IJPAM: Volume 58, No. 1 (2010)
AN EXTENSIBLE VISCOELASTIC BEAM WITH
ELASTIC EXTERNAL SUPPLY



University of Salerno
Via Ponte don Melillo, 84084, Fisciano (SA), ITALY
e-mail: ibochicchio@unisa.it

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 , 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