Caused by the problem of unilateral contact during vibrations of satellite solar arrays, the aim of this paper is to better understand such a phenomenon. Therefore, it is studied here a simplified model composed by a beam moving between rigid obstacles. Our purpose is to describe and compare some families of fully discretized approximations and their properties, in the case of non-penetration Signorini's conditions. For this, starting from the works of Dumont and Paoli, we adapt to our beam model the singular dynamic method introduced by Renard. A particular emphasis is given in the use of a restitution coefficient in the impact law. Finally, various numerical results are presented and energy conservation capabilities of the schemes are investigated.
Keywords: variational inequalities, finite element method, elastic beam, dynamics, unilateral constraints, restitution coefficient
@article{M2AN_2011__45_6_1163_0,
author = {Pozzolini, C. and Salaun, M.},
title = {Some energy conservative schemes for vibro-impacts of a beam on rigid obstacles},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1163--1192},
year = {2011},
publisher = {EDP-Sciences},
volume = {45},
number = {6},
doi = {10.1051/m2an/2011008},
mrnumber = {2833177},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2011008/}
}
TY - JOUR AU - Pozzolini, C. AU - Salaun, M. TI - Some energy conservative schemes for vibro-impacts of a beam on rigid obstacles JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2011 SP - 1163 EP - 1192 VL - 45 IS - 6 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/m2an/2011008/ DO - 10.1051/m2an/2011008 LA - en ID - M2AN_2011__45_6_1163_0 ER -
%0 Journal Article %A Pozzolini, C. %A Salaun, M. %T Some energy conservative schemes for vibro-impacts of a beam on rigid obstacles %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2011 %P 1163-1192 %V 45 %N 6 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an/2011008/ %R 10.1051/m2an/2011008 %G en %F M2AN_2011__45_6_1163_0
Pozzolini, C.; Salaun, M. Some energy conservative schemes for vibro-impacts of a beam on rigid obstacles. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 45 (2011) no. 6, pp. 1163-1192. doi: 10.1051/m2an/2011008
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