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Some energy conservative schemes for vibro-impacts of a beam on rigid obstacles*

Published online by Cambridge University Press:  04 July 2011

C. Pozzolini  and
M. Salaun
C. Pozzolini
Affiliation:
Pôle de Mathématiques, INSA de Lyon, 20 rue Albert Einstein, 69621 Villeurbanne Cedex, France. cedric.pozzolini@insa-lyon.fr Centre National d'Études Spatiales, 18 avenue Édouard Belin, 31401 Toulouse, France.
M. Salaun
Affiliation:
Université de Toulouse; INSA, UPS, EMAC, ISAE; ICA (Institut Clément Ader); 10 avenue Édouard Belin, 31055 Toulouse, France. michel.salaun@isae.fr
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Abstract

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 inequalitiesfinite element methodelastic beamdynamicsunilateral constraintsrestitution coefficient
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 45 , Issue 6 , November 2011 , pp. 1163 - 1192
Copyright
© EDP Sciences, SMAI, 2011

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