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Silvio SORRENTINO

Professore Associato
Dipartimento di Ingegneria "Enzo Ferrari"

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Pubblicazioni

2024 - Dynamic analysis of parametrically excited stable rotors with unbalance [Relazione in Atti di Convegno]
De Felice, Alessandro; Sorrentino, Silvio
abstract

The dynamic analysis of parametrically excited rotors is a research field of great interest and practical importance, since instability and resonant behavior can cause issues ranging from anomalous noise and wear to catastrophic failures. This study is focused on the effects of unbalance on a parametrically excited rotor operating in the asymptotically stable domain, a research topic which in the scientific literature has not been investigated. Rotor unbalance causes an additional harmonic load acting on flexural deflection, influencing the frequency response together with the parametric excitation, yielding additional combination external resonances. As a first insight into this problem, to study the effects of angular speed independently of variations of the natural frequencies, and to facilitate decoupling of the equations of motion, a simplified model of a distributed-parameter slender rotor is considered, consisting of a homogeneous Euler-Bernoulli beam with circular section, rotating at constant angular speed about its longitudinal axis on isotropic supports. It is affected by unbalance and loaded by an axial end thrust, assumed to have a harmonic time-dependent component. The steady-state response is studied after decoupling the equations of motion, reducing the problem to the analysis of a non-homogeneous single-degree-of-freedom damped Mathieu equation.

2024 - Identification of lumped stiffness parameters for a motorcycle model in investigating weave and wobble [Articolo su rivista]
Passigato, Francesco; Schramm, Alexander; Diermeyer, Frank; Sorrentino, Silvio; Gordner, Achim; De Felice, Alessandro
abstract

In motorcycle dynamics, great importance is attributed to the study of the weave and wobble vibration modes and, in particular, to the effects of the flexibility of structural components on their stability. Therefore, appropriate motorcycle models for studying weave and wobble should include flexible elements for describing the flexural behavior of components such as the main frame, front assembly, and rear swingarm. Different approaches are possible formodeling flexibilities: the most common among them are the lumped stiffness and the flexible multibody approaches. While the latter certainly provides higher accuracy, the former has advantages in terms of computational load, but, above all, it makes it easier to understand in the design phase how technical parameters, such as torsional and bending stiffness of a given structural component, can influence the stability of weave and wobble. The accuracy of lumped stiffness models strongly depends on parameter identification. In this study, a general method is proposed to determine appropriate lumped stiffness parameters for any given motorcycle component. The proposed method is tested and validated by comparing the weave and wobble modal behavior with the results of flexible multibody analysis. The lumped stiffness model is then adopted to carry out a sensitivity analysis aimed at identifying the effects on the weave and wobble stability of the torsional and bending stiffness of specific structural components of the motorcycle to optimize their design.

2023 - A new approach to the study and prevention of the clutch judder [Relazione in Atti di Convegno]
Tentarelli, Manuel; Cantelli, Stefano; Sorrentino, Silvio; DE FELICE, Alessandro
abstract

The clutch judder observed in hydraulically actuated dual clutch transmissions cannot be fully explained by the current scientific literature. Using a new methodological approach for the analysis of clutch judder, this study shows that a fluctuating oil pressure makes the clutch a parametrically excited system and gives rise to regions of instability as a function of the operating conditions of the clutch. The system’s dynamic behaviour, characterized by both mechanical and structural high complexity, is here investigated through stability analysis of a mathematical model of the driveline. In particular, stability boundaries are identified by means of Floquet analysis, as well as the occurrence of both parametric resonance regions and linear resonance conditions. This opens a new perspective on NVH of automotive drivelines, showing that clutch judder can potentially occur in a much wider range of conditions than documented in the current scientific literature. The results of the experiments in progress on a test bench, designed in partnership with CNH Industrial, are validating the proposed model and will allow to calibrate the parameters of a predictive mathematical model to avoid the phenomenon of clutch judder in the design phase.

2023 - Friction-induced parametric oscillations in automotive drivelines: experimental analysis and modelling [Relazione in Atti di Convegno]
Tentarelli, Manuel; Cantelli, Stefano; Sorrentino, Silvio; De Felice, Alessandro
abstract

Clutch judder is a friction-induced self-excited vibration occurring in automotive drivelines, an NVH issue studied for more than forty years and attributed by the scientific community to three possible causes: stick-slip, negative gradient of the coefficient of friction and geometric disturbances. However, these explanations fail to describe the kind of judder studied in this contribution, arising in presence of an oscillating component (dither) in the clutch actuation pressure. The analysis of experimental data collected on a dual-clutch transmission mounted on a specific test bench suggested the presence of a parametric resonance, generated by the dither. A specific 4 degrees of freedom model was then developed, able to predict with good accuracy the unstable parametric region in which judder occurs and useful in the design stage.

2023 - NONLINEAR EFFECTS ON THE SELF-EXCITED CHATTER OSCILLATIONS IN MOTORCYCLE DYNAMICS, INCLUDING TYRE RELAXATION [Articolo su rivista]
Schramm, ALEXANDER EUGENE; Sorrentino, Silvio; DE FELICE, Alessandro
abstract

Nonlinear effects on the stability of the motorcycle rear ‘chatter’ phenomenon are investi-gated by means of a minimal two degrees of freedom model, including tyre relaxation since this aspect has not been investigated in-depth in previous studies. Motorcycle ‘chat-ter’ manifests itself as a self-excited oscillation, which arises during braking in the fre-quency range between 17 and 22 Hz, affecting safety and performance. The study of the linearised system gives indications on the initiation of self-excited vibrations and thus helps to prevent them using proper design techniques. Post-bifurcation behaviour is ana-lysed focusing on limit cycles and bifurcation diagrams, studied by means of specific ap-plications of the harmonic balance method and Floquet theory. This allows the detection of the validity of the linear results, and to identify the meaningful parameters in limit cycle generation, their amplitude, and their stability.

2023 - On the self-excited chatter vibration in motorcycles [Abstract in Atti di Convegno]
Schramm, ALEXANDER EUGENE; Sorrentino, Silvio; DE FELICE, Alessandro
abstract

This study is focused on the understanding of the nonlinear effects of tyre forces and chain geometry on motorcycle chatter, a self-excited oscillation arising at the rear wheel during heavy braking manoeuvres. In particular the post-bifurcation criticality is assessed, whether subcritical or supercritical, with respect to travelling speed.

2023 - Parametric excitation as a cause of clutch judder: theoretical study and experimental validation [Articolo su rivista]
Tentarelli, Manuel; Cantelli, Stefano; Sorrentino, Silvio; DE FELICE, Alessandro
abstract

Judder is a friction-induced torsional vibration generated during clutch engagement in automotive drivelines. To the best of the authors’ knowledge, three are the causes attributed by the scientific community to the onset of the clutch judder: stick-slip phenomena, negative gradient of the coefficient of friction and geometric disturbances. With the help of a methodological approach that integrates the analysis of a mathematical model with the experimental data obtained on a specially designed test bench, this paper shows that, in some cases, the clutch judder may also be due to the presence of parametric excitation. This new understanding overcomes the limits of the existing explanations because it does not preclude the occurrence of clutch judder at high slip speeds, with positive gradients of the friction coefficient and at excitation frequencies different from the eigenfrequencies of the system. The four degrees of freedom model developed for the study of the transmission provides maps that allow to identify the instability conditions of the system. The analysis described in this paper has been aimed at solving a judder problem in a transmission already in production, but the same approach can be used to avoid the conditions that cause the onset of clutch judder on other transmissions in the design phase.

2023 - Some recent advances in the dynamic analysis of parametrically excited continuous rotor systems [Abstract in Atti di Convegno]
DE FELICE, Alessandro; Sorrentino, Silvio
abstract

Dynamic analysis of parametrically excited rotors is a research field of great interest and practical importance, since instability and resonant behavior can cause issues ranging from anomalous noise and wear to catastrophic failures. An overview is presented of some advances recently proposed by the authors on the dynamic analysis of parametrically excited continuous rotor systems, including results regarding stability analysis (parametric resonances) and preliminary insights into resonant behavior in the asymptotically stable domain, due to unbalance (external resonances). An axisymmetric shaft described by a spinning Timoshenko beam is studied, loaded by oscillating axial end thrust and twisting moment, carrying additional inertial elements like discs. Both isotropic and anisotropic supports are considered, as well as gyroscopic effects and different kinds of damping distributions (both external and internal), which represents a model including all the general features of slender rotors which are relevant for their dynamic analysis. Stability is studied after discretization of the equations of motion into a set of coupled ordinary differential Mathieu-Hill equations. Stability maps in the form of Ince-Strutt diagrams are discussed to highlight the occurrence of simple and combination critical solutions, as well as the influence of angular speed, damping, and anisotropy in the supports. Steady-state response is studied in the asymptotically stable domain under the effect of unbalance, yielding an additional external harmonic load, acting on flexural deflection. As a first insight into this problem, to study the effects of angular speed independently to variations of natural frequencies and to facilitate decoupling of the equations of motion, the Timoshenko model is simplified into the Euler-Bernoulli model, neglecting the gyroscopic effects, additional discs, anisotropy in the supports and twisting moment at the ends of the shaft.

2023 - Stability analysis of parametrically excited isotropic rotors on anisotropic supports [Relazione in Atti di Convegno]
DE FELICE, Alessandro; Sorrentino, Silvio
abstract

The stability of slender rotors which are parametrically excited by external loads is studied under the effects of an-isotropic supports. An axisymmetric shaft is considered, describ- ed by scaling a spinning Timoshenko beam, carrying a disk and loaded by oscillating axial end thrust and twisting moment. The supports are modelled including ‘principal’ stiffness and damp- ing distributions, able to modify the closely separated modes generated by angular speed (with ‘splitting’ of eigenfrequencies in forward and backward pairs). The proposed model includes all the general features of slender rotors which are relevant for this kind of stability analysis, gyroscopic effects comprised. Stability is studied after discretization of the equations of motion into a set of coupled ordinary differential Mathieu-Hill equations. The influence of angular speed combined with anisotropy in the supports is analyzed with respect to frequency and amplitude of the external loads on stability charts in the form of Ince-Strutt diagrams. The occurrence of different kinds of critical solutions, simple and combination, is investigated, highlighting their dependency on both the degree of anisotropy in the supports and angular speed.

2022 - Cold Judder in Tractor Drivelines: An Essential Model for Stability Analysis [Relazione in Atti di Convegno]
Tentarelli, M.; Cantelli, S.; De Felice, A.; Sorrentino, S.
abstract

Current scientific literature classifies the well-known clutch judder phenomenon in friction judder and pressure-induced judder, based on the mechanisms that generate it. Friction judder is associated to a negative gradient of the friction coefficient and to stick-slip phenomena, while pressure-induced judder is mainly caused by geometric disturbances. The peculiarities of the torsional oscillations experimentally observed in dual-clutch transmissions of tractors, incompatible with the explanations found in the current literature, led to consider parametric excitation as a possible cause of instability. Consequently, the clutch was modelled by means of a system of three coupled linear differential equations with time-periodic coefficients. Stability analysis, performed by adopting Floquet theory, allowed to draw stability maps as functions of the two excitation parameters, i.e. the frequency and the amplitude of the dither signal in the clutch actuation pressure. Stability maps proved to be particularly promising to explain the experimentally observed phenomenon. In addition, it was possible to show that clutch judder can also arise for positive gradients of the friction coefficient.

2022 - Driveline stability in racing motorcycles: analysis of a three degrees of freedom minimal model [Articolo su rivista]
Schramm, Alexander; Leonelli, Luca; Sorrentino, Silvio
abstract

Motorcycles under heavy braking conditions can experience a self-excited oscillation known as ‘chatter.’ A simplified three degrees of freedom model of the rear of a motorcycle is developed to study the stability of this mode with the inclusion of lateral dynamics introduced by roll angle. Since motorcycles achieve high roll angles during operation, the study of chatter during these manoeuvres is a topic of interest. The equations of motion are linearised about a quasistatic equilibrium and simplified to accommodate symbolic inspection. Power analysis, eigensystem analysis, eigenvalue sensitivity and Routh-Hurwitz stability criterion are used to study the stability of the system in the braking region. It was found that a driveline mode can become unstable at about 19 Hz, and that its tendency towards instability is increased with added roll angle. This mode is sensitive to model parameters affecting the system inertia and stiffness, as well as the chain geometry. Finally, it is found that the lateral dynamics and roll angle play no direct role in chatter but have a significant indirect effect on it through the working point of the force characteristic function of the tyre

2022 - Effects of anisotropic supports on the stability of parametrically excited slender rotors [Articolo su rivista]
De Felice, A.; Sorrentino, S.
abstract

This study is aimed at investigating the effects of anisotropic supports on the stability of slender rotors parametrically excited by external loads. An axisymmetric shaft described by scaling a spinning Timoshenko beam on anisotropic supports is studied, loaded by oscillating axial end thrust and twisting moment, with the possibility of carrying additional inertial elements like discs, which represents a model including all the general features of slender rotors which are relevant for this kind of stability analysis, gyroscopic effects comprised. Stability is studied after discretization of the equations of motion into a set of coupled ordinary differential Mathieu-Hill equations. The influence on stability of angular speed combined with anisotropy in the supports (including principal stiffness, principal damping and cross-elements) is analysed with respect to frequency and amplitude of the external loads on stability charts in the form of Ince-Strutt diagrams. The occurrence of different kinds of critical solutions, simple and combination, is investigated, highlighting their dependency on both the degree of anisotropy in the supports and angular speed.

2022 - Experimental Identification of Viscoelastic Properties of Plates Made of Quiet Aluminum [Capitolo/Saggio]
Grosso, P.; De Felice, A.; Sorrentino, S.
abstract

The present study is aimed at the identification of equivalent viscoelastic models for layered thin-walled structures, obtained from vibration measurement only. Accurate modeling of modal properties is fundamental for describing metal fatigue caused by forced vibration on structural components. A new approach is proposed, based on a definition of an equivalent modal damping ratio applied to the circle-fit technique, to overcome the difficulties related to the identification of modal parameters when adopting non-conventional viscoelastic models. When the structural internal dissipative effects are dominant, this procedure identifies the parameters of an equivalent Young’s modulus in the frequency domain. The proposed procedure is applied to the analysis of plates made by Quiet Aluminum, adopting the linear fractional Kelvin-Voigt viscoelastic model and assessing the accuracy of the identified parameters by comparison of numerically simulated with experimentally measured frequency response functions.

2022 - Experimental stability analysis of tractor drivelines affected by cold judder [Relazione in Atti di Convegno]
Tentarelli, Manuel; Cantelli, Stefano; Sorrentino, Silvio; DE FELICE, Alessandro
abstract

Clutch judder is a friction-generated self-excited vibration affecting automotive drivelines. Stick-slip, negative gradient of the friction coefficient and geometric disturbances are the only causes currently identified in the scientific literature. Nevertheless, they are not sufficient to explain the vibration occurring in drivelines (typically of tractors) with dither (oscillating component) added to clutch hydraulic actuation signals. In this study, experimental data acquired on a specifically designed test bench are processed to show that this particular kind of judder is an instability due to parametrical excitation exerted by the actuation pressure signal. A minimal model with four degrees of freedom is proposed, able to fit the experimental data, to explain the onset of the parametrically excited vibration, and to identify which parameters have a major role in controlling this phenomenon. Stability charts obtained from the proposed model also represent a useful tool to prevent instability already in the design phase.

2022 - Investigations of Motorcycle Mid-Corner Instability Using a Three Degree-of-Freedom Minimal Model [Relazione in Atti di Convegno]
Schramm, A. E.; Leonelli, L.; Sorrentino, S.
abstract

A minimal three degrees of freedom model is developed and used to investigate unstable modes during high roll angle and acceleration maneuvers. During high roll angle maneuvers, it is found that there are unstable modes in the 6 Hz to 9 Hz range. The modes share similar characteristics to that of the unstable driveline or “chatter” mode found in braking maneuvers, except at a lower frequency caused by the higher inertia about the roll axis, which is the facilitating factor to the tire vertical oscillations. Power analysis shows that a combination of tire frictional characteristics and governing relationships can lead to a phase lag between tire forces and tire slip velocities that causes to instability, and eigenvalue sensitivity analysis shows which modeling parameters have the most effect on the stability boundaries.

2022 - Motorcycle Driveline Stability in a Minimal Model Including Roll Angle During a Braking Maneuver [Relazione in Atti di Convegno]
Schramm, A. E.; Leonelli, Luca.; Sorrentino, S.
abstract

A minimal, three degrees of freedom model for the rear of a racing motorcycle is developed to study the effects of roll angle on the stability of the driveline mode, also known as “chatter”, under a heavy braking maneuver. It is found that the added roll angle degree of freedom does not play a large role in the unstable mode, but its addition to the linearized equations of motion does add to the instability of the system. This is attributed to the working point of the tire tangential forces changing as more lateral force is introduced. The mode becomes unstable during the given maneuver with a frequency of around 19 Hz. Power analysis reveals the source of instability, and that the longitudinal tire force gradients can change the stability by changing the phase relationship of the longitudinal force and slip velocity. Eigenvalue sensitivity analysis shows that splitting the rear-hop and driveline mode frequencies also leads to stability, and so does reducing the chain-to-swingarm angle.

2022 - Nonlinear effects on the self-excited oscillations known as motorcycle chatter [Relazione in Atti di Convegno]
Schramm, Alexander; Sorrentino, Silvio; DE FELICE, Alessandro
abstract

Nonlinear effects on the stability of the motorcycle rear ‘chatter’ phenomenon are investigated by means of a minimal two degrees of freedom model. Motorcycle ‘chatter’ consists of a self-excited oscillation which occurs during braking manoeuvres in the frequency range between 17 and 20 Hz. It causes loss of rider confidence and leads to decreased performance. The study of the linearised system gives indications on the initiation of self-excited vibrations and thus helps to prevent them using proper design techniques, while nonlinear analysis can lead to completely new insights. Post-bifurcation behaviour is analysed focusing on limit cycles, studied by means of an application of the harmonic balance method. This allows the detection of the validity of the linear results, and to identify the most influential parameters in limit cycle generation, their amplitude, and their stability.

2021 - A method for the experimental identification of equivalent viscoelastic models from vibration of thin plates [Articolo su rivista]
Grosso, Pasquale; DE FELICE, Alessandro; Sorrentino, Silvio
abstract

Aim of the present study is the identification of equivalent viscoelastic models for layered thin walled structures, obtained from vibration measurement only, able to fit the experimental data on a relatively wide frequency range by means of a minimum number of parameters. A novel approach is proposed, based on a definition of an equivalent modal damping ratio applied to the circle-fit technique, to overcome the difficulties related to the identification of modal parameters when adopting non-conventional viscoelastic models. When the structural internal dissipative effects are dominant, this procedure identifies the parameters of an equivalent Young’s modulus in the frequency domain, representing the viscoelastic properties of a homogenized structure as a scalar function with frequency-dependent real and imaginary parts. The proposed procedure is applied to the analysis of Aluminum plates coated by damping pads and of plates made by Quiet Aluminum. To fit the experimentally found equivalent modal damping ratios, several viscoelastic models are adopted and compared (viscous, hysteretic, generalized Maxwell, fractional derivative damping, and in particular the Fractional Kelvin-Voigt model), assessing the accuracy of the identified parameters by comparison of numerically simulated with experimentally measured frequency response functions

2021 - Damping and gyroscopic effects on the stability of parametrically excited continuous rotor systems. [Articolo su rivista]
DE FELICE, Alessandro; Sorrentino, Silvio
abstract

This study is aimed at analysing damping and gyroscopic effects on the stability of parametrically excited continuous rotor systems, taking into account both external (non-rotating) and internal (rotating) damping distributions. As case-study giving rise to a set of coupled differential Mathieu-Hill equations with both damping and gyroscopic terms, a balanced shaft is considered, modelled as a spinning Timoshenko beam loaded by oscillating axial end thrust and twisting moment, with the possibility of carrying additional inertial elements like discs or flywheels. After discretization of the equations of motion into a set of coupled ordinary differential Mathieu-Hill equations, stability is studied via eigenproblem formulation, obtained by applying the harmonic balance method. The occurrence of simple and combination parametric resonances is analysed introducing the notion of characteristic circle on the complex plane and deriving analytical expressions for critical solutions, including combination parametric resonances, valid for a large class of rotors. A numerical algorithm is then developed for computing global stability thresholds in presence of both damping and gyroscopic terms, also valid when closed-form expressions of critical solutions do not exist. The influence on stability of damping distributions and gyroscopic actions is then analysed with respect to frequency and amplitude of the external loads on stability charts in the form of Ince-Strutt diagrams.

2021 - Experimental identification of equivalent viscoelastic models for vibrating plates. [Relazione in Atti di Convegno]
Grosso, Pasquale; De Felice, Alessandro; Sorrentino, Silvio
abstract

Aim of the present study is the identification of equivalent viscoelastic models for layered plates, obtained from vibration measurements only, able to fit the experimental data on relatively broad frequency ranges by means of a minimum number of parameters. A novel approach is proposed, based on a definition of an equivalent modal damping ratio applied to the circle-fit technique, to overcome the difficulties related to the identification of modal parameters when adopting non-conventional viscoelastic models. If the structural internal dissipative effects are dominant, this procedure identifies the parameters of an equivalent Young’s modulus in the frequency domain, representing the viscoelastic properties of a homogenized structure as a scalar function with frequency-dependent real and imaginary parts. The proposed procedure is applied to the analysis of Aluminum plates coated by damping pads and of plates made by Quiet Aluminum. To fit the experimentally found equivalent modal damping ratios, the linear Fractional Kelvin-Voigt viscoelastic model is adopted, assessing the accuracy of the identified parameters by comparison of numerically simulated with experimentally measured frequency response functions.

2021 - Nonlinear investigation into the motorcycle chatter phenomenon using numerical simulation. [Relazione in Atti di Convegno]
Schramm, Alexander; Sorrentino, Silvio; DE FELICE, Alessandro
abstract

A minimal, two degrees of freedom model is used to investigate the nonlinear effects on the stability of the motorcycle rear ‘chatter’ phenomenon, which occurs during braking manoeuvres and has a frequency of approximately 20 Hz. Numerical simulations using the full non-linear equations of motion are performed at stable, neutral, and unstable equilibria, and with different initial conditions to investigate the nonlinear effects when compared to the linearised response. Attention is focused on the existence, stability, and amplitude of limit cycles in order to understand which are the most influential nonlinear terms and parameters, and in which conditions the results of linear analysis are still predictable.

2021 - Patter instability of racing motorcycles in straight braking manoeuvre [Articolo su rivista]
Cattabriga, Stefano; De Felice, Alessandro; Sorrentino, Silvio
abstract

The front wheel of a motorcycle during heavy braking in straight motion can lock before reaching the maximum longitudinal braking force, a problem affecting especially performances of road racing motorcycles. This is preceded by a self–excited vibration, referred to as front wheel patter, in the frequency range between 7 and 10 Hz. Aim of the present study is the identification of the actual switching mechanism to instability together with its governing parameters. A minimal model of the front assembly of a motorcycle is proposed, and its stability in equilibrium configurations is studied via eigenvalue analysis. The sensitivity with respect to all its governing parameters is analyzed by means of stability maps and the self–excitation mechanism is explained with the aid of energy balance analysis and phase–diagrams. The results are compared to those existing in the literature and to numerical simulations obtained from a full motorcycle multibody model.

2021 - Stability analysis of articulated bus in straight-ahead running manoeuvre [Articolo su rivista]
DE FELICE, Alessandro; Mercantini, Matteo; Sorrentino, Silvio
abstract

A comprehensive study on the stability of a planar linearized single-track model of a two-section pusher articulated bus is presented with the aid of a complete set of stability maps. The two sections of the vehicle model are connected at the hitch point by a revolute joint; an equivalent visco-elastic characteristic function describes its rotational visco-elastic properties, playing a major role in stability control and therefore in passive safety. The equations of motion are derived in analytical form, allowing easy implementation of the non-linear model (eventually including a non-linear viscoelastic characteristic functions of the joint). Stability of the linearized model is then studied in equilibrium configurations by means of sensitivity analysis with respect to the model’s governing parameters. Stability maps are drawn on the basis of sets of parameter values related to straight-ahead running, steady-state manoeuvres. The most important parameters controlling the onset of unstable motions are identified, paying attention to the role played by the equivalent rotational damping coefficient and the equivalent torsional stiffness characterizing the connection joint, with the aim of finding criteria for its design.

2020 - A new application of the Extended Kalman filter to the estimation of roll angles of a motorcycle with Inertial Measurement Unit [Articolo su rivista]
Romualdi, Lorenzo; Mancinelli, Nicolò; DE FELICE, Alessandro; Sorrentino, Silvio
abstract

The capability of providing a real–time reliable measure of the actual roll angle is of great importance for the racing motorcycle dynamics. This study presents a method based on an Extended Kalman Filter (EKF) for the estimation of the actual roll angle of a motorcycle equipped with an Inertial Measurement Unit (IMU), with the advantage of not needing the development and implementation of a complete motorcycle model. Measured data which, depending on the additional instrumentation available on the motorcycle, do not form a complete set of input data for the estimation algorithm, induce the introduction of approximations affecting the accuracy of the results. A thorough error analysis is carried out by means of numerical simulations along with experimental validations. As a result, a novel approximate form for the kinematical model of the IMU is developed, yielding an overall good accuracy in the roll angle estimates.

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

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

2020 - Experimental identification of viscoelastic properties of vibrating plates [Relazione in Atti di Convegno]
Grosso, Pasquale; DE FELICE, Alessandro; Sorrentino, Silvio
abstract

Aim of the present study is the identification of equivalent viscoelastic models for layered thin walled structures, obtained from vibration measurement only, able to fit the experimental data on a wide frequency range by means of a minimum number of parameters. An identification method of general validity is proposed, based on the concept of equivalent modal damping ratio and on the classical circle-fit technique. It is applied to the analysis of both Aluminum plates coated by damping pads and plates made by Quiet Aluminum. To fit the experimentally found equivalent modal damping ratios, the linear Fractional Kelvin viscoelastic model is adopted, assessing the accuracy of the identified parameters by comparison of numerically simulated with experimentally measured frequency response functions.

2020 - Front wheel patter instability of motorcycles in straight braking manoeuvre [Relazione in Atti di Convegno]
Cattabriga, Stefano; DE FELICE, Alessandro; Segatori, Davide; Sorrentino, Silvio
abstract

The front wheel of a motorcycle during heavy braking in straight motion can lock before reaching the maximum braking force. Before front locking, a self-excited vibration occurs, referred to as front wheel patter, in the frequency range between 7 and 10 Hz. In the present study the actual switching mechanism to instability is identified, together with its governing parameters. A minimal model of the front assembly of a motorcycle is defined, and its stability in equilibrium configurations is studied via eigenvalue analysis. The sensitivity with respect to all its governing parameters is analyzed by means of stability maps and the self-excitation mechanism is explained with the aid of energy balance analysis and phase-diagrams. The results are compared to those existing in the literature and to numerical simulations obtained from a full motorcycle multibody model.

2020 - Stability analysis of parametrically excited gyroscopic systems [Relazione in Atti di Convegno]
DE FELICE, Alessandro; Sorrentino, Silvio
abstract

This study is aimed at analyzing and clarifying gyroscopic effects on the stability of parametrically excited rotor systems, a topic which in the literature is not sufficiently investigated. As case–study giving rise to a set of coupled differential Mathieu–Hill equations with both gyroscopic and damping terms, a balanced shaft is considered, modelled as a spinning Timoshenko beam loaded by oscillating axial end thrust and twisting moment, with possibility of carrying additional inertial elements. After discretization of the equations of motion into a set of coupled ordinary differential Mathieu-Hill equations, stability of Floquet solutions is studied via eigenproblem formulation, obtained by applying the harmonic balance method. A numerical algorithm is then developed for computing global stability thresholds in presence of both gyroscopic and damping terms, aimed at reducing the computational load. Finally, the influence on stability of the main characteristic parameters of the shaft is analyzed with respect to frequency and amplitude of the external loads on stability charts in the form of Ince-Strutt diagrams. As a result, it has been demonstrated that gyroscopic terms produce substantial differences in both critical solutions and stability thresholds: the former are generally non-periodic limited-amplitude functions, and modifications induced on stability thresholds consist of shifts and merging of unstable regions, depending on the separation of natural frequencies into pairs of forward and backward values.

2019 - First assessment on suspension parameter optimization for a solar–powered vehicle [Relazione in Atti di Convegno]
Sorrentino, Silvio; DE FELICE, Alessandro; Grosso, Pasquale; Minak, Giangiacomo
abstract

Optimization of suspension parameters with respect to comfort and road holding is a challenging issue for solar–powered cars, due to in–wheel electric engines on very light vehicles, carrying payloads which can exceed their total mass. The solar–powered car considered in this study was designed and manufactured for racing by the University of Bologna; with a mass of 300 kg and a payload of 320 kg due to four occupants, using 5 m2 of monocrystalline silicon photovoltaic panel on the roof, 64 kg of lithium–ion batteries and two electric engines coupled directly to the rear wheels, it can achieve either a range of 600 km at cruising speed, or velocitiy peaks of 120 km/h. In this cantribution, equivalent vertical stiffness and equivalent damping coefficients are optimized for both axles, achieving results that in terms of comfort and road holding are comparable to those of standard passenger cars.

2019 - In–plane vibration analysis of plates with periodic skeletal truss micro–structures [Articolo su rivista]
DE FELICE, Alessandro; Sorrentino, Silvio
abstract

The present contribution analyzes the dynamic in–plane behaviour of two–dimen- sional finite lattices consisting of periodic micro–skeletal truss structures made either by bar or beam elements. An homogenization asymptotic technique, employing the Fourier transform of the dynamic equilibrium equations of the discretized medium, is applied to derive the partial differential equations describing the in–plane vibration of an equivalent homogeneous plate. The resulting set of partial differential equations is then analyzed for deriving explicit relationships between reference–cell properties and homogenized continuum properties, i.e. parent material properties. Specific selection criteria are found for geometric and material parameters of the reference–cell in view of getting orthotropic as well as isotropic homogenized plates. Finally, the effects of micro–structural properties on the vibrating behaviour of the homogenized plate are investigated in terms of modal analysis, studying their influence on natural frequencies.

2019 - On the dynamic behaviour of rotating shafts under combined axial and torsional loads [Articolo su rivista]
De Felice, Alessandro; Sorrentino, Silvio
abstract

A comprehensive dynamic study on a distributed parameter model of a straight uniform rotating shaft is developed, aimed at presenting some clarifications and corrections to published results, together with novel contributions. The model includes the effects of transverse shear, rotatory inertia and gyroscopic moments with additional combined end thrust and twisting moment. The equations of motion are derived in both Newtonian and Lagrangian formulations according to the Timoshenko beam theory. A novel contribution is given in the development of complete modal analysis of the model under study, highlighting the properties of the operators involved and the relations among eigenfunctions represented in complex and real variables. The influence of the main governing parameters (slenderness ratio, angular velocity, external axial end thrust and twisting moment) is studied on natural frequencies, modal shapes and critical speeds of the rotor. New evidence of existence of a second frequency spectrum in the Timoshenko beam theory is presented, together with a novel definition for its identification, only possible if considering gyroscopic effects.

2019 - On the stability of parametrically excited continuous gyroscopic systems [Relazione in Atti di Convegno]
DE FELICE, Alessandro; Sorrentino, Silvio
abstract

2019 - Passenger car steering pull and drift reduction considering suspension tolerances [Relazione in Atti di Convegno]
De Rosa, Mariano; DE FELICE, Alessandro; Fragassa, Cristiano; Sorrentino, Silvio
abstract

Pull to side, Steering wheel misalignment and Drift leeward are handling anomalies affecting passenger cars travelling on straight paths. They represent a cost factor in the automotive industry, occurring in small but not negligible percentage of the overall car production. The present contribution is aimed at understanding which are their causes in terms of suspension tolerances, and at reducing their extent, in the specific case of vehicles with front Double wishbone suspension and rear Five arms suspension. The most influential parameters on handling irregularities have been identified through a design of experiment analysis. Then, after performing a sensitivity analysis by multibody virtual modelling, a correlation with experimental data from presetting and wheel aligner benches has provided sufficient information for setting tolerance thresholds, able to keep the handling anomalies under study within acceptable bounds. Pull to side and Steering wheel misalignment have been found to be mainly related to the set up phase of wheel angles (front camber angles influencing Pull to side, front and rear toe angles influencing Steering wheel misalignment), while the main cause of Drift leeward has been identified with (rear) ride steer.

2019 - Power spectral density response of bridge–like structures loaded by stochastic moving forces [Articolo su rivista]
Sorrentino, Silvio
abstract

In this study simple and manageable closed form expressions are obtained for the mean value, the spectral density function and the standard deviation of the deflection induced by stochastic moving loads on bridge–like structures. As basic case, a simply supported beam is considered, loaded by a sequence of concentrated forces moving in the same direction, with random instants of arrival, constant random crossing speeds and constant random amplitudes. The loads are described by three stochastic processes, representing an idealization of vehicular traffic on a bridge in case of negligible inertial coupling effects between moving masses and structure. System’s responses are analytically determined in terms of mean values and power spectral density functions, yielding standard deviations, with the possibility to easily extend the results to more refined models of single span bridge–like structures. Potential applications regard structural analysis, vibration control and condition monitoring of traffic excited bridges.

2019 - Static stress analysis of suspension systems for a solar-powered car [Articolo su rivista]
Odabasi, Vuslat; Maglio, Stefano; Martini, Alberto; Sorrentino, Silvio
abstract

Suspension systems are designed aiming at providing adequate handling, road holding, comfort and vibration control to terrestrial vehicles. Being an important issue not only for regular road models, suspension design is a matter of concern that also regards solar electric cars, in which, due to limited power supply, stabilization and energy conservation are of utmost importance. Considering three basic types of suspension widely adopted in road vehicle design, this study presents a preliminary comparison among MacPherson, double wishbone and longitudinal arms with leaf spring systems, aimed at pointing out the most appropriate design for the solar-powered vehicle hereby considered. It includes a finite element static stress analysis, performed with parametric values for a quarter-car model.

2019 - Straight path handling anomalies of passenger cars induced by suspension component and assembly tolerances [Articolo su rivista]
De Rosa, Mariano; DE FELICE, Alessandro; Grosso, Pasquale; Sorrentino, Silvio
abstract

The effects on handling due to suspension component and assembly tolerances are analysed focusing on three anomalies affecting passenger cars travelling on straight paths, namely ‘pull to side’, ‘steering wheel misalignment’ and ‘drift leeward’. These anomalies do not constitute safety problems but represent a cost factor in the automotive industry since they occur in small but not negligible percentage of the overall car production. The present contribution is therefore focused on understanding which are their causes, and on reducing their extent, in the specific case of vehicles with front Double wishbone suspension and rear Five arms suspension. To this purpose, the vehicle assembly process is analysed in terms of errors and tolerances for identify the most influential parameters on handling irregularities. Sensitivity analysis by multibody virtual modelling, and subsequent correlation with experimental data from pre-setting and wheel aligner benches, have provide sufficient information for setting tolerance thresholds, able to keep the handling anomalies under study within acceptable bounds. As a result, ‘pull to side’ and ‘steering wheel misalignment’ has been found to be mainly related to the set up phase of wheel angles (front camber angles influencing pull to side, front and rear toe angles influencing steering wheel misalignment), while the main cause of ‘drift leeward’ has been identified with (rear) ride steer. Application of the procedure to a production line led to a consistent reduction (from 3% down to about 1% of the overall production) of anomalous vehicles.

2018 - Driveline instability of racing motorcycles in straight braking manoeuvre [Articolo su rivista]
Leonelli, Luca; Cattabriga, Stefano; Sorrentino, Silvio
abstract

Experimental evidence shows that a self-excited vibration may appear during braking manoeuvres performed by road-racing motorcycles. It involves vertical oscillation of front and rear wheel axles as well as angular oscillation of the driveline in a frequency range between 17 and 22 Hz. As a consequence, severe oscillations of the tyre-ground vertical loads can be observed, leading to a loss of grip and ultimately weakening the vehicle overall performance. Several contributions on this topic can be accounted for in the literature; however, a comprehensive description of the phenomenon has not been given yet. The present work is aimed at simulating the above vibration with a planar multibody motorcycle model, and then at analyzing its driving mechanism. Stability maps are drawn for time-invariant braking manoeuvres, and validated with respect to time domain simulations.

2018 - Dynamic analysis of rectangular plates crossed by distributed moving loads [Articolo su rivista]
Sorrentino, Silvio; Catania, Giuseppe
abstract

This study investigates the dynamic behaviour of plates crossed by distributed moving gravita-tional and inertial loads, in the case in which the relative magnitude of the moving mass introduces a coupling effect with the structure, with possible applications to vibration analysis of railway bridges. A rectangular Kirchhoff plate is considered, simply supported on two opposite edges and free on the other two edges, loaded by a partially distributed mass travelling in parallel direction with respect to the free edges. The formulation includes damping, and it is accomplished by the Rayleigh–Ritz method, expressing the solution in semi–analytical form. The shape functions for describing the transverse displacement field of the plate are selected as tensor products of linearly independent eigenfunctions of homogeneous uniform beams in flexural vibration, yielding a low order model with time–dependent coefficients. Numerical examples are then presented and discussed, aimed at investigating the effects of each of the model governing parameters.

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

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

2018 - Stability analysis of rotating shafts under axial and torsional periodic loads [Relazione in Atti di Convegno]
DE FELICE, Alessandro; Sorrentino, Silvio
abstract

A contribution is given to clarify gyroscopic effects on stability of parametrically excited rotor systems, highlighting the role played by stabilizing damping distributions. As case–study of general interest, giving rise to a set of coupled differential Mathieu–Hill equations with both gyroscopic and damping terms, a continuous perfectly balanced shaft is considered, modelled as a spinning Timoshenko beam loaded by oscillating axial end thrust and twisting moment. After discretization of the equations of motion into a set of coupled ordinary differential Mathieu–Hill equations, stability of Floquet solutions is studied via eigenproblem formulation, obtained by applying the harmonic balance method. A numerical algorithm is then developed for computing global stability thresholds in presence of both gyroscopic and damping terms, aimed at reducing the computational load. Finally, the influence on stability of the main characteristic parameters of the shaft is analyzed with respect to frequency and amplitude of the external loads on stability charts in the form of Ince–Strutt diagrams.

2018 - The second spectrum in Timoshenko beam theory: a new approach for its identification [Relazione in Atti di Convegno]
DE FELICE, Alessandro; Sorrentino, Silvio
abstract

The problem of existence and identification of a second frequency spectrum in the Timoshenko beam theory is reconsidered from a novel perspective, studying a Timoshenko beam rotating with constant angular speed about its longitudinal axis. The existence of a second spectrum in the case of non–rotating beams and general boundary conditions has been much debated in the literature, since it is possible to easily identify the companion natural frequencies constituting the second spectrum only in particular cases. Its existence in a non–rotating finite–length beam has been recently demonstrated on the basis of accurate experimental results, at least for free–free boundary conditions, and also by considering free waves in beams of infinite length. In this study new evidence of existence of a second spectrum together with a novel definition for its identification are presented, possible when considering gyroscopic effects. As a secondary result, it can be stated that the whole second spectrum gives no contribution to the forward critical speeds of the rotating beam.

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 - A study on the stability of a motorcycle wheel-swingarm suspension with chain transmission [Articolo su rivista]
Sorrentino, Silvio; Leonelli, Luca
abstract

The present study describes a possible driving mechanism for a self–excited oscillation observed in motorcycle dynamics, often referred to as chatter. This phenomenon, affecting the performance of road racing motorcycles, has been simulated in straight running braking manoeuvres with multibody motorcycle models. It involves rear suspension bounce and driveline oscillation in the frequency range between 17 and 22 Hz. A simplified model of a motorcycle rear suspension with chain transmission is proposed and its stability in equilibrium configurations is studied via eigenvalue analysis. The sensitivity with respect to all its governing parameters is analyzed by means of stability maps and the self–excitation mechanism is explained with the aid of energy balance analysis and phase diagrams. It is found that the key role for the instability onset is played by the gradient of the nonlinear characteristic slip function of the tyre.

2017 - Distributed parameter and finite element models for wave propagation in railway contact lines [Articolo su rivista]
Sorrentino, Silvio; Anastasio, Dario; Fasana, Alessandro; Marchesiello, Stefano
abstract

A distributed parameter model of a railway two–level catenary system is presented for the analysis of the coupled wave dynamics. The wires are modelled as two straight axis parallel beams, with linear equilibrium equations, and the moving load applied by the pantograph is modelled as a constant concentrated travelling force. The general solution is sought by an application of the Ritz–Galerkin method, and then compared with direct time integrations of a finite element model (FEM), achieved by two different integration schemes. The proposed model provides a valid reference for appropriately selecting the FEM parameters, in order to reduce the errors due to spurious modes, affecting the numerical integrations especially at high speeds of the moving pantograph.

2017 - Insights into the gyroscopic behaviour of axially and torsionally loaded rotating shafts [Relazione in Atti di Convegno]
DE FELICE, Alessandro; Sorrentino, Silvio
abstract

A distributed parameter model of a straight uniform shaft rotating at constant angular velocity is analytically investigated including the effects of transverse shear, rotatory inertia, gyroscopic moments and considering the additional contribution of combined end thrust and twisting moment. The equations of motion are derived by applying Hamilton’s principle according to the Timoshenko beam theory, and cast in dimensionless form to highlight the influence of the main governing parameters (slenderness ratio, angular velocity, applied external end thrust and twisting moment) on natural frequencies and critical speeds of the rotor. The results of this study constitute the basis for further developments, including comparison with finite element models and rotor stability analysis under combined loads.

2017 - In–plane vibration analysis of plates with periodic skeletal truss micro–structures [Relazione in Atti di Convegno]
DE FELICE, Alessandro; Sorrentino, Silvio
abstract

The present contribution focuses on the dynamic in–plane behaviour of two–dimen- sional lattices consisting of periodic micro–skeletal truss structures. An established homogenization asymptotic technique is applied to derive the partial differential equations describing the in–plane vibration of an equivalent homogeneous plate. A discretized formulation is adopted for studying a planar reticulated medium, whose periodic pattern in this specific case is described by a rectangular reference–cell composed by truss elements. The size of the reference–cell is assumed to be much smaller than the length–scale of the whole structure. The adopted homogenization technique employs the Fourier transform of the dynamic equilibrium equations in both the time and space domains, leading to the definition of the so–called symbol of the periodic structure, which embodies all its elastodynamic properties. Upon Taylor series expansions and inverse transformation, the asymptotic value of the symbol yields continuous dynamic equilibrium equations, whose solution describes the system’s response as the reference–cell characteristic dimension tend to zero. The resulting set of partial differential equations is then analyzed for deriving explicit relationships between reference–cell properties and homogenized continuum properties, i.e. parent material properties. Specific selection criteria are found for geometric and material parameters of the reference–cell in view of getting orthotropic as well as isotropic homogenized plates. Finally, the effects of micro–structural properties on the vibrating behaviour of the homogenized plate are investigated in terms of modal analysis, studying their influence on natural frequencies.

2016 - A study of motorcycle chatter vibration with multibody models of increasing complexity [Relazione in Atti di Convegno]
Leonelli, Luca; Mancinelli, Nicolò; Sorrentino, Silvio
abstract

The chatter phenomenon of road racing motorcycles consists of self-excited vertical oscillations of both the front and rear unsprung masses. Even though in recent years this problem has been studied by several authors, its causing factors are still not clear. In the present study three different motorcycle models of increasing complexity are considered, from planar to three-dimensional multibody, in order to investigate the possible driving mechanism generating this self-excited vibration, and consequently to identify which of the model features may play a role in the actual vibration onset.

2015 - Dynamical analysis of fluid lines coupled to mechanical systems taking into account fluid frequency-dependent damping and non-conventional constitutive models: part 1 – modelling fluid lines [Articolo su rivista]
Catania, Giuseppe; Sorrentino, Silvio
abstract

The design of hydraulic transmission systems for control and actuation requires accurate knowledge of their dynamic response: some standard techniques are known to obtain a consistent dynamic model of a fluid line, including the contribution of inertia, compressibility and friction. In this paper an efficient procedure is developed for simulating the dynamic response of a fluid line in both the frequency and time domains, focusing the attention on the modal analysis of a discretized model, in view of coupling with mechanical systems. A bi–dimensional approach is adopted, and the laminar flow frequency-dependent friction is modelled using non-integer order differential laws, which may improve the accuracy of the simulated responses in comparison with more traditional Newtonian models.

2015 - Dynamical analysis of fluid lines coupled to mechanical systems taking into account fluid frequency-dependent damping and non-conventional constitutive models: part 2 – coupling with mechanical systems. [Articolo su rivista]
Giuseppe, Catania; Sorrentino, Silvio
abstract

The design of hydraulic transmission systems for control and actuation requires accurate knowledge of their dynamic response: some standard techniques are known to obtain a consistent dynamic model of a fluid line, including the contribution of inertia, compressibility and friction. In this study an efficient procedure is developed for simulating the dynamic response of a fluid line coupled with mechanical systems, in both the frequency and time domains. A bi-dimensional approach is adopted for the fluid line, and the laminar flow frequency-dependent friction is modelled using non-integer order differential laws, which may improve the accuracy in comparison with more traditional Newtonian models. The coupling problem with mechanical systems is studied by means of both continuous models of the fluid line (yielding frequency response functions in exact analytical form), and discretized models of the fluid line (to express time response functions in approximate analytical form), foucusing on the damping properties of the resulting vibrating systems.

2013 - Analysis of friction in bi-dimensional pipe flow using non conventional constitutive models [Relazione in Atti di Convegno]
Catania, G.; Sorrentino, S.
abstract

The design of hydraulic transmission lines for control and actuation requires accurate knowledge of their dynamic response: some standard techniques are known to obtain a consistent dynamic model of a fluid line, including the contribution of inertia, compressibility and friction. In this paper an efficient procedure is developed for simulating the dynamic response in both the frequency and time domains, focusing the attention on the modal analysis of a discretized model of a fluid line. A bi-dimensional approach is adopted, modeling the laminar flow frequency-dependent friction by means of non-integer order differential laws, which may improve the accuracy of the simulated responses in comparison with more traditional Newtonian models. Copyright © 2013 by ASME.

2013 - Analysis of friction in bi-dimensional pipe-flow using non conventio- nal constitutive models (IMECE2013-66617). [Relazione in Atti di Convegno]
Giuseppe, Catania; Sorrentino, Silvio
abstract

The design of hydraulic transmission lines for control and actuation requires accurate knowledge of their dynamic response: some standard techniques are known to obtain a consistent dynamic model of a fluid line, including the contribution of inertia, compressibility and friction. In this paper an efficient procedure is developed for simulating the dynamic response in both the frequency and time domains, focusing the attention on the modal analysis of a discretized model of a fluid line. A bi-dimensional approach is adopted, modeling the laminar flow frequency-dependent friction by means of non-integer order differential laws, which may improve the accuracy of the simulated responses in comparison with more traditional Newtonian models.

2013 - Coupling mechanical systems and fluid transmission lines with bi-dimensional flow and non-conventional constitutive models. [Relazione in Atti di Convegno]
Giuseppe, Catania; Sorrentino, Silvio
abstract

The design of hydraulic transmission systems for control and actuation requires accurate knowledge of their dynamic response: some standard techniques are known to obtain a consistent dynamic model of a fluid line, including the contribution of inertia, compressibility and friction. In this study an efficient procedure is developed for simulating the dynamic response of a fluid line coupled with mechanical systems, in both the frequency and time domains. A bi-dimensional approach is adopted for the fluid line, and the laminar flow frequency-dependent friction is modelled using non-integer order differential laws, which may improve the accuracy in comparison with more traditional Newtonian models. The coupling problem with mechanical systems is studied by means of both continuous models of the fluid line (yielding frequency response functions in exact analytical form), and discretized models of the fluid line (to express time response functions in approximate analytical form).

2012 - Spectral modeling of vibrating plates with general shape and general boundary conditions [Articolo su rivista]
G., Catania; Sorrentino, Silvio
abstract

The analysis and design of lightweight plate structures require efficient computational tools, because exact analytical solutions for vibrating plates are currently known only for some standard shapes in conjunction with a few basic boundary conditions. This paper deals with vibration analysis of Kirchhoff plates of general shape with non-standard boundary conditions, adopting a Rayleigh-Ritz approach. Three different coordinate mappings are considered, using different kinds of functions: 1) trigonometric and polynomial interpolation functions for mapping the shape of the plate, 2) trigonometric and polynomial interpolation functions for mapping a constraint domain of general shape, 3) products of linearly independent eigenfunctions evaluated from a standard beam in flexural vibration for describing the transverse displacement field of the plate. Flexural free vibration analysis of different shaped plates is then performed using the same approach: skew, trapezoid and triangular plates, plates with parabolic curved edges, sectors of circular plates, circular and elliptic annular plates. Purely elastic plates are considered, but the method may also be applied to the analysis of viscoelastic plates. The results are compared with those available in the literature and using standard finite element analysis.

2011 - Dynamic analysis of railway bridges by means of the spectral method [Relazione in Atti di Convegno]
Catania, Giuseppe; Sorrentino, Silvio
abstract

This study investigates the dynamic behaviour of railway bridges crossed by travelling trains. A simplified formulation was adopted in order to perform a direct analysis of the effects of the parameters involved in the problem. The bridge is modelled as a rectangular plate, while the trains are modelled as travelling inertial distributed loads. The formulation is accomplished by the use of the Rayleigh-Ritz method, yielding a low order model with time-dependent coefficients. Several numerical examples are presented and discussed, aimed at investigating the effects of each of the model-governing parameters.

2011 - Pescara benchmark: overview of modelling, testing and identification [Relazione in Atti di Convegno]
A., Bellino; F., Brancaleoni; L., Bregant; A., Carminelli; G., Catania; A., Di Evangelista; S., Gabriele; L., Garibaldi; S., Marchesiello; Sorrentino, Silvio; D., Spina; C., Valente; L., Zuccarino
abstract

The “Pescara benchmark” is part of the national research project “BriViDi” (BRIdge VIbrations and DIagnosis) supported by the Italian Ministero dell’Università e Ricerca. The project is aimed at developing an integrated methodology for the structural health evaluation of railway r/c, p/c bridges. The methodology should provide for applicability in operating conditions, easy data acquisition through common industrial instrumentation, robustness and reliability against structural and environmental uncertainties. The Pescara benchmark consisted in lab tests to get a consistent and large experimental data base and subsequent data processing. Special tests were devised to simulate the train transit effects in actual field conditions. Prestressed concrete beams of current industrial production both sound and damaged at various severity corrosion levels were tested. The results were collected either in a deterministic setting and in a form suitable to deal with experimental uncertainties. Damage identification was split in two approaches: with or without a reference model. In the first case f.e. models were used in conjunction with non conventional updating techniques. In the second case, specialized outputonly identification techniques capable to deal with time-variant and possibly non linear systems were developed. The lab tests allowed validating the above approaches and the performances of classical modal based damage indicators.

2011 - Spectral analysis of vibrating plates with general shape [Relazione in Atti di Convegno]
Catania, Giuseppe; Sorrentino, Silvio
abstract

Lightweight plate structures are widely used in many engineering and practical applications. The analysis and design of such structures call for efficient computational tools, since exact analytical solutions for vibrating plates are currently known only for some standard shapes in conjunction with a few basic boundary conditions. The present paper deals with the adoption of a set of eigenfunctions evaluated from a simple structure as a basis for the analysis of plates with both general shape and general boundary conditions in the Rayleigh-Ritz condensation method. General boundary conditions are introduced in the functional of the potential energy by additional terms, and both trigonometric and polynomial interpolation functions are implemented for mapping the shape of the plate in Cartesian coordinates into natural coordinates. Flexural free vibration analysis of different shaped plates is then performed: skew, trapezoid and triangular plates, plates with parabolic edges, elliptic sector and annular plates. The proposed method can also be directly applied to variable thickness plates and non-homogeneous plates, with variable density and stiffness. Purely elastic plates are considered; however the method may also be applied to the analysis of viscoelastic plates. The results are compared to those available in the literature and using standard finite element analysis.

2009 - Experimental evaluation of the damping properties of beams and thin-walled structures made of polymeric materials [Relazione in Atti di Convegno]
Catania, Giuseppe; Sorrentino, Silvio
abstract

In the field of structural vibrations, an appropriate rheological model should be accurate in fitting the experimental data on a wide interval of frequencies by means of a minimum number of parameters and, in particular, it should be able to reproduce the experimentally found behavior of the damping ratio ζ n as a function of the natural angular frequency ω n. In this study a non-integer order differential linear rheological model is considered, discussing its effectiveness in solving the above mentioned problem. This model, refferred to as the Fractional Double Kelvin model, combines the properties of both the Fractional Kelvin and Fractional Zener models, which are considered to be very effective in describing the viscoelastic dynamic behavior of mechanical structures made of polymers. An identification method of general validity for viscoelastic models is adopted, based on the concept of equivalent damping ratio and on the circle-fit technique. It is applied to the analysis of vibrating beams and plates of different sizes, made of polymeric materials such as Polyethylene, Polyvinyl-chloride and Delrin.

2009 - Experimental validation of non-conventional viscoelastic models via equivalent damping estimates [Relazione in Atti di Convegno]
Catania, Giuseppe; Sorrentino, Silvio
abstract

Non-conventional rheological models based on non-integer order differential operators can be used to describe the viscoelastic behavior of materials, especially of polymers. These models are usually selected and then validated by means of creep and relaxation tests. However, engineers dealing with structural dynamic problems may need to obtain model identification from vibration measurement data. In this case, however, the direct identification of an optimal set of parameters of a viscoelastic model from time or frequency domain measurements is a difficult task, especially if the structural dissipative contributions are slight. In this paper, an indirect approach is adopted, based on the concept of damping ratio. When dealing with standard linear viscous dissipative models, a damping ratio modal parameter ζn can be analytically defined and experimentally estimated. But this theoretical parameter shows a dependency from the modal frequency that may dramatically fail in fitting the experimental data. On the contrary, it is known that a better agreement between theory and experiments can be achieved by means of non-integer order differential models, even though in this case analytical expressions for ζn are difficult to find. To overcome this difficulty, a method of general validity for viscoelastic models is developed, based on the concept of equivalent damping ratio and on the circle-fit technique. The proposed method is applied to experimental damping estimates from plane flexural vibrations of clamped-free beams, obtained from specimens of different size made of materials such as Polyethylene, Polyvinyl-chloride and Delrin.

2009 - Identification of non-conventional viscoelastic models for polymeric vibrating structures [Relazione in Atti di Convegno]
Catania, Giuseppe; Sorrentino, Silvio
abstract

In the field of structural vibrations, an appropriate rheological model should be accurate in fitting the experimental data on a wide interval of frequencies by means of a minimum number of parameters and, in particular, it should be able to reproduce the experimentally found behavior of the damping ratio ζn as a function of the natural angular frequency ωn. In this study a non-integer order differential linear rheological model is considered, and its effectiveness in solving the above mentioned problem is discussed. This model, refferred to as the Fractional Double Kelvin model, combines the properties of both the Fractional Kelvin and Fractional Zener models, which are considered to be very effective in describing the viscoelastic dynamic behavior of mechanical structures made of polymers. An identification method of general validity for viscoelastic models is adopted, based on the concept of equivalent damping ratio and on the circlefit technique. It is applied to the analysis of vibrating beams and plates of different sizes, made of polymeric materials such as Polyethylene, Polyvinyl-chloride and Delrin.

2009 - Rayleigh- Ritz analysis of vibrating plates based on a class of eigenfunctions [Relazione in Atti di Convegno]
Catania, G.; Sorrentino, S.
abstract

In the Rayleigh-Ritz condensation method the solution of the equation of motion is approximated by a linear combination of shape-functions selected among appropriate sets. Extensive literature dealing with the choice of appropriate basis of shape functions exists, the selection depending on the particular boundary conditions of the structure considered. This paper is aimed at investigating the possibility of adopting a set of eigenfunctions evaluated from a simple stucture as a general basis for the analysis of arbitrary-shaped plates. The results are compared to those available in the literature and using standard finite element analysis. Copyright © 2009 by ASME.

2009 - Rayleigh- Ritz analysis of vibrating plates based on a class of eigenfunctions [Relazione in Atti di Convegno]
Catania, Giuseppe; Sorrentino, Silvio
abstract

In the Rayleigh-Ritz condensation method the solution of the equation of motion is approximated by a linear combination of shape-functions selected among appropriate sets. Extensive literature dealing with the choice of appropriate basis of shape functions exists, the selection depending on the particular boundary conditions of the structure considered. This paper is aimed at investigating the possibility of adopting a set of eigenfunctions evaluated from a simple stucture as a general basis for the analysis of arbitrary-shaped plates. The results are compared to those available in the literature and using standard finite element analysis.

2008 - A condensation technique for the FE dynamic analysis with fractional derivative viscoelastic models [Articolo su rivista]
Giuseppe, Catania; Alessandro, Fasana; Sorrentino, Silvio
abstract

Fractional derivative rheological models are known to be very useful for describing the viscoelastic behaviour of materials, especially of polymers, and when applied to dynamic problems, the resulting equations of motion, after a fractional state-space expansion, can still be studied in terms of modal analysis. The increase in matrix dimensions produced by this expansion, however, is often so fast as to make the calculations too cumbersome for finite element applications. This article presents a condensation technique based on the computation of two reduced-size eigenproblems. The rheological model adopted is the fractional Zener (fractional standard linear solid) model, but the same methodology can be applied to problems using different fractional derivative linear models.

2008 - Discrete spectral modelling of continuous structures with fractional derivative viscoelastic behaviour [Relazione in Atti di Convegno]
Catania, Giuseppe; Sorrentino, Silvio
abstract

Fractional derivative rheological models were recognised to be very effective in describing the viscoelastic behaviour of materials, especially of polymers, and when applied to dynamic problems the resulting equations of motion, after a fractional state-space expansion, can still be studied in terms of modal analysis. But the growth in matrix dimensions brought about by this expansion is in general so fast as to make the calculations too cumbersome. In this paper a discretization method for continuous structures is presented, based on the Rayleigh-Ritz method, aimed at reducing the computational effort. The solution of the equation of motion is approximated by a linear combination of shapefunctions selected among the analytical eigenfunctions of standard known structures. The resulting condensed eigen-problem is then expanded in a low dimension fractional statespace. The Fractional Standard Linear Solid is the adopted rheological model, but the same methodology could be applied to problems involving different fractional derivative linear models. Examples regarding two different continuous structures are proposed and discussed in detail.

2007 - Analysis of frequency-dependent friction in transient pipe-flow using non-integer order derivative models [Relazione in Atti di Convegno]
Catania, Giuseppe; Sorrentino, Silvio
abstract

The design of hydraulic transmission lines for control and actuation requires accurate knowledge of their dynamic response. Some standard techniques are known to obtain a consistent dynamic model of a fluid line, including the contribution of inertia, compressibility and friction. In this paper an efficient procedure is developed for simulating frequency-dependent friction in transient laminar liquid flow. This is investigated by means of a bi-dimensional approach and the laminar flow frequency-dependent friction is modelled using non-integer order derivatives, which may consistently improve the accuracy of the simulated line response in comparison with more traditional newtonian models. The results of the theoretical analysis are compared with experimental data obtained from frequency-response tests, and discussed in detail.

2007 - Analysis of non-homogeneous Timoshenko beams with generalized damping distributions [Articolo su rivista]
Sorrentino, Silvio; A., Fasana; S., Marchesiello
abstract

This paper presents a study on the effects of generalized damping distributions on non-homogeneous Timoshenko beams. On the basis of some fundamentals of modal analysis for damped continuous systems applied to the particular case of the Timoshenko beam model, the eigenproblem is solved by applying a method combining a state-space representation with a transfer matrix technique, yielding closed-form expressions for the eigenfunctions. After validation by means of numerical examples using the Finite Element Method, response functions in both the time and the frequency domain are discussed and compared according to different damping distributions.

2007 - Analytical modelling and experimental identification of viscoelastic mechanical systems [Capitolo/Saggio]
Catania, Giuseppe; Sorrentino, Silvio
abstract

In the present study non-integer order or fractional derivative rheological models are applied to the dynamical analysis of mechanical systems. Their effectiveness in fitting experimental data on wide intervals of frequency by means of a minimum number of parameters is first discussed in comparison with classical integer order derivative models. A technique for evaluating an equivalent damping ratio valid for fractional derivative models is introduced, making it possible to test their ability in reproducing experimentally obtained damping estimates. A numerical procedure for the experimental identification of the parameters of the Fractional Zener rheological model is then presented and applied to a high-density polyethylene (HDPE) beam in axial and flexural vibrations.

2007 - Finite element analysis of linear systems with fractional derivative damping models [Articolo su rivista]
Sorrentino, Silvio; A., Fasana
abstract

This paper presents a method for reducing the computational effort due to finite element analysis of vibrating linear systems with fractional derivative viscoelastic models. Fractional derivative rheological models are known to be very effective in describing the viscoelastic behaviour of materials, especially of polymers, and when applied to dynamic problems the resulting equations of motion, after a fractional state-space expansion, can still be studied in term of modal analysis. But the growth in matrix dimensions carried by this expansion is in general so fast to make the calculations too cumbersome for finite element applications. However, according to the technique proposed in this paper, the computational effort can be taken under control by reducing the main eigenproblem of large dimension to the solution of two related eigenproblems of lower size. Numerical examples are provided in order to validate both the accuracy and the efficiency of the proposed methodology.

2006 - Finite element analysis of vibrating non-homogeneous beams with fractional derivative viscoelastic models [Relazione in Atti di Convegno]
Catania, Giuseppe; Fasana, Alessandro; Sorrentino, Silvio
abstract

Fractional derivative rheological models are known to be very effective in describing the viscoelastic behaviour of materials, especially of polymers, and when applied to dynamic problems the resulting equations of motion, after a fractional state-space expansion, can still be studied in terms of modal analysis. However the growth in matrix dimensions carried by this expansion is in general so fast to make the calculations too cumbersome for finite element applications. This paper presents a condensation technique based on the computation of two reduced-size eigenproblems. The rheological model adopted is the Fractional Zener or Fractional Standard Linear Solid model, but the same methodology applies to problems involving different fractional derivative linear models.

2006 - Fractional derivative linear models for describing the viscoelastic dynamic behaviour of polymeric beams [Relazione in Atti di Convegno]
Catania, Giuseppe; Sorrentino, Silvio
abstract

Non integer, fractional derivative order rheological models are known to be very effective in describing the linear viscoelastic dynamic behavior of mechanical structures made of polymers. The application of fractional calculus to viscoelasticity can be physically consistent and the resulting non integer order differential stress-strain constitutive relation provides good curve fitting properties, requires only a few parameters and leads to causal behavior. In this paper a fractional Zener model is adopted for describing the viscoelastic dynamic behavior of High Density Polyethylene (HDPE) beams. A procedure for estimating an equivalent damping ratio is introduced, in order to check the ability of the selected model in reproducing experimentally obtained damping estimates. A frequency domain technique is then proposed to compute the frequency dependent complex stress-strain relationship parameters related to the material.

2005 - Experimental identification of a fractional derivative linear model for viscoelastic materials [Relazione in Atti di Convegno]
G., Catania; Sorrentino, Silvio
abstract

Non integer, fractional order derivative rheological models are known to be very effective in describing the linear viscoelastic dynamic behaviour of mechanical structures made of polymers. The application of fractional calculus to viscoelasticity can be physically consistent and the resulting non integer order differential stress-strain constitutive relation provides good curve fitting properties, requires only a few parameters and leads to causal behaviour. When using such models the solution of direct problems, i.e. the evaluation of time or frequency response from a known excitation can still be obtained from the equations of motion using standard tools such as modal analysis. But regarding the inverse problem, i.e. the identification from measured input-output vibrations, no general technique has so far been established, since the current methods do not seem to easily work with differential operators of non integer order. In this paper a frequency domain method is proposed for the experimental identification of a linear viscoelastic model, namely the Fractional Zener also known as Fractional Standard Linear Solid, to compute the frequency dependent complex stress-strain relationship parameters related to the material. The procedure is first checked with respect to numerically generated frequency response functions for testing its accuracy, and then to experimental inertance data from a free-free homogeneous beam made of High Density Polyethylene (HDPE) in plane flexural and axial vibration.

2005 - Frequency domain analysis of a fractional derivative SDOF system [Relazione in Atti di Convegno]
Sorrentino, Silvio; L., Garibaldi
abstract

This paper presents a study of the frequency domain behaviour of a single degree of freedom (SDOF) system with a fractional derivative model, named Fractional Kelvin-Voigt. Frequency response functions (FRFs) as receptance and transmissibility are analytically studied. Then the model is applied to describe the dynamic behaviour of a magnetomechanic system in the frequency domain, consisting of a body of para or dia-magnetic material vibrating in a field created by a pair of magnets.

2004 - Frequency domain analysis of continuous systems with viscous generalized damping [Articolo su rivista]
Sorrentino, Silvio; A., Fasana; S., Marchesiello
abstract

This paper deals with the effects of generalized damping distributions on vibrating linear systems. The attention is focused on continuous linear systems with distributed and possibly non-proportional viscous damping, which are studied in terms of modal analysis, defining and discussing the orthogonality properties of their eigenfunctions. Exact expressions of the frequency response functions obtained by direct integration of the equations of motion are compared with the analogous formulas based on the superposition of modes. In addition, approximate expressions of the frequency response functions of both continuous and discrete (finite element models) systems in terms of their undamped eigenfunctions / eigenvectors are also considered and discussed. The presented methods are explained, compared and validated by means of numerical examples on a clamped-free Euler-Bernoulli beam.

2004 - Modal analysis of continuous systems with damping distributions defined according to fractional derivative models [Relazione in Atti di Convegno]
Sorrentino, Silvio; L., Garibaldi
abstract

In this paper vibrating continuous linear systems with generalized damping distributions defined according to fractional derivative models are studied in terms of modal analysis, defining and discussing the orthogonality properties of their eigenfunctions. Closed form expressions are presented for the response functions both in the time and in the frequency domain. The attention is focused on the impulse response functions and the receptances, the former enabling the calculation of both transients and responses due to arbitrary distributions of external forces. In particular, the free response problem is analyzed considering different ways of expressing the initial conditions. As a numerical example, the developed theoretical tools are applied to the study of a viscoelastic cantilever Euler-Bernoulli beam.

2003 - A new analytical technique for vibration analysis of non-proportionally damped beams [Articolo su rivista]
Sorrentino, Silvio; S., Marchesiello; B. A. D., Piombo
abstract

Vibrating linear mechanical systems, in particular continuous systems, are often modelled considering proportional damping distributions only, although in many real situations this simplified approach does not describe the dynamics of the system with sufficient accuracy. In this paper an analytical method is given to take into account the effects of a more general viscous damping model, referred to as non-proportional damping, on a class of vibrating continuous systems. A state-form expansion applied in conjunction with a transfer matrix technique is adopted to extract the eigenvalues and to express the eigenfunctions in analytical form, i.e., complex modes corresponding to non-synchronous motions. Numerical examples are included in order to show the efficiency of the proposed method; non-proportional damping distributions of different type, such as internal and external lumped or distributed viscous damping, are tested on non-homogeneous Euler-Bernoulli beams in bending vibration with different boundary conditions. Finally, a discussion on root locus diagrams behaviour and on modal damping ratio significance for non-proportionally damped systems is presented.

2002 - An experimental validation of complex damping and fractional derivative models on vibrating structures under magnetic effects [Relazione in Atti di Convegno]
B. A. D., Piombo; Sorrentino, Silvio; E., Bonisoli
abstract

The paper presents a comparison between dynamic models with complex viscous-type damping coefficients and dynamic models with fractional derivative damping terms in order to describe the behaviour of vibrating paramagnetic or diamagnetic conductible structures interacting with rare-earth permanent magnets. A complex viscous damping model is derived from a magnetic theoretical model, which predicts both a viscous damping effect and an interesting dynamic stiffening due to eddy currents. The complex viscous damping model is then compared and related to a fractional derivative model, suitable to extend the analysis in transients. Finally, theoretical and experimental results are compared for a uniform cantilever clamped-free beam, whose frequency response is modified by the presence of a pair of discordant magnets settled at the free end

2001 - An error estimate for CVA [Capitolo/Saggio]
Fasana, A.; Garibaldi, L.; Marchesiello, S.; Sorrentino, Silvio
abstract

The Canonical Variate Analysis has been applied in many circumstances as a powerful dynamic identification tool. Its capability of overcoming the high modal density matter is also improved by implemented special tools such as Probability Density Function and Modal Assurance Criterion stabilisation, making the CVA technique very reliable to monitor systems with unknown imput. Such a situation frequently occours due to the practical impossibility of measuring the imput dynamic load, as in the case of a bridge excited by traffic or in the case of a car running over a rough pavement. In this paper it is shown how the data processing can be improved by following some guidelines, based on an analytical approach to the model order choice, problem coupled with the already mentioned tools, i.e the PDF and the MAC functions.

2001 - Application of the CVA-BR method to the Z24 Bridge vibration data [Relazione in Atti di Convegno]
S., Marchesiello; B. A. D., Piombo; Sorrentino, Silvio
abstract

In this paper the Canonical Variate Analysis (CVA) is applied to accelometric measurements. The data are relative to the Z24 bridge located in Canton Bern (Switzerland) and were sampled during full scale tests carried out as validation of vibration monitoring on bridges. Frequencies and mode shapes obtained by means of the described procedure are compared with those obtained by other authors also presenting their results in this conference.

2001 - Recent Advances in Identification and Fault Detection on Bridge Structures [Relazione in Atti di Convegno]
L., Garibaldi; S., Marchesiello; A., Fasana; E., Giorcelli; D., Sabia; Sorrentino, Silvio
abstract

The paper resumes the activity of the authors concerning the development of a monitoring tool (BriViD project), whic has been successfully applied in the field of bridge maintenance and sourveillance. This tool is based on a miscellaneous of different techniques, such as advanced signal processing, FEM and analytical methods, up-dating techniques.

2001 - Viscoelastically damped plates: a comparison of analytical approaches [Relazione in Atti di Convegno]
B. A. D., Piombo; E., Bonisoli; A., Fasana; Sorrentino, Silvio
abstract

The passive reduction of vibration in structures by means of viscoelastic materials has been investigated by a number of researchers in the past decades and, starting from the earlier studies, great attention was dedicated to the analysis of beams and plates with various damping treatments. This work presents a comparison of the results obtained by applying four analytical approaches and a finite element model to the problem of determining the complex modal frequencies of simply supported plates containing a constrained damping layer.