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Vibrations of a beam between obstacles. Convergence of a fully discretized approximation

Published online by Cambridge University Press:  15 November 2006

Yves Dumont  and
Laetitia Paoli
Yves Dumont
Affiliation:
IREMIA, Université de La Réunion, 15 avenue R. Cassin, 97715 Saint-Denis Messag. 9, France. Yves.Dumont@univ-reunion.fr
Laetitia Paoli
Affiliation:
LaMUSE, Université de St-Étienne, 23 rue P. Michelon, 42023 St-Étienne Cedex 2, France. laetitia.paoli@univ-st-etienne.fr
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Abstract

We consider mathematical models describing dynamics of an elastic beam which is clamped at its left end to a vibrating support and which can move freely at its right end between two rigid obstacles. We model the contact with Signorini's complementary conditions between the displacement and the shear stress. For this infinite dimensional contact problem, we propose a family of fully discretized approximations and their convergence is proved. Moreover some examples of implementation are presented. The results obtained here are also valid in the case of a beam oscillating between two longitudinal rigid obstacles.

Keywords

Dynamics with impactSignorini's conditionsspace and time discretizationconvergence.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 40 , Issue 4 , July 2006 , pp. 705 - 734
Copyright
© EDP Sciences, SMAI, 2006

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