Vibrations of a beam between obstacles. Convergence of a fully discretized approximation

Yves Dumont; Laetitia Paoli

ESAIM: Mathematical Modelling and Numerical Analysis (2006)

  • Volume: 40, Issue: 4, page 705-734
  • ISSN: 0764-583X

Abstract

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We consider mathematical models describing dynamics of an elastic beam which is clamped at its left end to a vibrating support and which can move freely at its right end between two rigid obstacles. We model the contact with Signorini's complementary conditions between the displacement and the shear stress. For this infinite dimensional contact problem, we propose a family of fully discretized approximations and their convergence is proved. Moreover some examples of implementation are presented. The results obtained here are also valid in the case of a beam oscillating between two longitudinal rigid obstacles.

How to cite

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Dumont, Yves, and Paoli, Laetitia. "Vibrations of a beam between obstacles. Convergence of a fully discretized approximation." ESAIM: Mathematical Modelling and Numerical Analysis 40.4 (2006): 705-734. <http://eudml.org/doc/249721>.

@article{Dumont2006,
abstract = { We consider mathematical models describing dynamics of an elastic beam which is clamped at its left end to a vibrating support and which can move freely at its right end between two rigid obstacles. We model the contact with Signorini's complementary conditions between the displacement and the shear stress. For this infinite dimensional contact problem, we propose a family of fully discretized approximations and their convergence is proved. Moreover some examples of implementation are presented. The results obtained here are also valid in the case of a beam oscillating between two longitudinal rigid obstacles. },
author = {Dumont, Yves, Paoli, Laetitia},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Dynamics with impact; Signorini's conditions; space and time discretization; convergence.; Signorini conditions; P3 finite element; infinite-dimensional contact problem},
language = {eng},
month = {11},
number = {4},
pages = {705-734},
publisher = {EDP Sciences},
title = {Vibrations of a beam between obstacles. Convergence of a fully discretized approximation},
url = {http://eudml.org/doc/249721},
volume = {40},
year = {2006},
}

TY - JOUR
AU - Dumont, Yves
AU - Paoli, Laetitia
TI - Vibrations of a beam between obstacles. Convergence of a fully discretized approximation
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2006/11//
PB - EDP Sciences
VL - 40
IS - 4
SP - 705
EP - 734
AB - We consider mathematical models describing dynamics of an elastic beam which is clamped at its left end to a vibrating support and which can move freely at its right end between two rigid obstacles. We model the contact with Signorini's complementary conditions between the displacement and the shear stress. For this infinite dimensional contact problem, we propose a family of fully discretized approximations and their convergence is proved. Moreover some examples of implementation are presented. The results obtained here are also valid in the case of a beam oscillating between two longitudinal rigid obstacles.
LA - eng
KW - Dynamics with impact; Signorini's conditions; space and time discretization; convergence.; Signorini conditions; P3 finite element; infinite-dimensional contact problem
UR - http://eudml.org/doc/249721
ER -

References

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