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

ESAIM: Mathematical Modelling and Numerical Analysis (2006)

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

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topDumont, 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 -

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