerical approach”) is based on the Sanders-Koiter shell theory and the Rayleigh-Ritz numerical procedure. The nanotube deformation is described in terms of longitudinal, circumferential and radial displacement fields, which are expanded by means of a double mixed series based on Chebyshev polynomials for the longitudinal variable and harmonic functions for the circumferential variable. The Rayleigh-Ritz method is then applied to obtain numerically approximate natural frequencies and mode shapes. The second approach is based on a reduced version of the Sanders-Koiter shell theory, obtained by assuming small ring and tangential shear deformations. These assumptions allow to condense both the longitudinal and the circumferential displacement fields. A fourth-order partial differential equation for the radial displacement field is derived. Eigenfunctions are formally obtained analytically, then the numerical solution of the dispersion equation gives the natural frequencies and the corresponding normal modes. The methods are fully validated by comparing the natural frequencies of the SWNTs with data available in literature, namely: experiments, molecular dynamics simulations and finite element analyses. A comparison between the results of the numerical and analytical approach is carried out in order to check the accuracy of the last one. It is worthwhile to stress that the analytical model allows to obtain results with very low computational effort. On the other hand the numerical approach is able to handle the most realistic boundary conditions of SWNTs (free-free, clamped-free) with extreme accuracy. Both methods are suitable for a forthcoming extension to multi-walled nanotubes and nonlinear vibrations.

2014 - Low-frequency linear vibrations of single-walled carbon nanotubes: Analytical and numerical models [Articolo su rivista]
Strozzi, Matteo; L. I., Manevitch; Pellicano, Francesco; V. V., Smirnov; D. S., Shepelev
abstract

Low-frequency vibrations of single-walled carbon nanotubes with various boundary conditions are considered in the framework of the Sanders–Koiter thin shell theory. Two methods of analysis are proposed. The first approach is based on the Rayleigh–Ritz method, a double series expansion in terms of Chebyshev polynomials and harmonic functions is considered for the displacement fields; free and clamped edges are analysed. This approach is partially numerical. The second approach is based on the same thin shell theory, but the goal is to obtain an analytical solution useful for future developments in nonlinear fields; the Sanders–Koiter equations are strongly simplified neglecting in-plane circumferential normal strains and tangential shear strains. The model is fully validated by means of comparisons with experiments, molecular dynamics data and finite element analyses obtained from the literature. Several types of nanotubes are considered in detail by varying aspect ratio, chirality and boundary conditions. The analyses are carried out for a wide range of frequency spectrum. The strength and weakness of the proposed approaches are shown; in particular, the model shows great accuracy even though it requires minimal computational effort.

2014 - Non-smooth active control of seismic vibrations [Relazione in Atti di Convegno]
Barbieri, Marco; Ilanko, Sinniah; Pellicano, Francesco
abstract

In order to prevent seismic damage in civil buildings and mechanical equipment, e.g. during transport, passive isolators and dampers are commonly used. In the present work, a non-smooth strategy for active seismic isolation is presented. The method provides isolation from base excitation by dynamically switching the stiffness of the foundation. The controller works as follows: when the seismic movement is active, the velocity of the moving mass is monitored as the reference velocity. When such reference velocity is positive, the stiffness is reduced; when it is negative, the stiffness is increased. Numerical investigations show that the controller is capable to filter seismic excitation close to the natural frequency of the controlled system, and to reduce the total seismic energy transfer up to 5 times. The role played by the gravity in the active vibration filtering is pointed out by showing that no filtering action can be observed in gravity-free simulations. Even though the controlled system is linear, the controller presents a non-smooth fluctuation of the stiffness, so that a limit cycle occurs within the system.

2014 - Nonlinear Dynamics of Single-Walled Carbon Nanotubes [Relazione in Atti di Convegno]
Strozzi, Matteo; Manevitch, Leonid I.; Pellicano, Francesco
abstract

The nonlinear dynamics of Single-Walled Carbon Nanotubes is studied. The Sanders-Koiter elastic shell theory is applied. The carbon nanotube deformation is described in terms of longitudinal, circumferential and radial displacement fields. Free boundary conditions are considered. The total energy distribution of the system is studied by considering the combinations of different vibration modes. The effect of the companion mode participation on the energy distribution is analysed.

2014 - Nonlinear dynamics of axially loaded shells: experimental study [Relazione in Atti di Convegno]
Pellicano, Francesco; Zippo, Antonio; Barbieri, Marco
abstract

In this paper recent experiments on nonlinear dynamics of shells are described, such experiments were focused to circular cylindrical shells subjected to axial loads. Different types of axial loads were considered: inertial loads due to rigid bodies connected to the shell; static and dynamic loads induced by direct shell excitation. The latter type of loading allows to study the effect of pre-compression, which typically induces natural frequency variation and changing of the dynamic scenario. The experiments show an extremely complex dynamic scenario, which needs a deep analysis to be interpreted and explained. The goal of the present work is twice: describe experimental evidence of complex dynamics and furnish explanation when possible.

2014 - Nonlinear oscillations and energy localization in carbon nanotubes [Relazione in Atti di Convegno]
Andrisano, Angelo Oreste; Manevitch, Leonid I.; Pellicano, Francesco; Strozzi, Matteo
abstract

In this paper, the low-frequency nonlinear oscillations and energy localizations of Single-Walled Carbon Nanotubes (SWNTs) are analysed. The SWNTs dynamics is studied within the framework of the Sanders-Koiter thin shell theory. The circumferential flexure vibration modes (CFMs) are considered. Simply supported boundary conditions are investigated. Two different approaches are compared, based on numerical and analytical models. The numerical model uses a double series expansion for the displacement fields based on the Chebyshev polynomials and harmonic functions. The Lagrange equations are considered to obtain a set of nonlinear ordinary differential equations of motion which are solved using the implicit Runge-Kutta numerical method. The analytical model considers a reduced form of the shell theory assuming small circumferential and tangential shear deformations. The Galerkin procedure is used to get the nonlinear ordinary differential equations of motion which are solved using the multiple scales analytical method. The natural frequencies obtained by considering the two approaches are compared in linear field. The effect of the aspect ratio on the analytic and numerical values of the localization threshold is investigated in nonlinear field.

2013 - Active vibration control of seismic excitation [Relazione in Atti di Convegno]
Barbieri, Marco; Cinque, Fabio; Ilanko, Sinniah; Pellicano, Francesco
abstract

Seismic wave control is very important both in civil and mechanical engineering. Common passive methods for isolating a building or a device include Base Isolators (BI) and Tuned Mass Dampers (TMD). In the present paper, a time varying controllable spring is considered as a vibration isolator for a linear mechanical system. The controller works as follows: when the seismic movement is active, the velocity of the moving mass is monitored as the reference velocity. When such reference velocity is positive, the stiffness is reduced; when it is negative, the stiffness is increased. Numerical investigations show that the controller is capable to filter seismic excitation close to the natural frequency of the controlled system, and to reduce the total seismic energy transfer up to 5 times. The role played by the gravity in the active vibration filtering is pointed out by showing that no filtering action can be observed in gravity-free simulations. Even though the controlled system is linear, the controller presents a non-smooth fluctuation of the stiffness, so that a limit cycle occur within the system.

2013 - Behavior of lubricant fluid film in gears under dynamic conditions [Articolo su rivista]
Barbieri, Marco; Lubrecht Antonius, A.; Pellicano, Francesco
abstract

This paper presents a new method for modeling the fluid film lubrication in gears, considering the actual meshing conditions and gear dynamics. The model takes into account both the elastohydrodynamic lubrication (EHL) and the dynamic load between the mating tooth pair. The EHL film is described as a fully flooded elliptical contact. The present approach is validated by means of comparison with other methods found in the literature, in which dynamic effects were neglected. The effect of the gear dynamics on the fluid film is investigated. It is shown that pressure and film thickness are strongly modified by the dynamics of the gear pair. The dependence of the dynamic gear lubrication on dimensionless parameters is investigated: a new dimensionless inertia parameter is added to the standard Moes' parameters. These parameters are useful to describe the lubrication conditions in gear pairs.

2013 - Circular Cylindrical Shells under combined axial loads: an experimental study [Relazione in Atti di Convegno]
Zippo, Antonio; Barbieri, Marco; Pellicano, Francesco
abstract

Thin shells structures have an important role in engineering; several important examples can be found in Structural Engineering, Mechanical Engineering and Aerospace: water tanks, containment shells of nuclear power plants, concrete arch domes, piping systems, pressure vessels, aircrafts, missiles, rockets, ships. Even though many researchers have extensively studied nonlinear vibrations of cylindrical shells, experimental studies are rather limited in number; in particular, rare experimental reports have been published about shells loaded with in-plane . In this paper the response of a circular cylindrical shells subjected to axial compressive and periodic loads has been experimentally investigated. The experimental setup is explained and deeply described along with the analysis of preliminary results. The linear shell behavior is investigated by means of a finite element model in order to enhance the comprehension of experimental results in the linear field. The main goal is to investigate the nonlinear phenomena associated with a combined effect of compressive static and a periodic axial loads, the investigation have been carried out for different combinations of loads. Several interesting nonlinear phenomena have been observed such as softening-type non-linearity and non stationary response when the periodic axial load is resonant with one of the shell modes.

2013 - Modelling lubrication in gear pairs [Relazione in Atti di Convegno]
Barbieri, Marco; Pellicano, Francesco
abstract

The lubrication regime in gear pairs is usually elasto-hydrodynamic, i.e. solid deformations due to the fluid pressure are not negligible. It is well known that lubrication in gear pairs depends upon a number of kinematical parameters, so that it is a non stationary EHD problem. Moreover, it depends upon the dynamic response (i.e. the dynamic load) of the gear pair [1-5]. The problem of finding the dynamic response in gear systems, especially spur gears, has been studied by many research works. Most of them consider as the main source of vibration the time variation of the number of teeth pairs that are in contact at the same time. This fluctuation makes the transmission more stiff, when two pair of teeth are in contact, more deformable when only one pair is in contact. This behaviour can cause oscillations of the gears, and eventually detachment of the teeth in contact, with impacts and noise. The purpose of the present work is to investigate the effect of the varying rotational velocity of the gear pair on the film thickness and the contact pressure distribution. The lubrication regime in spur gear pairs is investigated using an EHL lubrication model. The solver described by Venner and Lubrecht [6] is adapted to the specific transient problem. Different test cases at different speeds are presented, in order to point out the role of the dynamic coupling on the lubricated contact.

2013 - Nonlinear dynamics of Single-Walled Carbon Nanotubes [Relazione in Atti di Convegno]
Strozzi, Matteo; Manevitch, Leonid I.; Pellicano, Francesco
abstract

The nonlinear vibrations of Single-Walled Carbon Nanotubes are analysed. The Sanders-Koiter elastic shell theory is applied in order to obtain the elastic strain energy and kinetic energy. The carbon nanotube deformation is described in terms of longitudinal, circumferential and radial displacement fields. The theory considers geometric nonlinearities due to large amplitude of vibration. The displacement fields are expanded by means of a double series based on harmonic functions for the circumferential variable and Chebyshev polynomials for the longitudinal variable. The Rayleigh-Ritz method is applied to obtain approximate natural frequencies and mode shapes. Free boundary conditions are considered. In the nonlinear analysis, the three displacement fields are re-expanded by using approximate eigenfunctions. An energy approach based on the Lagrange equations is considered in order to obtain a set of nonlinear ordinary differential equations. The total energy distribution of the shell is studied by considering combinations of different vibration modes. The effect of the conjugate modes is analysed.

2013 - Nonlinear vibrations and energy conservation of Single-Walled Carbon Nanotubes [Relazione in Atti di Convegno]
Zippo, Antonio; Strozzi, Matteo; Manevitch, Leonid I.; Pellicano, Francesco; Barbieri, Marco
abstract

The nonlinear vibrations of Single-Walled Carbon Nanotubes are analysed. The Sanders-Koiter elastic shell theory is applied in order to obtain the elastic strain energy and kinetic energy. The carbon nanotube deformation is described in terms of longitudinal, circumferential and radial displacement fields. The theory considers geometric nonlinearities due to large amplitude of vibration. The displacement fields are expanded by means of a double series based on harmonic functions for the circumferential variable and Chebyshev polynomials for the longitudinal variable. The Rayleigh-Ritz method is applied in order to obtain approximate natural frequencies and mode shapes. Free boundary conditions are analysed. In the nonlinear analysis, the three displacement fields are re-expanded by using approximate eigenfunctions; an energy approach based on the Lagrange equations is considered in order to reduce the nonlinear partial differential equations to a set of nonlinear ordinary differential equations. Nondimensional parameters are considered. The total energy conservation of the system is verified by considering the combinations of different vibration modes. The effect of the companion mode participation on the nonlinear vibrations of the carbon nanotube is analysed.

2013 - Nonlinear vibrations and energy distribution of Single-Walled Carbon Nanotubes [Relazione in Atti di Convegno]
Strozzi, Matteo; Manevitch, Leonid I.; Pellicano, Francesco
abstract

The nonlinear vibrations of Single-Walled Carbon Nanotubes are analysed. The Sanders-Koiter elastic shell theory is applied in order to obtain the elastic strain energy and kinetic energy. The carbon nanotube deformation is described in terms of longitudinal, circumferential and radial displacement fields. The theory considers geometric nonlinearities due to large amplitude of vibration. The displacement fields are expanded by means of a double series based on harmonic functions for the circumferential variable and Chebyshev polynomials for the longitudinal variable. The Rayleigh-Ritz method is applied in order to obtain approximate natural frequencies and mode shapes. Free boundary conditions are considered. In the nonlinear analysis, the three displacement fields are re-expanded by using approximate eigenfunctions. An energy approach based on the Lagrange equations is considered in order to obtain a set of nonlinear ordinary differential equations. The energy distribution of the system is studied by considering combinations of different vibration modes. The effect of the conjugate modes participation on the energy distribution is analysed.

2013 - Nonlinear vibrations and energy distribution of carbon nanotubes [Relazione in Atti di Convegno]
Andrisano, Angelo Oreste; Manevitch, Leonid I.; Pellicano, Francesco; Strozzi, Matteo
abstract

The nonlinear vibrations of Single-Walled Carbon Nanotubes are analysed. The Sanders-Koiter thin shell theory is applied in order to obtain the elastic strain and kinetic energy. The carbon nanotube deformation is described in terms of axial, circumferential and radial displacement fields. The theory considers geometric nonlinearities due to large amplitude of vibration. The displacement fields are expanded by means of a double series based on harmonic functions for the circumferential variable and Chebyshev polynomials for the longitudinal variable. The Rayleigh-Ritz method is applied to obtain approximate natural frequencies and mode shapes. Free boundary conditions are considered. In the nonlinear analysis, the three displacement fields are re-expanded by using approximate eigenfunctions. An energy approach based on the Lagrange equations is then considered to obtain a set of nonlinear ordinary differential equations. The total energy distribution of the shell is studied by considering combinations of different vibration modes. The effect of the conjugate modes is analysed.

2013 - Nonlinear vibrations and energy distribution of carbon nanotubes [Capitolo/Saggio]
Strozzi, Matteo; Manevitch, Leonid I.; Pellicano, Francesco; Smirnov, Valeri V.; Shepelev, Denis S.
abstract

The nonlinear vibrations of Single-Walled Carbon Nanotubes are analysed. The Sanders-Koiter elastic shell theory is applied in order to obtain the elastic strain energy and kinetic energy. The carbon nanotube deformation is described in terms of longitudinal, circumferential and radial displacement fields. The theory considers geometric nonlinearities due to large amplitude of vibration. The displacement fields are expanded by means of a double series based on harmonic functions for the circumferential variable and Chebyshev polynomials for the longitudinal variable. The Rayleigh-Ritz method is applied to obtain approximate natural frequencies and mode shapes. Free boundary conditions are considered. In the nonlinear analysis, the three displacement fields are re-expanded by using approximate eigenfunctions. An energy approach based on the Lagrange equations is considered in order to obtain a set of nonlinear ordinary differential equations. The total energy distribution of the shell is studied by considering combinations of different vibration modes. The effect of the conjugate modes participation is analysed.

2013 - Nonlinear vibrations of functionally graded circular cylindrical shells subjected to harmonic external load [Relazione in Atti di Convegno]
Strozzi, Matteo; Pellicano, Francesco
abstract

The nonlinear vibrations of functionally graded (FGM) circular cylindrical shells are analysed. The Sanders-Koiter theory is applied in order to model the nonlinear dynamics of the system. The shell deformation is described in terms of longitudinal, circumferential and radial displacement fields. Simply supported boundary conditions are considered. The displacement fields are expanded by means of a double mixed series based on Chebyshev polynomials for the longitudinal variable and harmonic functions for the circumferential variable. Both driven and companion modes are considered. Numerical analyses are carried out in order to characterize the nonlinear response when the shell is subjected to a harmonic external load. A convergence analysis is carried out to obtain the correct number of axisymmetric and asymmetric modes describing the actual nonlinear behaviour. The influence of the material distribution on the nonlinear response is analysed considering different configurations and volume fractions of the constituent materials. The effect of the companion mode participation on the nonlinear response of the shell is analysed.

2013 - Nonlinear vibrations of functionally graded cylindrical shells [Articolo su rivista]
Strozzi, Matteo; Pellicano, Francesco
abstract

In this paper, the nonlinear vibrations of functionally graded (FGM) circular cylindrical shells are analysed. The Sanders–Koiter theory is applied to model the nonlinear dynamics of the system in the case of finite amplitude of vibration. The shell deformation is described in terms of longitudinal, circumferential and radial displacement fields. Simply supported, clamped and free boundary condi- tions are considered. The displacement fields are expanded by means of a double mixed series based on Chebyshev orthogonal polynomials for the longitudinal variable and harmonic functions for the circumferential variable. Both driven and companion modes are considered; this allows the travelling- wave response of the shell to be modelled. The model is validated in the linear field by means of data retrieved from the pertinent literature. Numerical analyses are carried out in order to characterise the nonlinear response when the shell is subjected to a harmonic external load; a convergence analysis is carried out by considering a variety of axisymmetric and asymmetric modes. The present study is focused on determining the nonlinear character of the shell dynamics as the geometry (thickness, radius, length) and material properties (constituent volume fractions and configurations of the constituent materials) vary.

2013 - Performances of Nonlinear Vibration Absorbers for Beams subjected to Moving Loads [Articolo su rivista]
F. S., Samani; Pellicano, Francesco; Masoumi, Asma
abstract

The goal of this work is a general assessment regarding the performances of linear and nonlinear dynamic vibration absorbers (DVAs) applied to the specific problem of moving loads or vehicles. The problem consists of a simply supported linear Euler-Bernoulli beam excited with a moving load/vehicle; a DVA is connected to the beam in order to reduce the vibrations. The moving vehicle is modeled by a single degree of freedom mass spring system. The partial differential equations governing the beam dynamics is reduced to a set of ordinary differential equations by means of the Bubnov-Galerkin method. A parametric analysis is carried out to find the optimal parameters of the DVA that minimize the maximum vibration amplitude of the beam. For the case of a moving vehicle, the energy absorbed by the DVA is evaluated. Comparisons among the performances of different types of linear and DVAs are carried out. The goal is to clarify if the use of nonlinearities in the DVAs can effectively improve their performances. The study shows that the most effective type of DVA for the test cases considered is the piecewise linear elastic restoring force.

2013 - Simplified modeling technique for damping materials on light structures: Experimental analysis and numerical tuning [Relazione in Atti di Convegno]
Splendi, Luca; D'Agostino, Luca; Baldini, Andrea; Castignani, Luca; Pellicano, Francesco; Pinelli, Marco
abstract

Specific polymeric and asphaltic materials are widely used for NVH automotive applications. If patches of such materials are properly collocated on vehicle's panels, they are able to improve significantly noise and vibration performance by modulating damping and stiffness. This work presents a methodology for tuning a FE composite model, using optimization techniques to improve the correlation with the experimental modal tests performed. In particular, plain and ribbed aluminum plates have been considered for several covering ratios of three damping materials. The correlation between numerical and experimental data is achieved by monitoring dynamic parameters such as natural frequencies, mode shapes, and frequency response functions (FRFs). The optimization strategy consists of two steps and makes use of evolutionary and gradient-based algorithms. LMS Virtual.Lab® is used in this part of the work as an environment for correlation and optimization. In order to verify the reliability of the correlation, modal tests are performed on a particular vehicle's panel. Copyright © 2013 by ASME.

2013 - Vibrations of Carbon Nanotubes: nonlinear models and energy distribution [Relazione in Atti di Convegno]
Pellicano, Francesco; Strozzi, Matteo; Manevitch, Leonid I.
abstract

Vibrations of Single-Walled Carbon Nanotubes for various boundary conditions are considered in the framework of the Sanders-Koiter thin shell theory. A double series expansion of displacement fields, based on the Chebyshev orthogonal polynomials and harmonic functions, is used to analyse numerically the natural frequencies of shells having free or clamped edges. A reduced form of the Sanders-Koiter theory is developed by assuming small circumferential and shear deformations; such approach allows to determine an analytical solution for the natural frequencies. The numerical model is validated with the results of molecular dynamics and finite element analyses present in literature. The analytical model is validated by means of comparisons with the numerical approach. Nonlinear vibrations and energy distribution of carbon nanotubes are then considered.

2012 - Corrigendum to: Optimum profile modifications of spur gears by means of genetic algorithms [Articolo su rivista]
Barbieri, Marco; Bonori, Giorgio; Pellicano, Francesco
abstract

The purpose of the present work is to correct some inaccuracies of the paper "Bonori, G., Barbieri, M., Pellicano, F., 2008, Optimum Profile Modifications of Spur Gears by Means of Genetic Algorithms, Journal of Sound and Vibration, 313, pp. 603-616"; in that work, the aim was the reduction of vibrations in spur gears by means of profile modifications. This goal was achieved by using an ad hoc genetic algorithm, where the objective function was the peak to peak or the harmonic content of the Static Transmission Error (STE) computed by Finite Element calculations.The efficiency in terms of vibration reduction of the optimized profile reliefs was checked using a one degree of freedom dynamic model. This dynamic model considers time varying mesh stiffness, backlash, and profile error. In the original paper the effect of intentional profile modifications was considered as part of the mesh stiffness, thus overestimating their effect in vibration reduction.In the present corrigendum, the dynamic model is updated, keeping into account profile deviations by means of an error function. Finally, the optimal profile modifications found in the original paper are checked using the updated model.

2012 - Dynamic instability of circular cylindrical shells subject to base excitation [Relazione in Atti di Convegno]
Pellicano, F.
abstract

This paper is focused on the experimental and theoretical analysis of circular cylindrical shells subject to base excitation. The shell axis is vertical, it is clamped at the base and connected to a rigid body on the top; the base provides a vertical seismic-like excitation. The goal is to investigate the shell response when a resonant harmonic forcing is applied: the first axisymmetric mode is excited around the resonance at relatively low frequency and low amplitude of excitation. A violent resonant phenomenon is experimentally observed as well as an interesting saturation phenomenon close to the previously mentioned resonance. A theoretical model is developed to reproduce the experimental evidence and provide an explanation of the complex dynamics observed experimentally; the model takes into account geometric shell nonlinearities, electro-dynamic shaker equations and the shell shaker interaction. © Civil-Comp Press, 2012.

2012 - Experimental Study on Prestressed Circular Cylindrical Shell [Relazione in Atti di Convegno]
Zippo, Antonio; Barbieri, Marco; Strozzi, Matteo; Errede, Vito; Pellicano, Francesco
abstract

In this paper an experimental study on circular cylindrical shells subjected to axial compressive and periodic loads is presented. Even though many researchers have extensively studied nonlinear vibrations of cylindrical shells, experimental studies are rather limited in number. The experimental setup is explained and deeply described along with the analysis of preliminary results. The linear and the nonlinear dynamic behavior associated with a combined effect of compressive static and a periodic axial load have been investigated for different combinations of loads; moreover, a non stationary response of the structure has been observed close to one of the resonances. The linear shell behavior is also investigated by means of a finite element model, in order to enhance the comprehension of experimental results.

2012 - Fluid-structure interaction in EHD lubricated contacts close to the elastic resonance [Relazione in Atti di Convegno]
Barbieri, Marco; Pellicano, Francesco
abstract

Elasto-hydrodynamical lubrication is governed by a set of non-linear integro-differential equa- tions describing the coupling between fluid properties in a thin lubricant film and elastic defor- mations in contacting bodies. In the present paper, the non-stationary behavior of an elliptic lubricated contact in Elasto-hydrodynamical lubrication regime is investigated. Non-linear contacts in gear pairs are considered as a case study: a comparison between dry contact and lubricated contact is drawn. The lubrication conditions close to the main resonance of the linearized elastic system are pointed out. The multilevel technique is used to solve the EHD lubrication problem, together with the equation describing the relative motion of the mating gears.

2012 - Linear and nonlinear dynamics of a circular cylindrical shell under static and periodic axial load [Relazione in Atti di Convegno]
Zippo, Antonio; Barbieri, Marco; Strozzi, Matteo; Errede, Vito; Pellicano, Francesco
abstract

In this paper an experimental study on circular cylindrical shells subjected to axial compres- sive and periodic loads is presented. The setting of the experiment is explained and deeply described along with a complete analysis of the results. The linear and the nonlinear dynamic behaviour associated with a combined effect of compressive static and a periodic axial load has been considered and a chaotic response of the structure has been observed close to the resonance. The linear shell behaviour is also investigated by means of a theoretical and finite element model, in order to enhance the comprehension of experimental results, i.e. the natural frequencies of the system and their ratios.

2012 - Nonlinear vibrations of functionally graded cylindrical shells: Effect of companion mode participation [Relazione in Atti di Convegno]
Strozzi, Matteo; Pellicano, Francesco
abstract

In this paper, the nonlinear vibrations of functionally graded (FGM) circular cylindrical shells are analyzed. The Sanders-Koiter theory is applied to model the nonlinear dynamics of the system in the case of finite amplitude of vibration. The shell deformation is described in terms of longitudinal, circumferential and radial displacement fields. Simply supported boundary conditions are considered. The displacement fields are expanded by means of a double mixed series based on Chebyshev orthogonal polynomials for the longitudinal variable and harmonic functions for the circumferential variable. Both driven and companion modes are considered, allowing for the travelling-wave response of the shell. Numerical analyses are carried out in order to characterize the nonlinear response when the shell is subjected to an harmonic external load. A convergence analysis is carried out to obtain the correct number of axisymmetric and asymmetric modes describing the actual nonlinear behavior of the shells. The effect of the geometry on the nonlinear vibrations of the shells is analyzed, and a comparison of nonlinear amplitude-frequency curves of cylindrical shells with different geometries is carried out. The influence of the companion mode participation on the nonlinear response of the shells is analyzed; frequency-response curves with companion mode participation (i.e. the actual response of the shell) are obtained. The present model is validated in the linear field (natural frequencies) by means of data present in the literature.

2012 - Nonlinear vibrations of functionally graded cylindrical shells: Effect of the geometry [Relazione in Atti di Convegno]
Strozzi, Matteo; Pellicano, Francesco; Zippo, Antonio
abstract

In this paper, the effect of the geometry on the nonlinear vibrations of functionally graded (FGM) cylindrical shells is analyzed. The Sanders-Koiter theory is applied to model the nonlinear dynamics of the system in the case of finite amplitude of vibration. The shell deformation is described in terms of longitudinal, circumferential and radial displacement fields. Simply supported boundary conditions are considered. The displacement fields are expanded by means of a double mixed series based on harmonic functions for the circumferential variable and Chebyshev polynomials for the longitudinal variable. In the linear analysis, after spatial discretization, mass and stiff matrices are computed, natural frequencies and mode shapes of the shell are obtained. In the nonlinear analysis, the three displacement fields are re-expanded by using approximate eigenfunctions obtained by the linear analysis; specific modes are selected. The Lagrange equations reduce nonlinear partial differential equations to a set of ordinary differential equations. Numerical analyses are carried out in order to characterize the nonlinear response of the shell. A convergence analysis is carried out to determine the correct number of the modes to be used. The analysis is focused on determining the nonlinear character of the response as the geometry of the shell varies.

2012 - Nonlinear vibrations of functionally graded cylindrical shells: effect of the companion mode participation [Relazione in Atti di Convegno]
Andrisano, Angelo Oreste; Pellicano, Francesco; Strozzi, Matteo
abstract

In this paper, the effect of the companion mode participation on the nonlinear vibrations of functionally graded (FGM) cylindrical shells is analyzed. The Sanders-Koiter theory is applied to model the nonlinear dynamics of the system in the case of finite amplitude of vibration. The shell deformation is described in terms of longitudinal, circumferential and radial displacement fields. Simply supported boundary conditions are considered. The displacement fields are expanded by means of a double mixed series based on Chebyshev polynomials for the longitudinal variable and harmonic functions for the circumferential variable. Both driven and companion modes are considered. Numerical analyses are carried out in order to characterize the nonlinear response when the shell is subjected to an harmonic external load. A convergence analysis is carried out by considering a different number of axisymmetric and asymmetric modes. The present study is focused on modelling the nonlinear travelling-wave response of the shell in the circumferential direction with the companion mode participation.

2012 - Vibration reduction of beams under successive traveling loads by means of linear and nonlinear dynamic absorbers [Articolo su rivista]
F. S., Samani; Pellicano, Francesco
abstract

The goal of the present work is to assess the performances of dynamic vibration absorbers (DVA) in suppressing the vibrations of a simply supported beam subjected to an infinite sequence of regularly spaced concentrated moving loads. In particular, several types of DVA are considered: linear, cubic, higher odd-order monomials and piecewise linear stiffness; linear, cubic and linear-quadratic viscous damping. The purpose is to clarify if nonlinear DVAs show improvements with respect to the classical linear devices.The dynamic scenario is deeply investigated in a wide range of operating conditions, spanning the parameter space of the DVA (damping, stiffness). Nonlinear stiffness can lead to complex dynamics such as quasi-periodic, chaotic and sub-harmonic responses; moreover, acting on the stiffness nonlinearity no improvement is found with respect to the linear DVA. A nonlinear non-symmetric dissipation in the DVA leads to a great reduction of the beam response, the reduction is larger with respect to the linear DVA.

2011 - 3D Nonlinear Finite Element Modeling of Helical Gears [Relazione in Atti di Convegno]
Zippo, Antonio; Barbieri, Marco; Pellicano, Francesco
abstract

A method for carrying out the Loaded Tooth Contact Analysis (LTCA) of helical gear pairs is described in this paper. Gear profiles are obtained by means of numerical simulation of the cutting process and an accurate description is provided in terms of NURBS curves or surfaces.The minimum number of parameters needed to describe accurately the profile in presence of tip and root reliefs, helix modification and crowning is discussed. Some cases are presented and discussed.

2011 - Adaptive Grid-Size Modelling of Helical Gear Pairs [Relazione in Atti di Convegno]
Barbieri, Marco; Zippo, Antonio; Pellicano, Francesco
abstract

Amethod for solving the contact problem in a generic helical gear pair (either external or internal) is described. Gear profiles are obtained by means of numerical simulation of the cutting process and an accurate description is provided in terms of NURBS curves or surfaces. The minimum number of parameters needed to describe accurately the profile in presence of tip and root reliefs, helix modification and crowning is discussed. A reference structured grid is defined on the tooth, then refinement criteria are discussed in order to obtain accurate solutions in terms of tooth deflection, contact pressure and fillet stress. A comparison with other approaches is given.

2011 - Dynamic Optimization of Spur Gears [Articolo su rivista]
M., Faggioni; F. S., Samani; G., Bertacchi; Pellicano, Francesco
abstract

This paper presents a global optimization method focused on gear vibration reduction by means of profile modifications. A nonlinear dynamic model is used to study the vibration behavior; such model is validated using data available in literature. The optimization method considers different regimes and torque levels; the objective function can be the static transmission error or the maximum amplitude of the gear vibration in terms of dynamic transmission error. The procedure finds the optimal profile modification that reduces the vibrations over a wide range of operating conditions. In order to reduce the computational cost, a Random–Simplex optimization algorithm is developed; the optimum reliability is estimated using a Monte Carlo simulation. The approach shows good performances for the computational efficiency as well as the reliability of results. Finally, an application to High Contact Ratio (HCR) gears is presented and an extremely good performance is obtained by combining optimization procedures and HCR properties.

2011 - Dynamic instability of a circular cylindrical shell carrying a top mass under base excitation: Experiments and theory [Articolo su rivista]
Pellicano, Francesco
abstract

The present paper is focused on the experimental and theoretical analysis of circular cylindrical shells under base excitation. The shell axis is vertical, it is clamped at the base and connected to a rigid body on the top; the base provides a vertical seismic-like excitation. The goal is to investigate the shell response when a resonant harmonic forcing is applied: the first axisymmetric mode is excited around the resonance at relatively low frequency and low amplitude of excitation. A violent resonant phenom- enon is experimentally observed as well as an interesting saturation phenomenon close to the previously mentioned resonance. A theoretical model is developed to reproduce the experimental evidence and pro- vide an explanation of the complex dynamics observed experimentally; the model takes into account geometric shell nonlinearities, electrodynamic shaker equations and the shell shaker interaction.

2011 - Effect of the boundary conditions on the vibrations of functionally graded shells [Relazione in Atti di Convegno]
Andrisano, Angelo Oreste; Pellicano, Francesco; Strozzi, Matteo
abstract

In this paper, the effect of the boundary conditions on the nonlinear vibration of functionally graded circular cylindrical shells is analyzed. The Sanders-Koiter theory is applied to model the nonlinear dynamics of the system in the case of finite amplitude of vibration. The shell deformation is described in terms of longitudinal, circumferential and radial displacement fields. Numerical analyses are carried out in order to characterize the nonlinear response when the shell is subjected to an harmonic external load; different geometries and material distributions are considered. A convergence analysis is carried out in order to determine the correct number of the modes to be used; the role of the axisymmetric and asymmetric modes is carefully analyzed. The effect of the geometry on the nonlinear response is investigated; i.e. thickness and radius are varied; simply supported, clamped-clamped and free-free shells are considered. The effect of the constituent volume fractions and the configurations of the constituent materials on the natural frequencies and nonlinear response are studied.

2011 - Effect of the geometry on the nonlinear vibrations of functionally graded cylindrical shells [Relazione in Atti di Convegno]
Pellicano, Francesco; Strozzi, Matteo; Zippo, Antonio
abstract

In this paper, the effect of the geometry on the nonlinear vibrations of functionally graded (FGM) cylindrical shells is analyzed. The Sanders-Koiter theory is applied to model nonlinear dynamics of the system in the case of finite amplitude of vibration. Shell deformation is described in terms of longitudinal, circumferential and radial displacement fields; the theory considers geometric nonlinearities due to the large amplitude of vibration. Simply supported boundary conditions are considered. The displacement fields are expanded by means of a double mixed series based on harmonic functions for the circumferential variable and Chebyshev polynomials for the longitudinal variable. Both driven and companion modes are considered, allowing for the travelling-wave response of the shell. The functionally graded material is made of a uniform distribution of stainless steel and nickel, the material properties are graded in the thickness direction, according to a volume fraction power-law distribution.The first step of the procedure is the linear analysis, i.e. after spatial discretization mass and stiff matrices are computed and natural frequencies and mode shapes of the shell are obtained, the latter are represented by analytical continuous functions defined over all the shell domain. In the nonlinear model, the shell is subjected to an external harmonic radial excitation, close to the resonance of a shell mode, it induces nonlinear behaviors due to large amplitude of vibration. The three displacement fields are re-expanded by using approximate eigenfunctions, which were obtained by the linear analysis; specific modes are selected. An energy approach based on the Lagrange equations is considered, in order to reduce the nonlinear partial differential equations to a set of ordinary differential equations.Numerical analyses are carried out in order characterize the nonlinear response, considering different geometries and material distribution. A convergence analysis is carried out in order to determine the correct number of the modes to be used; the role of the axisymmetric and asymmetric modes carefully analyzed. The analysis is focused on determining the nonlinear character of the response as the geometry (thickness, radius, length) and material properties (power-law exponent and configurations of the constituent materials) vary; in particular, the effect of the constituent volume fractions and the configurations of the constituent materials on the natural frequencies and nonlinear response are studied.Results are validated using data available in literature, i.e. linear natural frequencies.

2011 - Energy dissipation in EHL Film in Gear Lubrication [Relazione in Atti di Convegno]
Barbieri, Marco; Pellicano, Francesco
abstract

A characterization of the energy dissipation of the lubricant film between mating teeth in gear pairs is proposed. The film fluid is modeled using the fully flooded elastohydrodynamical point contact and the solution is found by means of a numerical multilevel solver. Some comparison with other solutions proposed in the literature for the line contact problem are drawn to validate the proposed approach. In order to understand the effect of the lubricant film on the vibration of the gear pair, it is important to describe both the stiffness of the film and the viscous energy dissipation: in the present paper, some initial results about this problem are presented.

2011 - Nonlinear vibration of functionally graded cylindrical shells: effect of constituent volume fractions and configurations [Relazione in Atti di Convegno]
Strozzi, Matteo; Pellicano, Francesco
abstract

In this paper, the nonlinear vibration of functionally graded (FGM) cylindrical shells under different constituent volume fractions and configurations is analyzed. The Sanders-Koiter theory is applied to model nonlinear dynamics of the system in the case of finite amplitude of vibration. The shell deformation is described in terms of longitudinal, circumferential and radial displacement fields. Simply supported boundary conditions are considered. Displacement fields are expanded by means of a double mixed series based on harmonic functions for the circumferential variable and Chebyshev polynomials for the longitudinal variable. Both driven and companion modes are also considered, allowing for the travelling-wave response of the shell. The functionally graded material considered is made of stainless steel and nickel, properties are graded in the thickness direction according to a real volume fraction power-law distribution. In the nonlinear model, shells are subjected to an external radial excitation. Nonlinear vibrations due to large amplitude of excitation are considered. Specific modes are selected in the modal expansions; a dynamical nonlinear system is then obtained. Lagrange equations are used to reduce nonlinear partial differential equations to a set of ordinary differential equations, from the potential and kinetic energies, and the virtual work of the external forces. Different geometries are analyzed; amplitude-frequency curves are obtained. Convergence tests are carried out considering a different number of asymmetric and axisymmetric modes. The present model is validated in linear field (natural frequencies) by means of data present in the literature.

2011 - Nonlinear vibrations of functionally graded circular cylindrical shells [Relazione in Atti di Convegno]
Strozzi, Matteo; Pellicano, Francesco; Zippo, Antonio
abstract

In this paper, the effect of the geometry on the nonlinear vibrations of functionally graded cy- lindrical shells is analyzed. The Sanders-Koiter theory is applied to model nonlinear dynamics of the system in the case of finite amplitude of vibration. Shell deformation is described in terms of longitudinal, circumferential and radial displacement fields. Simply supported boundary conditions are considered. Numerical analyses are carried out in order to characterize the nonlinear response when the shell is subjected to an harmonic external load; different geometries and material distribu- tions are considered. A convergence analysis is carried out in order to determine the correct number of the modes to be used; the role of the axisymmetric and asymmetric modes is carefully analyzed. The analysis is focused on determining the nonlinear character of the response as the geometry (thickness, radius, length) and material properties (power-law exponent N and configurations of the constituent materials) vary. The effect of the constituent volume fractions and the configurations of the constituent materials on the natural frequencies and nonlinear response are studied.

2010 - Coupling of two EHL-lubricated contacts in gear dynamics [Relazione in Atti di Convegno]
Barbieri, Marco; Pellicano, Francesco
abstract

In this paper, the effect of vibrations on the elastohydrodynamical lubrication in spur gear pairs will be described. The relevance of inertial effects on film fluid lubrication is clarified by means of comparisons with static formulations. The multilevel technique is used to solve the transient EHL problem for elliptical contacts. Coupling with load balance equation and with different equations of motion is studied. A new model describing the dynamic behavior of two coupled transient EHL elliptical contacts is developed and applied to characterize the dynamics of a spur gear pair.

2010 - Dynamic instabilities of circular cylindrical shells subjected to seismic excitations [Relazione in Atti di Convegno]
Pellicano, F.
abstract

The present paper is focused on the dynamic analysis of circular cylindrical shells under seismic excitation: the excitation direction is the cylinder axis, the shell is clamped at the base and connected to a rigid body on the top, the base provides the seismic excitation which is supposed sinusoidal. The goal is to investigate the shell response when a resonant forcing is applied: the first axisymmetric mode is excited around the resonance at relatively low frequency and low amplitude excitation. A violent resonant phenomenon is experimentally observed as well as an interesting saturation phenomenon close to the previously mentioned resonance. A theoretical model is developed to reproduce the experimental evidence and provide an explanation of the complex dynamics observed experimentally.

2010 - Imperfection sensitivity of compressed circular cylindrical shells under periodic axial loads [Relazione in Atti di Convegno]
Pellicano, F.
abstract

In the present paper the dynamic stability of circular cylindrical shells is investigated; the combined effect of compressive static and periodic axial loads is considered. The Sanders-Koiter theory is applied to model the nonlinear dynamics of the system in the case of finite amplitude of vibration; Lagrange equations are used to reduce the nonlinear partial differential equations to a set of ordinary differential equations. The dynamic stability is investigated using direct numerical simulation and a dichotomic algorithm to find the instability boundaries as the excitation frequency is varied; the effect of geometric imperfections is investigated in detail. The accuracy of the approach is checked by means of comparisons with the literature. Copyright © 2010 by ASME.

2010 - Influence of dynamic effects on point EHL contacts in gear systems [Relazione in Atti di Convegno]
Barbieri, Marco; Pellicano, Francesco
abstract

In this paper, the effect of vibrations in elastohydrodynamical lubrication of spur gear pairs will be described. The relevance of inertial effects in the contacting bodies on film fluid lubrication will be clarified with comparisons to static formulations. A new model describing the dynamic behavior of two coupled transient EHL elliptical contacts will be presented and applied to characterize the dynamics of a spur gear pair.

2009 - Dynamic stability and sensitivity to geometric imperfections of strongly compressed circular cylindrical shells under dynamic axial loads [Articolo su rivista]
Pellicano, Francesco
abstract

In the present paper, the dynamic stability of circular cylindrical shells is investigated; thecombined effect of compressive static and periodic axial loads is considered. The Sanders–Koiter theory is applied to model the nonlinear dynamics of the system in the case of finiteamplitude of vibration; Lagrange equations are used to reduce the nonlinear partial differentialequations to a set of ordinary differential equations. The dynamic stability is investigatedusing direct numerical simulation and a dichotomic algorithm to find the instabilityboundaries as the excitation frequency is varied; the effect of geometric imperfections isinvestigated in detail. The accuracy of the approach is checked by means of comparisonswith the literature.

2009 - Spur gear vibration mitigation by means of energy pumping [Relazione in Atti di Convegno]
Scagliarini, G.; Viguie, R.; Kerschen, G.; Pellicano, F.
abstract

The dynamic behavior of a spur gear pair can be studied in terms of transmission error considering a single degree of freedom system. Thus, a mechanical system exhibiting combined parametric excitation and clearance type nonlinearity is examined by means of numerical integrations and continuation methods in an effort to explain its complex behaviour, as it is commonly observed in the steady state forced response of rotating machines. The specific case of a preloaded mechanical oscillator having a periodically time varying stiffness function and subject to a symmetric backlash condition is considered. Even if such an oscillator represents the simplest model able to analyze a single spur gear pair, it exhibits complex dynamic phenomena, including jumps, superharmonics, subharmonic resonances and dynamic bifurcations. In order to reduce the vibration of the system, a nonlinear absorber is applied. Unlike common linear and weakly nonlinear systems, systems with strongly nonlinear elements are able to react efficiently on the amplitude characteristics of the external forcing in a wide range of frequencies. A strongly and essentially nonlinear, lightweight, with cubic stiffness oscillator is then attached to the main nonlinear system under periodic parametric forcing and the performance of this nonlinear energy sink (NES) for vibration mitigation is investigated. © 2009 Society for Experimental Mechanics Inc.

2009 - Vibration reduction on beams subjected to moving loads using linear and nonlinear dynamic absorbers [Articolo su rivista]
F. S., Samani; Pellicano, Francesco
abstract

The present work is focused on the analysis of the effectiveness of dynamic vibrationabsorbers applied to beams excited by moving loads. The goal is to test the performanceof nonlinear dampers in comparison with the classical linear damper. Simply supportedbeams are analysed using the Euler–Bernoulli theory, the partial differential equationgoverning the beam dynamics are reduced to an ordinary differential equation set bymeans of the Galerkin–Bubnov method, and a multimode expansion of the displacementfield allows accurate analysis of the problem. The performance of the dynamicdampers in vibration reduction is estimated through two indicators, the maximumamplitude of vibration, and the portion of energy dissipated by the dynamic damper.The same indicators are used as objective functions for developing an optimisationapproach. Two conservation laws are found for the optimal parameters and beamgeometry for nonlinear (cubic) dynamic dampers.

2008 - Francesco Pellicano è Editore Associato Rivista Internazionale:"Mathematical Problems in Engineering" [Direzione o Responsabilità Riviste]
Jose Manoel, Balthazar; Pellicano, Francesco
abstract

2008 - Optimization Methods for Spur Gear Dynamics [Relazione in Atti di Convegno]
Barbieri, Marco; Scagliarini, Giorgio; Bonori, Giorgio; Pellicano, Francesco; Bertacchi, Gabriele
abstract

In the present paper two different approaches for spurgear noise reduction using micro-geometrical modifi-cations are compared. The two approaches are basedrespectively on the reduction of Static TransmissionError (STE) and Dynamic Transmission Error (DTE)fluctuations. The dynamic behaviour of the system iscomputed through a simple lumped parameter model.A genetic algorithm is proposed to find the best solu-tions inside the parameters space because the evalua-tion of the objective functions requires finite elementscalculations and numerical ODE integrations. A relia-bility analysis is afterwards performed to evaluate theeffect of manufacturing errors on the dynamic perfor-mance of the achieved optimum.

2008 - Optimum Profile Modifications of Spur Gears by Means of Genetic Algorithms [Articolo su rivista]
Bonori, Giorgio; Barbieri, Marco; Pellicano, Francesco
abstract

An original application of Genetic Algorithms (GAs) is developed in order to optimize spur gear pairs toward vibrationand noise reduction. The approach takes into account the most important parameters of micro-geometric modifications,namely tip and root relief, therefore the parameter space is eight dimensional. The objective function of the GA depends onthe static transmission error (STE) that is related to teeth flexibility. STE is estimated by means of a nonlinear finite elementapproach: either the amplitude of the STE fluctuation or its harmonic content are considered as objective functions.The effectiveness of the approach is checked on an actual test case: GAs are able to find the optimum after a reasonablenumber of steps; such optimum is obtained on static basis and gives a strong vibration reduction. The reliability test provesthat GAs lead to robust optima.

2007 - Dynamic optimization of spur gears [Relazione in Atti di Convegno]
Faggioni, Marcello; Pellicano, Francesco; Bertacchi, Gabriele; Andrisano, Angelo Oreste
abstract

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2007 - Dynamic optimization of spur gears [Relazione in Atti di Convegno]
Faggioni, Marcello; Pellicano, Francesco; Andrisano, Angelo Oreste; Bertacchi, Gabriele
abstract

This paper presents a global optimization method able to find gear profile modifications that minimize vibrations. A non linear dynamic model is used to study the vibrational behavior; the dynamic model is validated using data available in literature. The optimization method takes into account the influence of torque levels both on the static and the dynamic response. Therefore, two different objective functions are considered; the first one is based on static analysis and the second one is based on the dynamic behavior of a lumped mass system. The procedure can find the optimal profile modification that reduce the vibrations over a wide range of operating conditions. In order to reduce the computational cost, a Random-Simplex optimization algorithm is developed; the optimum reliability is also estimated using a Monte Carlo simulation. The approach shows good performances both for the computational efficiency and the reliability of results.

2007 - Linear and nonlinear dynamics of a circular cylindrical shell connected to a rigid disk [Articolo su rivista]
Pellicano, Francesco; Avramov, K. V.
abstract

The dynamics of a circular cylindrical shell carrying a rigid disk on the top and clamped at the base is investigated.The Sanders–Koiter theory is considered to develop a nonlinear analytical model for moderately largeshell vibration. A reduced order dynamical system is obtained using Lagrange equations: radial and in-planedisplacement fields are expanded by using trial functions that respect the geometric boundary conditions.The theoretical model is compared with experiments and with a finite element model developed withcommercial software: comparisons are carried out on linear dynamics.The dynamic stability of the system is studied, when a periodic vertical motion of the base is imposed.Both a perturbation approach and a direct numerical technique are used. The perturbation method allowsto obtain instability boundaries by means of elementary formulae; the numerical approach allows to performa complete analysis of the linear and nonlinear response.

2007 - NON-SMOOTH DYNAMICS OF SPUR GEARS WITH MANUFACTURING ERRORS [Articolo su rivista]
Bonori, G; Pellicano, Francesco
abstract

This paper presents a method for analysing nonlinear vibrations of spur gears in presence of manufacturing errors. Theapproach is based upon the classical one-degree-of-freedom model, with backlash and time varying stiffness.Manufacturing errors are treated stochastically, starting from the knowledge of the gear tolerance class. A randomprofile error distribution is given for each tooth; then teeth errors are combined in order to span all possible reciprocalteeth contacts. The result is an analytical forcing, in terms of transmission error, which includes statistically the effect oflocal errors. Finally, a full dynamic analysis is carried out in the case of perfect and imperfect gears, in order to show theeffect of profile errors and their variance on the gear vibration.

2007 - VIBRATIONS OF CIRCULAR CYLINDRICAL SHELLS: THEORY AND EXPERIMENTS [Articolo su rivista]
Pellicano, Francesco
abstract

In the present paper, a method for analysing linear and nonlinear vibrations of circular cylindrical shells having differentboundary conditions is presented; the method is based on the Sanders–Koiter theory. Displacement fields are expanded ina mixed double series based on harmonic functions and Chebyshev polynomials. Simply supported and clamped–clampedboundary conditions are analysed, as well as connections with rigid bodies; in the latter case experiments are carried out.Comparisons with experiments and finite-element analyses show that the technique is computationally efficient andaccurate in modelling linear vibrations of shells with different boundary conditions.An application to large amplitude of vibration shows that the technique is effective also in the case of nonlinearvibration: comparisons with the literature confirm the accuracy of the approach.The method proposed is a general framework suitable for analysing vibration of circular cylindrical shells both in thecase of linear and nonlinear vibrations.

2006 - Dynamic instability and chaos of empty and fluid-filled circular cylindrical shells under periodic axial loads [Articolo su rivista]
Pellicano, Francesco; M., Amabili
abstract

In the present paper the dynamic stability of circular cylindrical shells subjected to static and dynamic axial loads is investigated. Both Donnell´s nonlinear shallow shell and Sanders-Koiter shell theories have been applied to model finite-amplitude static and dynamic deformations. Results are compared in order to evaluate the accuracy of these theories in predicting instability onset and post-critical nonlinear response. The effect of a contained fluid on the stability and the post-critical behaviour is analyzed in detail. Geometric imperfections are considered and their influence on the dynamic instability and post-critical behaviour is investigated. Chaotic dynamics of pre-compressed shells is investigated by means of nonlinear time-series techniques, extracting correlation dimension and Lyapunov exponents.

2006 - Dynamical instability of cylindrical shell with big mass at the end [Articolo su rivista]
K. V., Avramov; Pellicano, Francesco
abstract

Parametric oscillations of cylindrical shell with big disk at the end are considered. TheSanders- Koiter shell theory is used to model the geometrically nonlinear shelloscillations. The multiple scales method is used to study the system of oscillationsdifferential equations.

2006 - Improved method of sea level forecasting at Venice (Northern Adriatic Sea) [Articolo su rivista]
Petaccia, S.; Serravall, R.; Pellicano, Francesco
abstract

In this paper a forecasting method for the extremely dangerous aqua alta phenomenon is developed. Thecity of Venice, which is located in the northeastern part of Italy, is often subjected to intense flooding, dueto increasing of the sea level. The classical methods used in Geophysics generally failed in forecasting thisphenomenon, because of the complexity of the physical modelling. Therefore, a method based on a nonlinearauto-regressive moving average (ARMA) approach is proposed here. It is found that the time series,corresponding to the sea level data, present a Gaussian distribution, but during short periods, of order offew days, a strong non-Gaussian behaviour is evident, which is concomitant with aqua alta events. Thissuggests the development of a non-linear version of the usual ARMA models. An empirical orthogonalfunction technique is applied in order to avoid numerical pathologies of the model due to the particularcharacteristics of the time series. The encouraging results indicate that such technique is a good tool forforecasting and alarm purposes.

2006 - Vibration of gears: A global optimization approach [Relazione in Atti di Convegno]
Bonori, G.; Scagliarini, G.; Barbieri, M.; Pellicano, F.
abstract

The importance of studying dynamic aspects of gear transmissions has been well established since many years; however, recently a new interest on this topics grew up because of significant improvement in gear design technology. The literature can supply different approaches to evaluate the vibrations response of simple and complex gears system. Numerical and analytical methods can provide important information on resonances, non linear behaviours and combined dynamic interactions in existing systems. In particular the reduction of vibrations is strictly related to minimize the value of the peak to peak of the static transmission error in a mesh cycle, through modifications of the tooth profile. The present paper combines a numerical model to study spur gear pair dynamics, with a genetic optimization technique to define the best profile modification capable to reduce the vibration. The numerical model is able to take into account gear geometry, profile modifications and profile manufacturing errors. The genetic optimization routine can provide the best set of profile modification considering the peak to peak value of the static transmission error or a generic number of its harmonic components. In the last part of this work some testcases are investigated and the improvement in the dynamics is shown. © (2006) by the Katholieke Universiteit Leuven Department of Mechanical Engineering All rights reserved.

2006 - Vibrations of circular cylindrical shells with complex boundary conditions [Relazione in Atti di Convegno]
Pellicano, F.
abstract

In the present paper vibrations of circular cylindrical shells having different boundary conditions are analyzed. Sanders-Koiter theory is considered for shell modeling: both linear and nonlinear vibrations are analyzed. An energy approach based on Lagrange equations is considered; a mixed expansion of displacement fields, based on harmonic functions and Tchebyshev polynomials, is applied. Several boundary conditions are analyzed: simply supported, clamped-clamped, connection with rigid bodies. Comparisons with experiments and finite element analyses show that the technique is capable to model several and complex boundary conditions. Applications to geometrically nonlinear shells show that the technique is effective also in the case of nonlinear vibration: comparisons with the literature confirm the accuracy of the approach. Copyright © 2006 by ASME.

2006 - Vibrations of circular cylindrical shells with complex boundary conditions [Relazione in Atti di Convegno]
Pellicano, F.
abstract

In the present paper vibrations of circular cylindrical shells having different boundary conditions are analyzed. Sanders-Koiter theory is considered for shell modeling: both linear and nonlinear vibrations are analyzed. An energy approach based on Lagrange equations is considered; a mixed expansion of displacement fields, based on harmonic functions and Tchebyshev polynomials, is applied. Several boundary conditions are analyzed: simply supported, clamped-clamped, connection with rigid bodies. Comparisons with experiments and finite element analyses show that the technique is capable to model several and complex boundary conditions. Applications to geometrically nonlinear shells show that the technique is effective also in the case of nonlinear vibration: comparisons with the literature confirm the accuracy of the approach. Copyright © 2006 by ASME.

2005 - Dynamic instability of circular cylindrical shells [Relazione in Atti di Convegno]
Pellicano, F.; Amabili, M.
abstract

In the present paper the nonlinear dynamic stability of circular cylindrical shells subjected to dynamic axial loads is investigated. Both Donnell's nonlinear shallow shell and Sanders' theories have been applied in order to evaluate their accuracy. The effect of a contained fluid on the dynamic stability and the postcritical behaviour is analysed in detail. Chaotic dynamics of compressed shells are investigated by means of nonlinear time series techniques, extracting correlation dimension and Lyapunov exponents. © 2005 Elsevier Ltd.

2005 - Modellazione bidimensionale CAD FEM di coppie d’ingranaggi cilindrici [Relazione in Atti di Convegno]
Andrisano, Angelo Oreste; Bertacchi, Gabriele; Bonori, Giorgio; Faggioni, Marcello; Pellicano, Francesco; G., Amedei; P., Montanari; S., Seghedoni
abstract

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2005 - NONLINEAR OSCILLATIONS AND STABILITY OF GEAR PAIR [Articolo su rivista]
Faggioni, Marcello; K., Avramov; Pellicano, Francesco; S. N., Reshetnikova
abstract

Nonlinear oscilIations of gear pair are analyzed by means of a single-degree-oFfieedompiecewise linear time variant oscillator. The harmonic balance method and a continuationtechnique are used to study periodic motions. The dynamic scenario for an actual gear pair isanalyzed for which concern periodic oscillations.

2005 - On the dynamic properties of axially moving systems [Articolo su rivista]
Pellicano, Francesco
abstract

The objective of the present paper is a deep analysis of some recent numerical and experimental results regarding the complex dynamics of axially moving systems. Such important mechanical systems exhibit interesting dynamic behaviors: homoclinic orbits; sub-harmonic responses; amplitude modulations; and chaos. These dynamics have been obtained numerically and in some cases have been experimentally observed. Using recent techniques of the non-linear time series analysis, the response of axially moving systems has been studied for a large variety of test cases. The correlation dimension of the time series, which is deeply related to the minimal dimension of a system able to reproduce the dynamics, is estimated. Lyapunov exponents are evaluated in order to quantify the response regularity. The present work gives a contribution towards understanding the complex dynamics observed both in conservative and dissipative systems. The dynamical phenomena are analyzed within the unified framework of the non-linear time series analysis. In the case of experimental data the new non-linear filtering techniques, based on the embedding techniques, have been applied to reduce high noise when classical techniques give bad results.

2004 - Dynamics of gear meshing: stiffness evaluation and vibration [Relazione in Atti di Convegno]
Bonori, Giorgio; Andrisano, Angelo Oreste; Pellicano, Francesco
abstract

In the present paper we are concerned with vibration problems in gears mesh. A 2D model is developed,which is able to create the teeth profile for the contact profile and the tooth fillet for a very large classes of 2Dgears. A single degree of freedom model is developed using lumped masses. The stiffness of the gears is cal-culated using the finite element code (MSC MARC) from different meshing position of two identical gears,using contact elements for the teeth interaction. This approach allows to evaluate accurately the variableglobal stiffness, which depends on the gear position, materials and teeth geometry. The variable stiffnessgives rise to a parametric excitation, which is periodic; therefore it gives rise to a Mathieu type instability. AFourier series of the variable stiffness is obtained from the numerical data evaluated with the FEM model.The dynamic model is analyzed by means of direct simulations and ontinuation techniques; the latter one areable to follow periodic responses and detect instabilities and dynamic bifurcations.

2004 - Metodologie di indagine sul comportamento dinamico di ingranaggi [Relazione in Atti di Convegno]
Andrisano, Angelo Oreste; Pellicano, Francesco; Bonori, Giorgio; G., Amedei; P., Montanari; C., Seghedoni
abstract

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2004 - Nonlinear dynamics and stability of circular cylindrical shells [Relazione in Atti di Convegno]
Pellicano, F.; Catellani, G.; Amabili, M.
abstract

The nonlinear dynamic response of an imperfect circular cylindrical shell under combined static and dynamic axial load is analyzed. A suitable expansion of the radial displacement, able to describe both buckling and dynamic behaviors is developed; the effect of geometric imperfections is accounted for. The response of the shell subjected to a sinusoidal axial excitation at its ends, giving rise to a parametric excitation, is considered. The effect of the imperfections on the critical value of the dynamic load, that causes the loss of stability of the system, is analyzed. Interesting nonlinear dynamic phenomena are observed: direct resonance with softening behavior and parametric instability with period doubling response. Copyright © 2004 by ASME.

2004 - Nonlinear dynamics of axially moving systems [Relazione in Atti di Convegno]
Pellicano, F.
abstract

The object of the present paper is a deep analysis of some recent numerical and experimental results regarding the complex dynamics of axially moving systems. Such important mechanical systems exhibit interesting dynamic behaviors: homoclinic orbits; sub-harmonic responses; amplitude modulations and chaos. These dynamics have been obtained numerically and in some case have been experimentally observed. Using recent techniques of the Nonlinear Time Series analysis, the response of axially moving systems is studied for a large variety of test cases. The correlation dimension of the time series, which is deeply related to the minimal dimension of a system able to reproduce the dynamics, is estimated. Lyapunov exponents are evaluated in order to quantify the response regularity. The present work give a contribution in understanding complex dynamics observed both in conservative and dissipative systems. The dynamical phenomena are analyzed within the unified framework fo the Nonlinear Time Series Analysis. In the case of experimental data the new nonlinear filtering techniques, based on the embedding techniques, have been applied to reduce high noise when classical techniques give bad results. Copyright © 2004 by ASME.

2004 - Parametric instability of a circular cylindrical shell with geometric imperfections [Articolo su rivista]
Catellani, Giulia; Pellicano, Francesco; D., Dall'Asta; M., Amabili
abstract

The static and dynamic behavior of a compressed circular cylindrical shell having geometric imperfections is analyzed. The analysis is mainly performed by means of the Donnell´s nonlinear shallow-shell theory. However, the refined Sanders shell theory is also used for comparison. A suitable expansion of the radial displacement, able to describe both buckling and dynamic behaviors is developed; the effect of geometric imperfections is accounted for by means of a modal representation. The response of the shell subjected to a sinusoidal axial excitation at its ends, giving rise to a parametric excitation, is considered. The effect of imperfections on the critical value of the dynamic load, that causes the loss of stability of the system, is analyzed. Interesting nonlinear dynamic phenomena are observed: direct resonance with softening behavior and parametric instability with period doubling response.

2004 - Parametric instability of belts: theory and experiments [Articolo su rivista]
Pellicano, Francesco; Catellani, Giulia; Fregolent, A.
abstract

In this paper, the dynamic stability of a power transmission belt excited by an eccentric pulley is investigated. A theoretical model is developed to predict the belt response: simply supported boundary conditions are considered, neglecting the pulley curvature, and including the effect of the lower belt span. The transverse displacement field is expanded into sine series and the Galerkin method is applied to reduce the partial differential equation (PDE) into a set of ordinary differential equations. In order to forecast the belt response, the elastic characteristics only of the belt must be provided to the theoretical model. An experimental investigation is performed on a belt-pulley system with a pulley eccentricity; a laser displacement transducer is used to measure the transverse displacement. The combination of a direct and a parametric excitation is analyzed in detail. Interesting post-critical nonlinear dynamic behaviors are found: sub-harmonic responses and quasi-periodic motions seem to coexist, depending on the initial conditions. Experiments confirm the numerical results, thus validating the present theoretical model.

2004 - Stiffness Evaluation and Vibration in a Tractor Gear [Relazione in Atti di Convegno]
Bonori, Giorgio; Andrisano, Angelo Oreste; Pellicano, Francesco
abstract

The problem of gear noise in vehicles has been intensively studied in the past; however, recently the interest about this problem grew because of great restrictions in the laws regarding noise level and the increase of international competition. One of the most important vibration and noise sources is transmission error that excites the gearbox as a dynamic system, the gearbox surfaces, and connected components; the external box radiates noise. However, the current understanding of gear vibration remains incomplete, even though there is general agreement about the nature of the phenomenon. Vibrations are due to several sources: torsion resonance, impulsive or cyclic fluctuations in drive torque, gear mesh transmission error, local component vibration responses and fluctuations in the output torque demand. The concept of a vibrating system made of two gears is generally modeled through two wheels linked by the teeth mesh stiffness. In its simplest form, this model can simulate the classical linear resonance, i.e. the resonant frequency of the system. However, more complex phenomena such as parametric instabilities can be an important source of noise. In the present paper vibration problems in the gears of an industrial vehicle are investigated through the use of perturbation technique. A suitable software has been developed to generate the gear profiles in order to evaluate global mesh stiffness using finite element analysis.

2004 - Vibration and stability of compressed shells with imperfections and fluid-structure interaction [Relazione in Atti di Convegno]
Pellicano, F.; Catellani, G.; Amabili, M.
abstract

In this work the nonlinear dynamic response of an imperfect circular cylindrical shell under combined static and dynamic axial load is analyzed. In order to define completely the shell behavior and to introduce a suitable expansion of the radial displacement, a buckling analysis, including the effect of geometric imperfections, is developed. The effect of the imperfections on the postbuckling path is studied. The response of the shell subjected to a sinusoidal axial excitation at its ends, giving rise to a parametric excitation, is considered. The effect of the imperfections on the critical value of the dynamic load, that causes the loss of stability of the system, is analyzed. Interesting nonlinear dynamic phenomena are observed: direct resonance with softening behavior and parametric instability with period doubling response. The effect of a contained heavy fluid on the shell vibration and stability is investigated.

2003 - Nonlinear dynamics and stability of compressed circular cylindrical shells [Capitolo/Saggio]
Pellicano, F.; Amabili, M.
abstract

The dynamic stability of simply supported, circular cylindrical shells under periodic axial loads is analysed. Nonlinearities due to finite-amplitude shell motion are considered by using the Donnell's nonlinear shallow-shell theory. A finite length, simply supported shell is considered; the boundary conditions are satisfied, including the contribution of external axial loads acting at the shell edges. The effect of a contained liquid on the dynamic stability is investigated.

2003 - Stability and vibration of empty and fluid-filled circular cylindrical shells under static and periodic axial loads [Articolo su rivista]
Pellicano, Francesco; M., Amabili
abstract

In the present study, the dynamic stability of simply supported, circular cylindrical shells subjected to dynamic axialloads is analysed. Geometric nonlinearities due to finite-amplitude shell motion are considered by using the Donnellsnonlinear shallow-shell theory. The effect of structural damping is taken into account. A discretization method based ona series expansion involving a relatively large number of linear modes, including axisymmetric and asymmetric modes,and on the Galerkin procedure is developed. Axisymmetric modes are included; indeed, they are essential in simulatingthe inward deflection of the mean oscillation with respect to the equilibrium position and in describing the axisymmetricdeflection due to axial loads. A finite length, simply supported shell is considered; the boundary conditions are satisfied,including the contribution of external axial loads acting at the shell edges. The effect of a contained liquid is investigated.The linear dynamic stability and nonlinear response are analysed by using continuation techniques and directsimulations.

2002 - Complex dynamics of high-speed axially moving systems [Articolo su rivista]
Pellicano, Francesco; F., Vestroni
abstract

In this paper, the dynamic response of a simply supported travelling beam subjected to a transverse load is investigated in the super-critical speed range. The well-known axially moving beam theory is considered and a simple viscous damping mechanism has been introduced. The displacement field is expanded in a series of the buckling modes, a sine series, and different techniques have been used in analyzing the response of the dynamical system. Periodic oscillations are studied by means of continuation techniques, while non-stationary dynamics are investigated through direct simulations. A comparison with the literature and a convergence test on the series expansion are performed. A sample case of a physical beam is developed and numerical results are presented concerning bifurcation analysis and stability, and direct simulations of global postcritical dynamics. A complex scenario of alternate regular and chaotic motions is found in a large range of the main parameters.

2002 - Dynamic Stability of a Pipe Subjected to a Pulsating Flow [Relazione in Atti di Convegno]
Catellani, Giulia; Milani, Massimo; Pellicano, Francesco
abstract

Power transmission pipes are widely present in industrial applications. Moreover, the physical and mathematical model describing the dynamics of a pipe is similar to that of many mechanical systems such as heat exchangers high-speed magnetic tapes, band saw blades, aerial cable threadlines, and sheet production processes. All previous systems are axially moving systems. The dynamic behaviour of an axially moving system is greatly influenced from the presence of the internal flowing fluid, which affects the pipes dynamics and stability. When a critical value of the axial speed is reached, the first linear natural frequency vanishes; the straight equilibrium position loses stability and bifurcates into new equilibrium states. In the sub-critical speed range, all natural frequencies decrease as the axial speed increases and the vibration modes are complex. In actual operating conditions, pipe lines are subjected to many external disturbances, such as external excitations or dynamic disturbances exerted by the flow fluctuations induced by a volumetric pump. Some example of pump-pipes interactions can be found in literature, that highlight the great influence of pump irregularity on lines stability and system noising. When an oscillating external excitation causes a resonance, very dangerous conditions can be met and the axially moving continuum can undergo to catastrophic failures. The presence of an internal flow can cause divergence and flutter type instabilities. The fluid structures interaction analysis requires a deep investigation of the internal velocity field

2002 - Effect of the geometry on the non-linear vibration of circular cylindrical shells [Articolo su rivista]
Pellicano, Francesco; M., Amabili; Mp, Paidoussis
abstract

The non-linear vibration of simply supported, circular cylindrical shells is analysed. Geometric non-linearities due to finite-amplitude shell motion are considered by using Donnell's non-linear shallow-shell theory; the effect of viscous structural damping is taken into account. A discretization method based on a series expansion of an unlimited number of linear modes, including axisymmetric and asymmetric modes, following the Galerkin procedure, is developed. Both driven and companion modes are included, allowing for travelling-wave response of the shell. Axisymmetric modes are included because they are essential in simulating the inward mean deflection of the oscillation with respect to the equilibrium position. The fundamental role of the axisymmetric modes is confirmed and the role of higher order asymmetric modes is clarified in order to obtain the correct character of the circular cylindrical shell non-linearity. The effect of the geometric shell characteristics, i.e., radius, length and thickness, on the non-linear behaviour is analysed: very short or thick shells display a hardening non-linearity; conversely, a softening type non-linearity is found in a wide range of shell geometries. (C) 2002 Elsevier Science Ltd. All rights reserved.

2002 - Large-amplitude vibrations of empty and fluid-filled circular cylindrical shells with imperfections: Theory and experiments [Relazione in Atti di Convegno]
Amabili, M.; Pellegrini, M.; Pellicano, F.
abstract

The large-amplitude response of perfect and imperfect, simply supported circular cylindrical shells to harmonic excitation in the spectral neighbourhood of some of the lowest natural frequencies is investigated. Donnell's nonlinear shallow-shell theory is used and the solution is obtained by Galerkin method. Several expansions involving 16 or more natural modes of the shell are used. The boundary conditions on the radial displacement (simply supported shell at both ends) and the continuity of circumferential displacement are exactly satisfied. The effect of internal quiescent, incompressible and inviscid fluid is investigated. The nonlinear equations of motion are studied by using a code based on arclength continuation method. A series of accurate experiments on forced vibrations of an empty and water-filled stainless-steel shell have been performed. Several modes have been intensively investigated for different vibration amplitudes. A closed loop control of the force excitation has been used. The actual geometry of the test shell has been measured and the geometric imperfections have been introduced in the theoretical model. Several interesting nonlinear phenomena have been experimentally observed and numerically reproduced, as: softening-type nonlinearity, different types of travelling wave response in the proximity of resonances and amplitude-modulated response. For all the modes investigated, the theoretical and experimental results are in strong agreement.

2002 - Large-amplitude vibrations of empty and fluid-filled circular cylindrical shells with imperfections: Theory and experiments [Relazione in Atti di Convegno]
Amabili, M.; Pellegrini, M.; Pellicano, F.
abstract

The large-amplitude response of perfect and imperfect, simply supported circular cylindrical shells to harmonic excitation in the spectral neighbourhood of some of the lowest natural frequencies is investigated. Donnell's nonlinear shallow-shell theory is used and the solution is obtained by Galerkin method. Several expansions involving 16 or more natural modes of the shell are used. The boundary conditions on the radial displacement (simply supported shell at both ends) and the continuity of circumferential displacement are exactly satisfied. The effect of internal quiescent, incompressible and inviscid fluid is investigated. The nonlinear equations of motion are studied by using a code based on arclength continuation method. A series of accurate experiments on forced vibrations of an empty and water-filled stainless-steel shell have been performed. Several modes have been intensively investigated for different vibration amplitudes. A closed loop control of the force excitation has been used. The actual geometry of the test shell has been measured and the geometric imperfections have been introduced in the theoretical model. Several interesting nonlinear phenomena have been experimentally observed and numerically reproduced, as: softening-type nonlinearity, different types of travelling wave response in the proximity of resonances and amplitude-modulated response. For all the modes investigated, the theoretical and experimental results are in strong agreement. Copyright © 2002 by ASME.

2002 - Multimode approach to nonlinear supersonic flutter of imperfect circular cylindrical shells [Articolo su rivista]
M., Amabili; Pellicano, Francesco
abstract

The aeroelastic stability of simply supported, circular cylindrical shells in supersonic flow is investigated by using both linear aerodynamics (first-order piston theory) and nonlinear aerodynamics (third-order piston theory). Geometric nonlinearities, due to finite amplitude shell deformations, are considered by using the Donnell's nonlinear shallow-shell theory,, and the effect of viscous structural damping is taken into account. The system is discretized by, Galerkin method and is investigated by using a model involving lip to 22 degrees-of-freedom, allowing for travelling-wave flutter around the shell and axisymmetric contraction of the shell. Asymmetric and axisymmetric geometric imperfections of circular cylindrical shells are taken into account. Numerical calculations are carried out for a very thin circular shell affixed Mach number 3 tested at the NASA Ames Research Center. Results show that the system loses stability, by travelling-wave flutter around the shell through supercritical bifurcation. Nonsimple harmonic motion is observed for sufficiently high post-critical dynamic pressure. A very good agreement between theoretical and existing experimental data has been found for the onset of flutter flutter amplitude, and frequency. Results show that onset of flutter is very sensible to small initial imperfections of the shells. The influence of pressure differential across the shell skin has also been deeply investigated. The present study gives, for the first time, results in agreement with experimental data obtained at the NASA Ames Research Center more than three decades ago.

2002 - Non-linear dynamics and stability of circular cylindrical shells conveying flowing fluid [Articolo su rivista]
M., Amabili; Pellicano, Francesco; Mp, Paidoussis
abstract

The non-linear dynamics and stability of simply supported, circular cylindrical shells containing inviscid, incompressible fluid flow is analyzed. Geometric non-linearities of the shell are considered by using the Donnell's non-linear shallow shell theory. A viscous damping mechanism is considered in order to take into account structural and fluid dissipation. Linear potential flow theory is applied to describe the fluid-structure interaction. The system is discretized by Galerkin's method and is investigated by using two models: (i) a simpler model obtained by using a base of seven modes for the shell deflection, and (ii) a relatively high-dimensional dynamic model with IS modes. Both models allow travelling-wave response of the shell and shell axisymmetric contraction. Boundary conditions on radial displacement and the continuity of circumferential displacement are exactly satisfied. Stability, bifurcation and periodic responses are analyzed by means of the computer code AUTO for the continuation of the solution of ordinary differential equations. Non-stationary motions are analyzed with direct integration techniques. An accurate analysis of the shell response is performed by means of phase space representation, Fourier spectra, Poincare sections and their bifurcation diagrams. A complex dynamical behaviour has been found. The shell bifurcates statically (divergence) in absence of external dynamic loads by using the flow velocity as bifurcation parameter. Under harmonic load a shell conveying flow can give rise to periodic, quasi-periodic and chaotic responses, depending on flow velocity, amplitude and frequency of harmonic excitation. (C) 2002 Elsevier Science Ltd. All rights reserved.

2002 - Nonlinear Dynamics of Shells with Fluid-Structure Interaction [Monografia/Trattato scientifico]
Pellicano, Francesco; Mikhlin, Y.; Zolotarev, I.
abstract

This book collects several contributions focused on the dynamics of shells with fluid structure interaction. Papers included in the book are the result of a NATO CLG Grant PST.CLF.977350.F. Pellicano and Y. Mikhlin were the coordinators of the international project and editors of the book, I. Zolotarev was the executive editor.

2002 - On a FRF based experimental sub-structuring technique for linear vibrating systems [Relazione in Atti di Convegno]
Andrisano, Angelo Oreste; Catellani, Giulia; Pellicano, Francesco
abstract

-

2002 - Parametric instability of belts: Theory and experiments [Relazione in Atti di Convegno]
Pellicano, F.; Catellani, G.; Fregolent, A.
abstract

In this paper, the dynamic stability of a power transmission belt excited by an eccentric pulley is investigated. A theoretical model has been developed in order to predict the belt response: simply supported boundary conditions are introduced, neglecting the pulley curvature, and considering the presence of the lower span of the belt. The transversal displacement field is expanded in sine series of the still belt modes; the Galerkin method is applied to reduce the partial differential equation of motion into a set of ordinary differential equations. In order performing an accurate response prediction, the following information must be supplied to the model: elastic characteristic; geometry; initial tension; damping. An experimental investigation is performed on a belt mounted on two pulleys and a tensioner, where one of the pulleys presents a variable eccentricity; measurement are performed using a Laser Displacement transducer. The combination of direct and parametric excitation is analyzed in detail. Interesting postcritical nonlinear dynamics are found: sub-harmonic responses and quasi-periodic motion seem to coexist, depending on the initial conditions. Experiments confirm the numerical findings validating the present theoretical model.

2002 - Stability of empty and fluid-filled circular cylindrical shells subjected to dynamic axial loads [Relazione in Atti di Convegno]
Pellicano, F.; Amabili, M.; Paidoussis, M. P.
abstract

In the present study the dynamic stability of simply supported, circular cylindrical shells subjected to dynamic axial loads is analyzed. Geometric nonlinearities due to finite-amplitude shell motion are considered by using the Donnell's nonlinear shallow-shell theory. The effect of structural damping is taken into account. A discretization method based on a series expansion involving a large number of linear modes, including axisymmetric and asymmetric modes, and on the Galerkin procedure is developed. Both driven and companion modes are included allowing for travelling-wave response of the shell. Axisymmetric modes are included because they are essential in simulating the inward deflection of the mean oscillation with respect to the equilibrium position. The shell is simply supported and presents a finite length. Boundary conditions are considered in the model, which includes also the contribution of the external axial loads acting at the shell edges. The effect of a contained liquid is also considered. The linear dynamic stability and nonlinear response are analysed by using continuation techniques. Copyright © 2002 by ASME.

2002 - Stability of empty and fluid-filled circular cylindrical shells subjected to dynamic axial loads [Relazione in Atti di Convegno]
Pellicano, F.; Amabili, M.; Paidoussis, M. P.
abstract

In the present study the dynamic stability of simply supported, circular cylindrical shells subjected to dynamic axial loads is analyzed. Geometric nonlinearities due to finite-amplitude shell motion are considered by using the Donnell's nonlinear shallow-shell theory. The effect of structural damping is taken into account. A discretization method based on a series expansion involving a large number of linear modes, including axisymmetric and asymmetric modes, and on the Galerkin procedure is developed. Both driven and companion modes are included allowing for travelling-wave response of the shell. Axisymmetric modes are included because they are essential in simulating the inward deflection of the mean oscillation with respect to the equilibrium position. The shell is simply supported and presents a finite length. Boundary conditions are considered in the model, which includes also the contribution of the external axial loads acting at the shell edges. The effect of a contained liquid is also considered. The linear dynamic stability and nonlinear response are analysed by using continuation techniques.

2001 - A multi-mode approach for the nonlinear vibrations of circular cylindrical shells [Relazione in Atti di Convegno]
Pellicano, F.; Paidoussis, M. P.; Amabili, M.
abstract

The nonlinear vibrations of simply supported, circular cylindrical shells, having geometric nonlinearities is analyzed. Donnell's nonlinear shallow-shell theory is used, and the partial differential equations are spatially discretized by means of the Galerkin procedure, using a large number of degrees of freedom. A symbolic manipulation code is developed for the discretization, allowing an unlimited number of modes. In the displacement expansion particular care is given to the comparison functions in order to reduce as much as possible the dimension of the dynamical system, without losing accuracy. Both driven and companion modes are included, allowing for traveling-wave response of the shell. The fundamental role of the axisymmetric modes, which are included in the expansion, is confirmed and a convergence analysis is performed. The effect of the geometric shell characteristics, radius, length and thickness, on the nonlinear behavior is analyzed.

2001 - A multi-mode approach for the nonlinear vibrations of circular cylindrical shells [Relazione in Atti di Convegno]
Pellicano, F.; Amabili, M.; Paidoussis, M. P.
abstract

The nonlinear vibrations of simply supported, circular cylindrical shells, having geometric nonlinearities is analyzed. Donnell's nonlinear shallow-shell theory is used, and the partial differential equations are spatially discretized by means of the Galerkin procedure, using a large number of degrees of freedom. A symbolic manipulation code is developed for the discretization, allowing an unlimited number of modes. In the displacement expansion particular care is given to the comparison functions in order to reduce as much as possible the dimension of the dynamical system, without losing accuracy. Both driven and companion modes are included, allowing for traveling-wave response of the shell. The fundamental role of the axisymmetric modes, which are included in the expansion, is confirmed and a convergence analysis is performed. The effect of the geometric shell characteristics, radius, length and thickness, on the nonlinear behavior is analyzed.

2001 - Comments on “The Effects of Large Vibration Amplitudes on the Mode Shapes and Natural Frequencies of thin Elastic Shells, Part I: ..." [Articolo su rivista]
Amabili, M.; Paidoussis, M. P.; Pellicano, Francesco
abstract

The recent paper by F. Moussaoui, R. Benamar and R. G. White [1] on large-amplitudevibrations of shells reintroduces an error that has been corrected many years ago byEvensen [2, 3] and many others [4}11].The paper deals with free, large-amplitude vibrations of in"nitely long circular cylindricalshells, neglecting motion in the longitudinal direction and assuming that the generatinglines of the shell remain straight after deformation. Thus, the model is suitable for rings butit is not adequate for real shells of "nite length. However, the main problem is not there. Thesystem is discretized by using a multi-mode expansion which excludes axisymmetric terms(refer to p. 921 and 927 in reference [1]). In fact all available studies, see e.g. references[2}11], show that the interaction between the asymmetric mode under consideration andthe axisymmetric modes is crucial, and that it is the most important of any such intermodalinteractions. In particular, Amabili et al. [9, 10] have shown that not only the "rstaxisymmetric mode, but also the third should be included for shells of "nite length, tocorrectly predict the trend of non-linearity: if the interaction with axisymmetric modes isneglected, as done by Moussaoui et al. [1], a strong hardening-type non-linearity isobtained (see Figure 2 in reference [1]); if it is included, as it ought to be, the non-linearity issoftening, for most cylindrical shell geometries. It is very curious that Moussaoui et al. [1]used for comparison of their results the single-mode approach used by Chu in 1961 whichhas been known to give wrong results since 1963 [2]....

2001 - Nonlinear resonance and parametric instability of a power transmission belt: Numerical analysis with experiments [Relazione in Atti di Convegno]
Vestroni, F.; Pellicano, F.; Catellani, G.; Fregolent, A.
abstract

In this paper a numerical approach is developed to forecast the dynamic behavior of a power transmission belt running on eccentric pulleys. Basic partial differential equations are developed, considering the elastic effect of the lower branch of the belt. Nonlinear resonances and dynamic instabilities are analyzed in detail using a high dimensional discrete model, obtained through the Galerkin procedure. The numerical analysis is performed by means of direct simulations and a continuation software. Numerical results are compared with available experimental data. It is shown that the numerical method is able to predict correctly the amplitudes of oscillation in several operating conditions: direct and parametric resonances. Frequency response curves are obtained when the belt is harmonically excited close to the first and second linear natural frequency. The damping ratio and the linear frequencies are identified at zero axial speed.

2001 - Nonlinear stability of circular cylindrical shells in annular and unbounded axial flow [Articolo su rivista]
M., Amabili; Pellicano, Francesco; Mp, Païdoussis
abstract

The stability of circular cylindrical shells with supported ends in compressible, inviscid axial flow is investigated. Nonlinearities due to finite-amplitude shell motion are considered by using Donnell's nonlinear shallow-shell theory; the effect of viscous structural damping is taken into account. Two different in-plane constraints are applied at the shell edges: zero a-vial force and Zero axial displacement; the other boundary conditions are those for simply supported shells. Linear potential flow theory, is applied to describe the fluid-stricture interaction. Both annular and unbounded external flow are considered by using two different sets of boundary conditions for the flow beyond the shell length: (i) a flexible wall of infinite extent in the longitudinal direction, and (ii) rigid extensions of the shell (baffles). The system is discretized by the Galerkin method and is investigated by using a model involving seven degrees-of-freedom, allowing for traveling-wave response of the shell and shell axisymmetric contraction. Results for both annular and unbounded external flow show that the system loses stability by divergence through strongly subcritical bifurcations. Jumps to bifurcated states can occur well before the onset of instability predicted by linear theory, showing that a linear study of shell stability is not sufficient for engineering applications.

2001 - Nonlinear supersonic flutter of circular cylindrical shells [Articolo su rivista]
M., Amabili; Pellicano, Francesco
abstract

The aeroelastic stability of simply supported, circular cylindrical shells in supersonic Row is investigated. Non-linearities caused by large-amplitude shell motion are considered by using the Donnell nonlinear shallow-shell theory, and the effect of viscous structural damping is taken into account, Two different in-plane constraints are applied to the shell edges: zero axial force and zero axial displacement; the other boundary conditions are those for simply supported shells. Linear piston theory is applied to describe the fluid-structure interaction by using two different formulations, taking into account or neglecting the curvature correction term. The system is discretized by Galerkin projections and is investigated by using a model involving seven degrees of freedom, allowing for traveling-wave flutter of the shell and shell axisymmetric contraction. Results show that the system loses stability by standing-wave flutter through supercritical bifurcation; however, traveling-wave flutter appears with a very small increment of the freestream static pressure that is used as the bifurcation parameter, A very good agreement between theoretical and existing experimental data has been found for flutter amplitudes. The influence of internal static pressure has also been studied.

2001 - Nonlinear supersonic flutter of imperfect circular cylindrical shells [Relazione in Atti di Convegno]
Amabili, M.; Pellicano, F.
abstract

The aeroelastic stability of simply supported, circular cylindrical shells in supersonic flow is investigated by using both linear aerodynamics (first-order piston theory) and nonlinear aerodynamics (third-order piston theory). Geometric nonlinearities, due to finite amplitude shell deformations, are considered by using the Donnell's nonlinear shallow-shell theory, and the effect of viscous structural damping is taken into account. The system is discretized by Galerkin method and is investigated by using a model involving up to 22 degrees of freedom, allowing for travelling-wave flutter around the shell and axisymmetric contraction of the shell. Asymmetric and axisymmetric geometric imperfections of circular cylindrical shells are taken into account. Results show that the system loses stability by travelling-wave flutter around the shell through supercritical bifurcation. Non-simple harmonic motion is observed for sufficiently high post-critical dynamic pressure. A good agreement between theoretical and existing experimental data has been found for the onset of flutter, flutter amplitude and frequency. Results show that onset of flutter is very sensible to small initial imperfections of the shells. The influence of pressure differential across the shell skin has also been deeply investigated. The present study gives, for the first time, results in good agreement with experimental data obtained at the NASA Ames Research Center more than three decades ago.

2001 - Nonlinear supersonic flutter of imperfect circular cylindrical shells [Relazione in Atti di Convegno]
Amabili, M.; Pellicano, F.
abstract

The aeroelastic stability of simply supported, circular cylindrical shells in supersonic flow is investigated by using both linear aerodynamics (first-order piston theory) and nonlinear aerodynamics (third-order piston theory). Geometric nonlinearities, due to finite amplitude shell deformations, are considered by using the Donnell's nonlinear shallow-shell theory, and the effect of viscous structural damping is taken into account. The system is discretized by Galerkin method and is investigated by using a model involving up to 22 degrees of freedom, allowing for travelling-wave flutter around the shell and axisymmetric contraction of the shell. Asymmetric and axisymmetric geometric imperfections of circular cylindrical shells are taken into account. Results show that the system loses stability by travelling-wave flutter around the shell through supercritical bifurcation. Non-simple harmonic motion is observed for sufficiently high post-critical dynamic pressure. A good agreement between theoretical and existing experimental data has been found for the onset of flutter, flutter amplitude and frequency. Results show that onset of flutter is very sensible to small initial imperfections of the shells. The influence of pressure differential across the shell skin has also been deeply investigated. The present study gives, for the first time, results in good agreement with experimental data obtained at the NASA Ames Research Center more than three decades ago.

2001 - Normal modes and boundary layers for a slender tensioned beam on a nonlinear foundation [Articolo su rivista]
Pellicano, Francesco; Vakakis, Af
abstract

In this paper, the nonlinear normal modes (NNMs) of a thin beam resting on a nonlinear spring bed subjected to an axial tension is studied. An energy-based method is used to obtain NNMs. In conjunction with a matched asymptotic expansion, we analyze, through simple formulas, the local effects that a small bending stiffness has on the dynamics, along with the secular effects caused by a symmetric nonlinearity. Nonlinear mode shapes are computed and compared with those of the unperturbed linear system. A double asymptotic expansion is employed to compute the boundary layers in the nonlinear mode shape due to the small bending stiffness. Satisfactory agreement between the theoretical and numerical backbone curves of the system in the frequency domain is observed.

2001 - Primary and parametric non-linear resonances of a power transmission belt: Experimental and theoretical analysis [Articolo su rivista]
Pellicano, Francesco; A., Fregolent; A., Bertuzzi; F., Vestroni
abstract

In this paper, the effect of pulley eccentricity on the vibration of a power transmission belt is experimentally investigated and a theoretical model is developed for validation and identification purposes. This eccentricity gives rise to dangerous operating conditions for the system, especially when it excites the frequency range of the belt resonances. As expected, the system shows a hardening non-linear behavior. Moreover, the fluctuation of the belt tension, due to the pulley eccentricity, gives rise to a parametric instability that can cause catastrophic failures of the structure. Laser displacement transducers are used to measure transversal vibrations of the belt. An approximate analytical solution of the travelling beam dynamics is developed in order to model the system and reproduce the experimental data. Comparisons between analytical solution and experimental data allow the identification of the unknown parameters of the analytical model. A validation of the identified model is performed by comparing analytical and experimental data in different operating conditions.

2000 - Experimental and theoretical analysis of a power transmission belt [Relazione in Atti di Convegno]
Pellicano, F.; Vestroni, F.; Fregolent, A.
abstract

In this paper, the effect of a pulley eccentricity on the vibration of a power transmission belt is experimentally investigated and a theoretical model is developed for validation and identification purposes. This eccentricity gives rise dangerous operating conditions for the system, especially when it excites the frequency range of the belt resonances. As expected, the system shows a hardening nonlinear behavior. Moreover, the fluctuation of the belt tension, due to the pulley eccentricity, gives rise to a parametric instability that can undergo to catastrophic failures of the structure. Experimental observations with quantitative measurements are obtained by means of a laser telemeter. Frequency response curves are drawn when the beam is harmonically excited close to the first and second linear natural frequency. A simple analytical approximation of the system response is obtained by one complex mode approximation. An asymptotic solution justifies the experimental evidence and allows the identification of the main parameters of the equation of motion. The excellent agreement between theoretical and experimental data confirms the consistency of the analytical model and the identification of the parameters.

2000 - Geometrically nonlinear forced vibrations of circular cylindrical shells containing flowing fluid [Relazione in Atti di Convegno]
Pellicano, F.; Amabili, M.; Paidoussis, M. P.
abstract

The response of a shell conveying fluid to harmonic excitation, in the spectral neighbourhood of one of the lowest natural frequencies, is investigated for different flow velocities. Nonlinearities due to moderately large amplitude shell motion are considered by using the nonlinear Donnell shallow shell theory. Linear potential flow theory is applied to describe the fluid-structure interaction by using the model proposed by Païdoussis and Denise. For different amplitude and frequency of the excitation and for different flow velocities, the following are investigated numerically: (i) periodic response of the system; (ii) unsteady and stochastic motion; (iii) loss of stability by jumps to bifurcated branches. The effect of the flow velocity on the nonlinear periodic response of the system has also been investigated. Poincaré maps and bifurcation diagrams are used to study the unsteady and stochastic dynamics of the system. Amplitude-modulated motions, multi-periodic solutions, chaotic responses and the so-called "blue sky catastrophe" phenomenon have been observed for different values of the system parameters; the latter two have been predicted here probably for the first time for the dynamics of circular cylindrical shells.

2000 - Non-linear dynamics and stability of circular cylindrical shells containing flowing fluid. Part III: Truncation effect without flow and experiments [Articolo su rivista]
M., Amabili; Pellicano, Francesco; Mp, Paidoussis
abstract

The response of simply supported circular cylindrical shells to harmonic excitation in the spectral neighbourhood of one of the lowest natural frequencies is investigated by using improved mode expansions with respect to those assumed in Parts I and II of the present study. Two cases are studied: (1) shells in vacuo; and (2) shells filled with stagnant water. The improved expansions allow checking the accuracy of the solutions previously obtained and giving definitive results within the limits of Donnell´s non-linear shallow-shell theory. The improved mode expansions include: (1) harmonics of the circumferential mode number n under consideration, and (2) only the principal n, but with harmonics of the longitudinal mode included. The effect of additional longitudinal modes is absolutely insignificant in both the driven and companion mode responses. The effect of modes with 2n circumferential waves is very limited on the trend of non-linearity, but is significant in the response with companion mode participation in the case of lightly damped shells (empty shells). In particular, the travelling wave response appears for much lower vibration amplitudes and presents a frequency range without stable responses, corresponding to a beating phenomenon. A liquid (water) contained in the shell generates a much stronger softening behaviour of the system. Experiments with a water-filled circular cylindrical shell made of steel are in very good agreement with the present theory.

2000 - Non-linear dynamics and stability of circular cylindrical shells containing flowing fluid. Part IV: Large-amplitude vibrations with flow [Articolo su rivista]
M., Amabili; Pellicano, Francesco; M. P., Païdoussis
abstract

The response of a shell conveying fluid to harmonic excitation, in the spectral neighbourhood of one of the lowest natural frequencies, is investigated for different flow velocities. The theoretical model has already been presented in Part I of the present study. Non-linearities due to moderately large-amplitude shell motion are considered by using Donnell´s non-linear shallow-shell theory. Linear potential flow theory is applied to describe the fluid-structure interaction by using the model proposed by Paidoussis and Denise. For different amplitudes and frequencies of the excitation and for different flow velocities, the following are investigated numerically: (1) periodic response of the system; (2) unsteady and stochastic motion; (3) loss of stability by jumps to bifurcated branches. The effect of the flow velocity on the non-linear periodic response of the system has also been investigated. Poincare maps and bifurcation diagrams are used to study the unsteady and stochastic dynamics of the system. Amplitude modulated motions, multi-periodic solutions, chaotic responses, cascades of bifurcations as the route to chaos and the so-called blue sky catastrophe phenomenon have all been observed for different values of the system parameters; the latter two have been predicted here probably for the first time for the dynamics of circular cylindrical shells.

2000 - Non-linear vibrations of fluid-filled, simply supported circular cylindrical shells: Theory and experiments [Relazione in Atti di Convegno]
Amabili, M.; Pellicano, F.; Paidoussis, M. P.
abstract

The large-amplitude response of thin, simply supported circular cylindrical shells to a harmonic excitation in the spectral neighbourhood of one of the lowest natural frequencies is investigated. Donnell's nonlinear shallow-shell theory is used and the solution is obtained by Galerkin projection. A mode expansion including driven and companion modes, axisymmetric modes and additional asymmetric modes is used. In particular, asymmetric modes with twice the number of circumferential waves of driven and companion modes are included in the analysis. The boundary conditions on radial displacement and the continuity of circumferential displacement are exactly satisfied. The effect of internal quiescent, incompressible and inviscid fluid is investigated. The equations of motion are studied by using a code based on the Collocation Method. Validation of the present model is obtained by comparison with other authoritative results and new experimental results. The effect of the number of axisymmetric modes used in the expansion on the response of the shell is investigated, clarifying questions open for a long time. The contribution of additional longitudinal modes is absolutely insignificant in both the driven and companion mode responses. The effect of modes with harmonics of the circumferential mode number n under consideration is limited so far as the trend of nonlinearity is concerned, but is significant in the response with companion mode participation for lightly damped shells (empty shells). Results show the occurrence of travelling wave response in the proximity of the resonance frequency, the fundamental role of the first and third axisymmetric modes in the expansion of the radial deflection with one longitudinal half-wave, and limit cycle responses. A liquid (water) contained in the shell generates a much stronger softening behaviour of the system. Experiments with a water-filled circular cylindrical shell made of steel are in very good agreement with the present theory.

2000 - Non-linear vibrations of fluid-filled, simply supported circular cylindrical shells: Theory and experiments [Relazione in Atti di Convegno]
Amabili, M.; Pellicano, F.; Paidoussis, M. P.
abstract

The large-amplitude response of thin, simply supported circular cylindrical shells to a harmonic excitation in the spectral neighbourhood of one of the lowest natural frequencies is investigated. Donnell's nonlinear shallow-shell theory is used and the solution is obtained by Galerkin projection. A mode expansion including driven and companion modes, axisymmetric modes and additional asymmetric modes is used. In particular, asymmetric modes with twice the number of circumferential waves of driven and companion modes are included in the analysis. The boundary conditions on radial displacement and the continuity of circumferential displacement are exactly satisfied. The effect of internal quiescent, incompressible and inviscid fluid is investigated. The equations of motion are studied by using a code based on the Collocation Method. Validation of the present model is obtained by comparison with other authoritative results and new experimental results. The effect of the number of axisymmetric modes used in the expansion on the response of the shell is investigated, clarifying questions open for a long time. The contribution of additional longitudinal modes is absolutely insignificant in both the driven and companion mode responses. The effect of modes with harmonics of the circumferential mode number n under consideration is limited so far as the trend of nonlinearity is concerned, but is significant in the response with companion mode participation for lightly damped shells (empty shells). Results show the occurrence of travelling wave response in the proximity of the resonance frequency, the fundamental role of the first and third axisymmetric modes in the expansion of the radial deflection with one longitudinal half-wave, and limit cycle responses. A liquid (water) contained in the shell generates a much stronger softening behaviour of the system. Experiments with a water-filled circular cylindrical shell made of steel are in very good agreement with the present theory.

2000 - Nonlinear dynamics and bifurcations of an axially moving beam [Articolo su rivista]
Pellicano, Francesco; F., Vestroni
abstract

The present paper analyzes the dynamic behavior of a simply supported beam subjected to an axial transport of mass. The Galerkin method is used to discretize the problem; a high dimensional system of ordinary differential equations with linear gyroscopic part and cubic nonlinearities is obtained. The system is studied in the sub and super-critical speed ranges with emphasis on the stability and the global dynamics that exhibits special features after the first bifurcation. A sample case of a physical beam is developed and numerical results are presented concerning the convergence of the series expansion, linens subcritical behavior, bifurcation analysis and stability, and direct simulation of global postcritical dynamics. A homoclinic orbit is found in a high dimensional phase space and its stability and collapse are studied.

2000 - Nonlinear stability of circular cylindrical shells in axially flowing fluid [Relazione in Atti di Convegno]
Amabili, M.; Paidoussis, M. P.; Pellicano, F.
abstract

The stability of supported, circular cylindrical shells in compressible, inviscid axial flow is investigated. Nonlinearities due to large amplitude shell motion are considered by using the nonlinear Donnell shallow shell theory and the effect of viscous structural damping is taken into account. Two different in-plane constraints are applied to the shell edges: zero axial force and zero axial displacement; the other boundary conditions are those for simply supported shells. Linear potential flow theory is applied to describe the fluid-structure interaction. Both annular and unbounded external flow are considered by using two different sets of boundary conditions for the flow beyond the shell length: (i) a flexible wall of infinite extent in the longitudinal direction, and (ii) rigid extensions of the shell (baffles). The system is discretised by Galerkin projections and is investigated by using a model involving seven degrees of freedom, allowing for travelling wave response of the shell and shell axisymmetric contraction. Results for both annular and unbounded external flow show that the system loses stability by divergence through strongly subcritical bifurcations. Jumps to bifurcated positions can happen much before the onset of instability predicted by linear theories, showing the necessity of a nonlinear study.

2000 - Nonlinear stability of circular cylindrical shells in axially flowing fluid [Relazione in Atti di Convegno]
Amabili, M.; Paidoussis, M. P.; Pellicano, F.
abstract

The stability of supported, circular cylindrical shells in compressible, inviscid axial flow is investigated. Nonlinearities due to large amplitude shell motion are considered by using the nonlinear Donnell shallow shell theory and the effect of viscous structural damping is taken into account. Two different in-plane constraints are applied to the shell edges: zero axial force and zero axial displacement; the other boundary conditions are those for simply supported shells. Linear potential flow theory is applied to describe the fluid-structure interaction. Both annular and unbounded external flow are considered by using two different sets of boundary conditions for the flow beyond the shell length: (i) a flexible wall of infinite extent in the longitudinal direction, and (ii) rigid extensions of the shell (baffles). The system is discretised by Galerkin projections and is investigated by using a model involving seven degrees of freedom, allowing for travelling wave response of the shell and shell axisymmetric contraction. Results for both annular and unbounded external flow show that the system loses stability by divergence through strongly subcritical bifurcations. Jumps to bifurcated positions can happen much before the onset of instability predicted by linear theories, showing the necessity of a nonlinear study.

2000 - Nonlinear vibrations and multiple resonances of fluid-filled, circular shells, part 1: Equations of motion and numerical results [Articolo su rivista]
M., Amabili; Pellicano, Francesco; A. F., Vakakis
abstract

The response-frequency relationship in the vicinity of a resonant frequency, the occurrenceof travelling wave response and the presence of internal resonances are investigatedfor simply supported, circular cylindrical shells. Donnell’s nonlinear shallow-shelltheory is used. The boundary conditions on radial displacement and the continuity ofcircumferential displacement are exactly satisfied. The problem is reduced to a system offour ordinary differential equations by means of the Galerkin method. The radial deflectionof the shell is expanded by using a basis of four linear modes. The effect of internalfluid is also investigated. The equations of motion are studied by using a code based onthe Collocation Method. The present model is validated by comparison of some resultswith others available. A water-filled shell presenting the phenomenon of 1:1:1:2 internalresonances is investigated for the first time; it shows intricate and interesting dynamics.

2000 - Nonlinear vibrations and multiple resonances of fluid-filled, circular shells. part 2: Perturbation analysis [Articolo su rivista]
Pellicano, Francesco; M., Amabili; Af, Vakakis
abstract

The nonlinear ordinary differential equations describing the dynamics of a fluid filled circular cylindrical shell, obtained in Part I of the present study, is studied by using a second order perturbation approach and direct simulations. Strong modal interactions are found when the structure is excited with small resonant loads. Modal interactions arise in the whole range of vibration amplitude, showing that the internal resonance condition makes the system non-linearizable even for extremely small amplitudes of oscillation. Stationary and nonstationary oscillations are observed and the complex nature of modal interactions is accurately analyzed. No chaotic motion is observed in the case of 1:1:1:2 internal resonance studied [S0739-3717(00)01304-0].

1999 - Further comments on nonlinear vibrations of shells [Articolo su rivista]
M., Amabili; Pellicano, Francesco; M. P., Païdoussis
abstract

THE RECENT LETTER by Dowell (1998) touched on several aspects of the literature and thephysics of nonlinear vibrations of circular cylindrical shells, clarifying some of the issueswhile attempting to reconcile some hitherto contradictory Þndings, and at the same timeoutlining some of the unresolved issues and potentially proÞtable directions for furtherresearch.The letter provided us with the impetus for some further thoughts on the subject, and herewe o¤er some complementary discussion to a few of the points raised by Dowell (1998) andclariÞcations to our own work (Amabili et al. 1998).The Þrst issue is that of the magnitude of the nonlinear e¤ects associated with forcedmotions of a simply supported, circular cylindrical shell. As pointed out by Dowell (1998),the degree of nonlinearity can be extremely weak: of the order of 0.5% (vis-a`-vis the linearfrequency) for amplitudes of the driven mode equal to the shell thickness. Such a small e¤ectrenders deliberation on whether the e¤ect is hardening or softening almost immaterial.......

1999 - Low-dimensional model for nonlinear vibrations of circular cylindrical shells [Relazione in Atti di Convegno]
Amabili, Marco; Pellicano, Francesco
abstract

The response-frequency relationship in the vicinity of a resonant frequency, the occurrence of travelling wave response and the presence of internal resonances are investigated for simply supported, circular cylindrical shells. Donnell's nonlinear shallow-shell theory is used. The boundary conditions on radial displacement and the continuity of circumferential displacement are exactly satisfied. The problem is reduced to a system of ordinary differential equations by means of the Galerkin method. The mode shape is expanded by using four degrees of freedom. The effect of internal dense fluid is studied. The solution is obtained by the Method of Normal Forms. Comparison of a three and a four degree-of-freedom model is performed. A water-filled shell presenting the phenomenon of 1:1:1:2 internal resonances is investigated; specific Normal Forms are developed for this study.

1999 - Non-linear dynamics and stability of circular cylindrical shells containing flowing fluid, part II: Large-amplitude vibrations without flow [Articolo su rivista]
Amabili, M; Pellicano, Francesco; Paidoussis, Mp
abstract

The non-linear response of empty and fluid-filled circular cylindrical shells to harmonic excitations is investigated. Both modal and point excitations have been considered. The model is suitable to study simply supported shells with and without axial constraints. Donnell´s non-linear shallow-shell theory is used. The boundary conditions on radial displacement and the continuity of circumferential displacement are exactly satisfied. The radial deflection of the shell is expanded by using a basis of seven linear modes. The effect of internal quiescent, incompressible and inviscid fluid is investigated. The equations of motion, obtained in Part I of this study, are studied by using a code based on the collocation method. The validation of the present model is obtained by comparison with other authoritative results. The effect of the number of axisymmetric modes used in the expansion on the response of the shell is investigated, clarifying questions open for a long time. The results show the occurrence of travelling wave response in the proximity of the resonance frequency, the fundamental role of the first and third axisymmetric modes in the expansion of the radial deflection with one longitudinal half-wave, and limit cycle responses. Modes with two longitudinal half-waves are also investigated.

1999 - Non-linear dynamics and stability of circular cylindrical shells containing flowing fluid. Part I: Stability [Articolo su rivista]
M., Amabili; Pellicano, Francesco; Mp, Paidoussis
abstract

The study presented is an investigation of the non-linear dynamics and stability of simply supported, circular cylindrical shells containing inviscid incompressible fluid flow. Non-linearities due to large-amplitude shell motion are considered by using the non-linear Donnell´s shallow shell theory, with account taken of the effect of viscous structural damping. Linear potential flow theory is applied to describe the fluid-structure interaction. The system is discretiszd by Galerkin´s method, and is investigated by using a model involving seven degrees of freedom, allowing for travelling wave response of the shell and shell axisymmetric contraction. Two different boundary conditions are applied to the fluid flow beyond the shell, corresponding to: (i) infinite baffles (rigid extensions of the shell), and (ii) connection with a flexible wall of infinite extent in the longitudinal direction, permitting solution by separation of variables; they give two different kinds of dynamical behaviour of the system, as a consequence of the fact that axisymmetric contraction, responsible for the softening non-linear dynamical behaviour of shells, is not allowed if the fluid flow beyond the shell is constrained by rigid baffles. Results show that the system loses stability by divergence;

1999 - Post-critical response of an axially moving beam [Relazione in Atti di Convegno]
Pellicano, F.; Vestroni, F.
abstract

In this paper the dynamic response of a simply supported traveling beam, subjected to a pointwise transversal load, is investigated. The motion is described by means of a high dimensional system of ordinary differential equations with linear gyroscopic part and cubic nonlinearities obtained through the Galerkin method. The system is studied in the super-critical speed range with emphasis on the stability and the global dynamics that exhibits special features after the first bifurcation. A sample case of a physical beam is developed and numerical results are presented concerning bifurcation analysis and stability, and direct simulations of global postcritical dynamics. In the supercritical speed range a regular motion around bifurcated equilibrium position becomes chaotic for particular values of frequency and force. The bifurcation diagram for varying force intensity is shown, it can be noticed that a chaotic motion occurs in a wide range of the forcing parameter, co-existiig with a 3T periodic solution in a limited window.

1998 - An experimental study on the transverse vibration of a power transmission belt [Relazione in Atti di Convegno]
Pellicano, F.; Fregolent, A.; Bertuzzi, A.
abstract

In this paper an experimental study on the transversal vibrations of a rubber flat belt is presented. The aim is to evaluate the influence of the axial velocity on system vibrations and to study the nonlinear system behaviour in resonance conditions. Since the transversal vibration of a non-still surface cannot be measured through classical testing tools such as accelerometers, strain-gauges, etc., the measurements are performed using a laser-Doppler vibrometer. The axial velocity is identified by a simple axially moving string model. Nonlinear vibrations are observed and qualitatively compared with those of a hardening Duffing oscillator. The experimental results are compared to, and explained through, the theoretical and numerical predictions presented in the literature.

1998 - Boundary layers and non-linear vibrations in an axially moving beam [Articolo su rivista]
Pellicano, Francesco; F., Zirilli
abstract

The non-linear oscillations of a one-dimensional axially moving beam with vanishing flexural stiffness and weak non-linearities are analysed. The solution of the initial-boundary value problem for the partial differential equation that describes the motion of the beam when two parameters related to the flexural stiffness and the non-linear terms vanish is expanded into a perturbative double series. Two singular perturbation effects due to the small flexural stiffness and to the weak non-linear terms arise: (i) a boundary layer effect when the flexural stiffness vanishes, (ii) a secular effect. Some tests are performed to compare the first order perturbative solution with an approximate solution obtained by a finite difference scheme. The effect of the oscillation amplitude combined with the presence of small bending stiffness and axial transport velocity is investigated enlighting some interesting aspects of axially moving systems. The value of the perturbative series as a computational tool is shown.

1998 - Internal resonances and travelling waves in a submerged structure [Relazione in Atti di Convegno]
Pellicano, F.; Amabili, M.; Paidoussis, M. P.
abstract

In the present paper the dynamic behaviour of a circular cylindrical shell submerged in a heavy quiescent fluid is studied with particular attention to realistic boundary conditions and to the modal interactions between resonant modes. Donnell's shallow shell theory is used, therefore the study is limited to moderately large amplitudes of vibration (the more realistic conditions). The Galerkin procedure is employed to perform the spatial discretization of the problem, and suitable assumed modes are used in order to capture the main phenomena present in the problem and to enhance the assumed mode shapes proposed in the literature. The resulting set of ordinary differential is studied using an efficient perturbation technique, the Method of Normal Forms. The use of perturbation methods is justified by the upper limits in the amplitude of vibration required by the Donnell shallow shell theory. The method is developed for systems having an arbitrary number of degrees of freedom. The numerical results are compared with experimental and analytical results available in the literature to test the expansion used in the paper. Moreover, new results concerning the combined effect of fluid structure interaction and nonlinearity are presented.

1998 - Nonlinear vibrations of circular cylindrical shells coupled to fluid: Discretization method [Relazione in Atti di Convegno]
Amabili, M.; Pellicano, F.; Paidoussis, M. P.
abstract

The large amplitude free and forced vibrations of a simply supported, circular cylindrical shell in contact with an incompressible and inviscid, quiescent and dense fluid are investigated. Donnell's shallow-shell theory is used, so that moderately large vibrations are analysed. The boundary conditions on radial displacement and the continuity of circumferential displacement are exactly satisfied, while axial constraint is satisfied on the average. The problem is reduced to a system of ordinary differential equations by means of the Galerkin method. The mode shape is expanded by using three degrees of freedom; in particular, two asymmetric modes (driven and companion modes), plus an axisymmetric mode are employed. Different tangential constraints can be imposed at the shell ends. Effects of both internal and external dense fluid are studied. Internally, the shell is considered completely filled, while externally, an unbounded fluid domain is considered around the shell in the radial direction. The solution is obtained by direct integration of the equations of motion.

1998 - Nonlinear vibrations of simply supported, circular cylindrical shells, coupled to quiescent fluid [Articolo su rivista]
M., Amabili; Pellicano, Francesco; Mp, Païdoussis
abstract

The nonlinear free and forced vibrations of a simply supported, circular cylindrical shell incontact with an incompressible and inviscid, quiescent and dense ßuid are investigated.DonnellÕs shallow-shell theory is used, so that moderately large vibrations are analysed. Theboundary conditions on radial displacement and the continuity of circumferential displacementare exactly satisÞed, while axial constraint is satisÞed on the average. The problem is reduced toa system of ordinary di¤erential equations by means of the Galerkin method. The mode shape isexpanded by using three degrees of freedom; in particular, two asymmetric modes (driven andcompanion modes), plus an axisymmetric mode are employed. The time dependence of eachterm of the expansion is general and the axisymmetric mode is obtained from a series involvingall axisymmetric linear modes. Di¤erent tangential constraints can be imposed at the shell ends.E¤ects of both internal and external dense ßuid are studied. Internally, the shell is consideredcompletely Þlled, while externally, an unbounded ßuid domain is considered around the shell inthe radial direction. The solution is obtained both numerically and by the Method of NormalForms. Numerical results are obtained for both free and forced vibrations of empty andwater-Þlled shells.

1997 - Applicability conditions of a Nonlinear Superposition Technique [Articolo su rivista]
Pellicano, Francesco; F., Mastroddi
abstract

The analytical conditions for the applicability of a Non!linear Superposition Technique"NST# are established by using the Normal Form Method "NFM#[ The superpositiontechnique represents the extension of modal analysis to weakly non!linear vibrationsystems[ In this paper it is shown that the NST leads to a non!uniform perturbationexpansion for the solution of dynamical systems when some special non!linear terms arepresent in the dynamical system[ An analytical proof for general dynamical systems anda numerical application to a simple mechanical system is included in the paper[

1997 - Nonlinear dynamics of a beam on elastic foundation [Articolo su rivista]
Pellicano, Francesco; F., Mastroddi
abstract

The nonlinear dynamics of a simply supported beam resting on a nonlinear spring bed with cubic stiffness is analyzed. The continuous differential operator describing the mathematical model of the system is discretized through the classical Galerkin procedure and its nonlinear dynamic behavior is investigated using the method of Normal Forms. This model can be regarded as a simple system describing the oscillations of flexural structures vibrating on nonlinear supports and then it can be considered as a simple investigation for the analysis of more complex systems of the same type. Indeed, the possibility of the model to exhibit actually interesting nonlinear phenomena (primary, superharmonic, subharmonic and internal resonances) has been shown in a range of feasibility of the physical parameters. The singular perturbation approach is used to study both the free and the forced oscillations; specifically two parameter families of stationary solutions are obtained for the forced oscillations.

1997 - Post-critical dynamics of an axially moving beam [Relazione in Atti di Convegno]
Vestroni, F.; Pellicano, F.
abstract

In the present paper, the dynamic behaviour of a beam subjected to an axial transport of mass is analyzed. The Galerkin method has been used to discretize the problem; a high dimensional system of ordinary differential equations with linear gyroscopic part and cubic nonlinearities is obtained. The system is studied in the sub and supercritical speed ranges with emphasis on the global dynamics that exhibits special features after the first bifurcation. A sample case of a physical beam is developed and numerical results are presented concerning linear subcritical behaviour, static bifurcation analysis including linear stability and direct simulation of global postcritical dynamics.