Exponential stability of a joint-leg-beam system with memory damping

Qiong Zhang

doi:10.3934/mcrf.2015.5.321

Article Contents

2015, Volume 5, Issue 2: 321-333. Doi: 10.3934/mcrf.2015.5.321

This issue Previous Article Stability and controllability of a wave equation with dynamical boundary control Next Article Global controllability and stabilizability of Kawahara equation on a periodic domain

Exponential stability of a joint-leg-beam system with memory damping

Qiong Zhang^1,

1.
School of Mathematics, Beijing Institute of Technology, Beijing, 100081

Received: March 2014

Revised: July 2014

Published: June 2015

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Abstract

In this paper, we consider a system for combined axial and transverse motions of two viscoelastic Euler-Bernoulli beams connected through two legs to a joint. This model comes from rigidizable and inflatable space structures. First, the exponential stability of the joint-leg-beam system is obtained when both beams are subject to viscoelastic damping and memory kernels satisfy reasonable assumptions. Then, we show the lack of uniform decay of the coupled system when only one beam is assumed to have a memory damping and the second beam has no damping.

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Mathematics Subject Classification: Primary: 37B35, 35B40.

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