Volume 45, Number 6, November-December 2011
|Page(s)||1163 - 1192|
|Published online||04 July 2011|
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. email@example.com
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. firstname.lastname@example.org
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.