Some energy conservative schemes for vibro-impacts of a beam on rigid obstacles
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 45 (2011) no. 6, p. 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 : https://doi.org/10.1051/m2an/2011008
Classification:  35L85,  65M12,  74H15,  74H45
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 - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {45},
     number = {6},
     year = {2011},
     pages = {1163-1192},
     doi = {10.1051/m2an/2011008},
     mrnumber = {2833177},
     language = {en},
     url = {http://www.numdam.org/item/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 - Modélisation Mathématique et Analyse Numérique, Volume 45 (2011) no. 6, pp. 1163-1192. doi : 10.1051/m2an/2011008. http://www.numdam.org/item/M2AN_2011__45_6_1163_0/

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