Evolution Equations and Control Theory (EECT)

Vibrations of a damped extensible beam between two stops

Pages: 35 - 54, Volume 2, Issue 1, March 2013      doi:10.3934/eect.2013.2.35

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Alessia Berti - Facoltà di Ingegneria, Università e-Campus Italia, Via Isimbardi 10, Novedrate (CO), 22060, Italy (email)
Maria Grazia Naso - Dipartimento di Matematica, Università degli Studi di Brescia, Via Valotti 9, Brescia, 25133, Italy (email)

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.

Keywords:  Dynamic contact, extensible elastic beam, asymptotic behavior of solutions, Signorini condition, normal compliance.
Mathematics Subject Classification:  Primary: 74H40, 74M15; Secondary: 35B40.

Received: July 2012;      Revised: July 2012;      Available Online: January 2013.