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

Hongliang Zhao; Kangsheng Liu; Zhuangyi Liu

doi:10.1023/B:ELAS.0000033863.20719.e2

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

Hongliang Zhao, Kangsheng Liu, Zhuangyi Liu

Mathematics & Statistics

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4 Scopus citations

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 language	English (US)
Pages (from-to)	175-183
Number of pages	9
Journal	Journal of Elasticity
Volume	74
Issue number	2
DOIs	https://doi.org/10.1023/B:ELAS.0000033863.20719.e2
State	Published - 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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title = "A note on the exponential decay of energy of a Euler-Bernoulli beam with local viscoelasticity",

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.",

keywords = "Boltzmann-type viscoelasticity, Euler-Bernoulli beam, Exponential stability, Semigroup",

author = "Hongliang Zhao and Kangsheng Liu and Zhuangyi Liu",

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.",

year = "2004",

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doi = "10.1023/B:ELAS.0000033863.20719.e2",

language = "English (US)",

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T1 - A note on the exponential decay of energy of a Euler-Bernoulli beam with local viscoelasticity

AU - Zhao, Hongliang

AU - Liu, Kangsheng

AU - Liu, Zhuangyi

N1 - 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.

PY - 2004/2

Y1 - 2004/2

N2 - 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.

AB - 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.

KW - Boltzmann-type viscoelasticity

KW - Euler-Bernoulli beam

KW - Exponential stability

KW - Semigroup

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SN - 0374-3535

VL - 74

SP - 175

EP - 183

JO - Journal of Elasticity

JF - Journal of Elasticity

IS - 2

ER -

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

Abstract

Bibliographical note

Keywords

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