An existence result for non-smooth vibro-impact problems |
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Authors: | Laetitia Paoli |
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Institution: | Equipe d’Analyse Numérique-UPRES EA 3058, Saint-Etienne, Faculté des Sciences, Université Jean Monnet, 23 Rue du Docteur Paul Michelon, 42023 St-Etienne Cedex 2, France |
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Abstract: | We are interested in mechanical systems with a finite number of degrees of freedom submitted to frictionless unilateral constraints. We consider the case of a convex, non-smooth set of admissible positions given by , ν?1, and we assume inelastic shocks at impacts. We propose a time-discretization of the measure differential inclusion which describes the dynamics and we prove the convergence of the approximate solutions to a limit motion which satisfies the constraints. Moreover, if the geometric properties ensuring continuity on data hold at the limit, we show that the transmission of velocities at impacts follows the inelastic shocks rule. |
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Keywords: | primary 34A60 34A12 secondary 70E55 46N40 |
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