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Francesco PELLICANO

Professore Ordinario presso: Dipartimento di Ingegneria "Enzo Ferrari"


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Pubblicazioni

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 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.


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 - 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.


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 - 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.


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 - 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 - 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 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.


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 - 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.


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 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 - 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 - 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 - 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; 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 - 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 - 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.


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 - 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.


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 - 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

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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 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 - 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 - 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 - Nonlinear Vibrations and Multiple Resonances of Fluid-Filled, Circular Cylindrical Shells. Part I: 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 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 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 - 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;


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 - 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.