On the viscoelastic coupled suspension bridge

Ivana Bochicchio; Claudio Giorgi; Elena Vuk

doi:10.3934/eect.2014.3.373

Article Contents

2014, Volume 3, Issue 3: 373-397. Doi: 10.3934/eect.2014.3.373

This issue Previous Article Lower semicontinuity for polyconvex integrals without coercivity assumptions Next Article Heat conduction with memory: A singular kernel problem

On the viscoelastic coupled suspension bridge

1.
Dipartimento di Matematica, Università degli studi di Salerno, Via Giovanni Paolo II 132, 84084 Fisciano (SA)
2.
DICATAM, Università degli studi di Brescia, Via D.Valotti 9, 25133 Brescia

Received: July 31, 2013

Revised: January 31, 2014

Published: August 2014

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Abstract

In this paper we discuss the asymptotic behavior of a doubly nonlinear problem describing the vibrations of a coupled suspension bridge. The single-span road-bed is modeled as an extensible viscoelastic beam which is simply supported at the ends. The main cable is modeled by a viscoelastic string and is connected to the road-bed by a distributed system of one-sided elastic springs. A constant axial force $p$ is applied at one end of the deck, and time-independent vertical loads are allowed to act both on the road-bed and on the suspension cable. For this general model we obtain original results, including the existence of a regular global attractor for all $p\in\mathbb{R}$.

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Mathematics Subject Classification: Primary: 35B41, 35Q74; Secondary: 74D05, 74H40.

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