A note on the exponential decay of energy of a Euler-Bernoulli beam with local viscoelasticity

Hongliang Zhao, Kangsheng Liu, Zhuangyi Liu

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Abstract

In this paper, we consider an Euler-Bernoulli beam equation with one segment of the beam made of viscoelastic material of Boltzmann type and the other segment made of elastic material. Strong stability and exponential stability of the associated semigroup are obtained under certain smoothness conditions imposed on the coefficient functions of the equation.

Original languageEnglish (US)
Pages (from-to)175-183
Number of pages9
JournalJournal of Elasticity
Volume74
Issue number2
DOIs
StatePublished - Feb 2004

Bibliographical note

Funding Information:
★ Permanent address: Department of Mathematics, Northeast Normal University, Changchun, 130024, China. E-mail: hlzhao@mail.jl.cn ★★ Supported partially by the National Natural Science Foundation of China grants 10271111 and 69874034.

Keywords

  • Boltzmann-type viscoelasticity
  • Euler-Bernoulli beam
  • Exponential stability
  • Semigroup

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