Vibrations of a beam between obstacles. Convergence of a fully discretized approximation
IREMIA, Université de La Réunion, 15 avenue R. Cassin,
97715 Saint-Denis Messag. 9, France. Yves.Dumont@univ-reunion.fr
2 LaMUSE, Université de St-Étienne, 23 rue P. Michelon, 42023 St-Étienne Cedex 2, France. email@example.com
Revised: 10 April 2006
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.
Mathematics Subject Classification: 35L85 / 65M12 / 74H45
Key words: Dynamics with impact / Signorini's conditions / space and time discretization / convergence.
© EDP Sciences, SMAI, 2006