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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