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Synthèse non-linéaire des systèmes vibrants. Application aux systèmes de freinage

Abstract : The study deals with the study of instability phenomena in non-linear model. To put it more precisely, we consider brake vibrations. The judder mode vibration in automobile braking and the whirl vibrations in an aircraft landing gear braking system are concerned. The purpose of this research is to develop a procedure of nonlinear methods in order to study instability phenomena in complex nonlinear systems. The non-linearities are expressed as a polynomial with quadratic and cubic terms.
First of all, a parameter model including mechanisms for friction induced system instability is established and the equations of motion of nonlinear systems are written. One of the most important phases in study of brake systems is the determination of the mechanism of the unstable friction induced vibration (stick-slip, variable dynamic friction coefficient, sprag-slip and coupling mechanism). The non-linear anamysis can be divided into two parts. First of all, the non-linear equations of motion are linearized at the steady-state operating point and a set of linearized perturbation equations obtained. Stability was investigated by determining eigenvalues of the linearized perturbation equations
about each steady-state operating point. Next, we use the nonlinear methods (center manifold approach, multivariable approximants, the alternate frequency/time domain (AFT) method,etc...) in order to predict limit cycle amplitudes. Results from these nonlinear methods will be compared with results obtained by integrating the full original system in order to validate this global procedure consisting to employ successively, in a certain order, non-linear methods to reduce, to simplify the original system.
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Contributor : Jean-Jacques Sinou <>
Submitted on : Wednesday, March 5, 2008 - 1:44:47 PM
Last modification on : Wednesday, November 20, 2019 - 2:27:17 AM
Long-term archiving on: : Friday, September 28, 2012 - 10:45:11 AM


  • HAL Id : tel-00260842, version 1



Jean-Jacques Sinou. Synthèse non-linéaire des systèmes vibrants. Application aux systèmes de freinage. Mécanique []. Ecole Centrale de Lyon, 2002. Français. ⟨tel-00260842⟩



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