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Dynamique et stabilité d'un système discret en présence de contact et de frottement

Abstract : This works aims at studying the stability of equilibrium states for a mechanical system
involving unilateral contact with Coulomb friction. The hypothesis of the classical stability
theorems are not verified and it is necessary to come back to the definition of stability by
studying the evolution in time of the distance between an equilibrium and the solution of a Cauchy
problem whose initial conditions belong to a given neighbourhood of the equilibrium. Consequently,
we are concerned by the existence and the uniqueness of solutions to the system with Cauchy data.
The existence of the solution is obtained under the hypothesis that the external force is integrable.
Then the question of uniqueness of the solution arises. A counter-example shows that the uniqueness of the solution does not
hold in general. We show that the Cauchy problem has a single solution if the external force is an
analytic function of time. Then we determine the set of solutions of the equilibrium problem under
a constant force. The dynamic problem being well-posed for analytic data, our concern is the study
of the stability of these equilibrium states. The specificity of the dynamic problem in the space
of the reactions lead to introduce new concepts of stability for systems with unilateral contact and Coulomb friction.
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Contributor : Stéphanie Basseville <>
Submitted on : Saturday, March 18, 2006 - 4:13:07 PM
Last modification on : Thursday, January 23, 2020 - 6:22:03 PM
Long-term archiving on: : Monday, September 17, 2012 - 12:40:50 PM


  • HAL Id : tel-00011976, version 1


Stéphanie Basseville. Dynamique et stabilité d'un système discret en présence de contact et de frottement. Mécanique []. Université de la Méditerranée - Aix-Marseille II, 2004. Français. ⟨tel-00011976⟩



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