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.
Mots clés : dynamics with impact, Signorini's conditions, space and time discretization, convergence
@article{M2AN_2006__40_4_705_0,
author = {Dumont, Yves and Paoli, Laetitia},
title = {Vibrations of a beam between obstacles. {Convergence} of a fully discretized approximation},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {705--734},
publisher = {EDP-Sciences},
volume = {40},
number = {4},
year = {2006},
doi = {10.1051/m2an:2006031},
mrnumber = {2274775},
zbl = {1106.74057},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2006031/}
}
TY - JOUR AU - Dumont, Yves AU - Paoli, Laetitia TI - Vibrations of a beam between obstacles. Convergence of a fully discretized approximation JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2006 SP - 705 EP - 734 VL - 40 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2006031/ DO - 10.1051/m2an:2006031 LA - en ID - M2AN_2006__40_4_705_0 ER -
%0 Journal Article %A Dumont, Yves %A Paoli, Laetitia %T Vibrations of a beam between obstacles. Convergence of a fully discretized approximation %J ESAIM: Modélisation mathématique et analyse numérique %D 2006 %P 705-734 %V 40 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2006031/ %R 10.1051/m2an:2006031 %G en %F M2AN_2006__40_4_705_0
Dumont, Yves; Paoli, Laetitia. Vibrations of a beam between obstacles. Convergence of a fully discretized approximation. ESAIM: Modélisation mathématique et analyse numérique, Tome 40 (2006) no. 4, pp. 705-734. doi : 10.1051/m2an:2006031. http://www.numdam.org/articles/10.1051/m2an:2006031/
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