Some energy conservative schemes for vibro-impacts of a beam on rigid obstacles*
Pôle de Mathématiques, INSA de Lyon, 20 rue Albert Einstein,
69621 Villeurbanne Cedex, France. firstname.lastname@example.org
2 Centre National d'Études Spatiales, 18 avenue Édouard Belin, 31401 Toulouse, France.
3 Université de Toulouse; INSA, UPS, EMAC, ISAE; ICA (Institut Clément Ader); 10 avenue Édouard Belin, 31055 Toulouse, France. email@example.com
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.
Mathematics Subject Classification: 35L85 / 65M12 / 74H15 / 74H45
Key words: Variational inequalities / finite element method / elastic beam / dynamics / unilateral constraints / restitution coefficient
© EDP Sciences, SMAI, 2011