Vibrations of a beam between obstacles. Convergence of a fully discretized approximation
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 40 (2006) no. 4, p. 705-734

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.

Classification:  35L85,  65M12,  74H45
Keywords: dynamics with impact, Signorini's conditions, space and time discretization, convergence
     author = {Dumont, Yves and Paoli, Laetitia},
     title = {Vibrations of a beam between obstacles. Convergence of a fully discretized approximation},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {40},
     number = {4},
     year = {2006},
     pages = {705-734},
     doi = {10.1051/m2an:2006031},
     zbl = {1106.74057},
     mrnumber = {2274775},
     language = {en},
     url = {}
Dumont, Yves; Paoli, Laetitia. Vibrations of a beam between obstacles. Convergence of a fully discretized approximation. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 40 (2006) no. 4, pp. 705-734. doi : 10.1051/m2an:2006031.

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