IJPAM: Volume 58, No. 1 (2010)

LONGTIME BEHAVIOR FOR OSCILLATIONS OF
AN EXTENSIBLE VISCOELASTIC BEAM WITH
ELASTIC EXTERNAL SUPPLY

Ivana Bochicchio$^1$, Elena Vuk$^2$
$^1$Department of Mathematics and Informatics
University of Salerno
Via Ponte don Melillo, 84084, Fisciano (SA), ITALY
e-mail: ibochicchio@unisa.it
$^2$Department of Mathematics
University of Brescia
9, Via Valotti, 25133, Brescia, ITALY
e-mail: vuk@ing.unibs.it


Abstract.This work is focused on a nonlinear equation describing the oscillations of an extensible viscoelastic beam with fixed ends, subject to distributed elastic external force. For a general axial load $\beta$, the existence of a finite/infinite set of stationary solutions and buckling occurrence are scrutinized. The exponential stability of the straight position is discussed. Finally, the related dynamical system in the history space framework is shown to possess a regular global attractor.

Received: December 15, 2009

AMS Subject Classification: 35B40, 35B41, 37B25, 74G60, 74H40, 74K10

Key Words and Phrases: extensible viscoelastic beam, Lyapunov functional, exponential stability, global attractor

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 58
Issue: 1