- Ecole Centrale de Lyon
LTDS UMR 5513
36 avenue Guy de Collongue
69134 Ecully cedex
France - +33(0)4 72 18 64 66
- Personal website: http://jean-jacques.sinou.fredit
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Research Interests: Physics and Humanities
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During the past decades, numerous studies have been done to understand and to model the nonlinear phenomena in structural dynamics. Most of these models deal with deterministic parameters. But in these systems, geometrical, materials and... more
During the past decades, numerous studies have been done to understand and to model the nonlinear phenomena in structural dynamics. Most of these models deal with deterministic parameters. But in these systems, geometrical, materials and non linear parameters are often uncertain due to the manufacturing process for example. The effects of uncertainties on the nonlinear dynamic responses remain misunderstood and most of the classical stochastic methods used in the linear case fail to solve a non linear problem. The Multi- Harmonic Balance Method is one of the most classical mathematical approaches to determine the nonlinear stationary response of mechanical systems with regular or non-regular non-linearities. To take into account uncertainties into non linear models, few methods have been developped e.g. the Monte Carlo simulations or the perturbation methods. However, these methods in the non linear case are either not enough accurate or difficult to implement or too costly. For example, the most general technique Monte Carlo Simulations, adapted for linear or non-linear problems, generates samples of the random input parameters and solve the determinist problem for each one. This method has then a high computational cost since a high number of samples is necessary to obtain the convergence of this method : it is then not realistic when the deterministic problems are already high-dimensional problems. Then, here, we choose another method that belongs to the parametric methods : the Polynomial Chaos Expansion that allows to reduce the computational cost. This method has proved its robustness and efficiency on linear dynamic problems. Here, it is extended on one non linear problem indeed by being coupled with the Multi- Harmonic Balance Method. Besides, the Multi- Harmonic Balance Method has to be used with an alternating time-frequency approach (AFT) in order to evaluate the non linear forces. Here again, to integrate the uncertainties into the stochastic model, we will use either an Alternating Frequency Time method with Probabilistic Collocation that is a theoretical extension of AFT for nonlinear mechanical systems with presence of uncertainties. To demonstrate the robustness and the efficiency of this new mixed method, the non linear dynamic response of the mechanical system in case of presence of various uncertainties will be investigated for mono or multiple excitation frequencies. The effects of the following three kinds of nonlinearities will be examined: cubic stiffness, contact/no contact, systems with frictional interface. Finally, the case of a non linear rotor system will be treated. Besides, a comparison of the results will be done with those obtained from the Monte Carlo Simulations.
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Aeronautical structures are commonly assembled with bolted joints in which friction phenomena provide damping on the dynamic behaviour. Some models, mostly non linear, have consequently been developed and the harmonic balance method (HBM)... more
Aeronautical structures are commonly assembled with bolted joints in which friction phenomena provide damping on the dynamic behaviour. Some models, mostly non linear, have consequently been developed and the harmonic balance method (HBM) is adapted to compute non linear response functions in the frequency domain. The basic idea is to develop the response as a Fourier series and to solve equations linking Fourier coefficients. One specific HBM feature is that response accuracy improves as the number of harmonics increases, at the expense of larger computational time. Thus the aim of this study is to develop an adaptive HBM which appreciates numerically the contribution of each harmonic on the dynamic response. For a given precision, the number of retained harmonics is adapted by an algorithm which integrates a numerical criterion based on an approximate strain energy. The application case is an asymmetrical two cantilever beam system linked by a bolted joint represented by a nonlinear LuGre model. Condensation and continuation methods are used to accelerate calculation. Adaptive HBM shows that, for a given value of the criterion, the number of harmonics may increase on resonances indicating that non linear effects are predominant.
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Le crissement est un bruit strident frequemment produit par les systemes de freinage. Dans le milieu ferroviaire, des releves de niveau acoustique ont montre que le rissement du a l'arrivee en gare de certains trains pouvait atteindre... more
Le crissement est un bruit strident frequemment produit par les systemes de freinage. Dans le milieu ferroviaire, des releves de niveau acoustique ont montre que le rissement du a l'arrivee en gare de certains trains pouvait atteindre 110 dB a un metre du bord du quai. Ainsi, la problematique liee au crissement de freins a disque ferroviaires vise a traiter la gene occasionnee par le crissement, principalement pour les passagers presents sur le quai lors de l'arrivee d'un train en gare, mais aussi pour les riverains et le personnel present dans les gares. Cette etude vise donc a mieux comprendre les phenomenes vibratoires et mecanismes generes lors de l'apparition du crissement des freins a disque ferroviaires. Pour ce faire, des essais experimentaux varies, ainsi que des confrontations avec des modeles elements finis et simulations numeriques complexes sont proposes. Cette etude s'insere plus globalement dans le projet de recherche AcouFren, subventionne par l'ADEME, dont l'objectif est de proposer de developper des outils d'aide a la specification et a la conception de freins a disque ferroviaires optimises vis-a-vis du crissement.
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Cette etude s'interesse a l'influence des fissures transversales sur les systemes tournants. Les variations des frequences propres ainsi que le changement du comportement dynamique du systeme fissure sont examines a partir... more
Cette etude s'interesse a l'influence des fissures transversales sur les systemes tournants. Les variations des frequences propres ainsi que le changement du comportement dynamique du systeme fissure sont examines a partir d'une modelisation elements finis d'un rotor comportant une fissure tournante. De plus, l'evolution des orbites du rotor fissure a la moitie de la premiere frequence de resonance est etudie. La reponse dynamique systeme est evaluee par l'intermediaire de la methode de la balance harmonique. Les orbites pour differentes vitesses de rotations sont presentees afin de proposer des criteres de detection de fissures pour les systemes tournants.
Research Interests: Physics and Humanities
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Research Interests: Physics and Humanities
This study focuses on a hybrid surrogate modelling technique in order to predict parameter-dependent mode coupling instabilities for uncertain mechanical systems subjected to friction-induced vibration. For this purpose, the most common... more
This study focuses on a hybrid surrogate modelling technique in order to predict parameter-dependent mode coupling instabilities for uncertain mechanical systems subjected to friction-induced vibration. For this purpose, the most common strategy consists in associating a Monte Carlo procedure and/or a scanning technique together with the Complex Eigenvalue Analysis (CEA). This numerical strategy is computationally too prohibitive, particularly in an industrial context such as in the brake systems. To overcome this drawback, a novel approach is proposed. It consists in the combination of the generalized polynomial chaos (GPC) together with the kriging based meta-models. The association of both methods gives rise to a hybrid meta-model allowing taking into account two sets of uncertain parameters in the prediction of mode coupling instabilities. Moreover, it permits avoiding the use of the prohibitive MC and scanning methods. Thereby, this study analyses the feasibility of the proposed meta-model and its potential to be an efficient predictor of squeal propensity under parameter uncertainty.
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This paper presents a research devoted to the study of instability phenomena in non-linear model with a constant brake friction coefficient. The condition of stability is based on the resolution of a generalized eigenvalue problem and the... more
This paper presents a research devoted to the study of instability phenomena in non-linear model with a constant brake friction coefficient. The condition of stability is based on the resolution of a generalized eigenvalue problem and the limit cycle amplitude are determined by the center manifold reduction. A model is presented for the analysis of whirl mode vibration in aircraft braking systems. In this study, a non-linear material behaviour of the brake heat stack is considered. This non-linearity is expressed as a polynomial. The model does not require the use of brake negative damping and predicts that instability can occur with a constant brake friction coefficient. The center manifold approach is used to obtain equations for the limit cycle amplitude. The brake friction coefficient is used as unfolding parameter of the fundamental Hopf bifurcation point. The analysis shows that stable and unstable limit cycles can exist for a given constant brake friction coefficient.