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

C. Pozzolini; M. Salaun

ESAIM: Mathematical Modelling and Numerical Analysis (2011)

  • Volume: 45, Issue: 6, page 1163-1192
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Pozzolini, C., and Salaun, M.. "Some energy conservative schemes for vibro-impacts of a beam on rigid obstacles*." ESAIM: Mathematical Modelling and Numerical Analysis 45.6 (2011): 1163-1192. <http://eudml.org/doc/276347>.

@article{Pozzolini2011,
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. },
author = {Pozzolini, C., Salaun, M.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Variational inequalities; finite element method; elastic beam; dynamics; unilateral constraints; restitution coefficient; variational inequalities},
language = {eng},
month = {7},
number = {6},
pages = {1163-1192},
publisher = {EDP Sciences},
title = {Some energy conservative schemes for vibro-impacts of a beam on rigid obstacles*},
url = {http://eudml.org/doc/276347},
volume = {45},
year = {2011},
}

TY - JOUR
AU - Pozzolini, C.
AU - Salaun, M.
TI - Some energy conservative schemes for vibro-impacts of a beam on rigid obstacles*
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2011/7//
PB - EDP Sciences
VL - 45
IS - 6
SP - 1163
EP - 1192
AB - 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.
LA - eng
KW - Variational inequalities; finite element method; elastic beam; dynamics; unilateral constraints; restitution coefficient; variational inequalities
UR - http://eudml.org/doc/276347
ER -

References

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  13. L. Paoli and M. Schatzman, Numerical simulation of the dynamics of an impacting bar. Comput. Methods Appl. Mech. Eng.196 (2007) 2839–2851.  
  14. A. Petrov and M. Schatzman, Viscolastodynamique monodimensionnelle avec conditions de Signorini. C. R. Acad. Sci. Paris, I334 (2002) 983–988.  
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