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.

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.

DOI : 10.1051/m2an/2011008
Classification : 35L85, 65M12, 74H15, 74H45
Mots-clés : variational inequalities, finite element method, elastic beam, dynamics, unilateral constraints, restitution coefficient 
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     title = {Some energy conservative schemes for vibro-impacts of a beam on rigid obstacles},
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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. http://www.numdam.org/articles/10.1051/m2an/2011008/

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