Vibrations of a damped extensible beam  between two stops

Alessia Berti; Maria Grazia Naso

doi:10.3934/eect.2013.2.35

Article Contents

2013, Volume 2, Issue 1: 35-54. Doi: 10.3934/eect.2013.2.35

This issue Previous Article Spectral analysis and exponential or polynomial stability of some indefinite sign damped problems Next Article Sensitivity analysis for a free boundary fluid-elasticity interaction

Vibrations of a damped extensible beam between two stops

Alessia Berti^1, and
Maria Grazia Naso^2,

1.
Facoltà di Ingegneria, Università e-Campus Italia, Via Isimbardi 10, Novedrate (CO), 22060
2.
Dipartimento di Matematica, Università degli Studi di Brescia, Via Valotti 9, Brescia, 25133

Received: June 30, 2012

Revised: June 30, 2012

Published: February 2013

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Abstract

A PDE system modeling the dynamics of an extensible beam having one of its ends constrained between two stops is considered. The existence of a weak global-in-time solution is established by a penalization method. In addition, the asymptotic behavior of such a solution is analyzed and the exponential decay rate for the related energy is shown.

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Mathematics Subject Classification: Primary: 74H40, 74M15; Secondary: 35B40.

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