Stability of a Timoshenko system with local Kelvin–Voigt damping

Xinhong Tian; Qiong Zhang

doi:10.1007/s00033-016-0765-5

Stability of a Timoshenko system with local Kelvin–Voigt damping

Xinhong Tian, Qiong Zhang^*

^*Corresponding author for this work

School of Mathematics and Statistics

Beijing Institute of Technology

Research output: Contribution to journal › Article › peer-review

27 Citations (Scopus)

Abstract

In this paper, we study a Timoshenko system with local Kelvin–Voigt damping, which models the dynamics of a beam. We prove that the energy of the system decays exponentially or polynomially and the decay rate depends on properties of material coefficient function. The method is based on the frequency analysis and inequalities of Poincaré’s and Hardy’s type.

Original language	English
Article number	20
Journal	Zeitschrift fur Angewandte Mathematik und Physik
Volume	68
Issue number	1
DOIs	https://doi.org/10.1007/s00033-016-0765-5
Publication status	Published - 1 Feb 2017

Keywords

C semigroup
Exponential stability
Kelvin–Voigt damping
Polynomial stability
Timoshenko beam

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10.1007/s00033-016-0765-5

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abstract = "In this paper, we study a Timoshenko system with local Kelvin–Voigt damping, which models the dynamics of a beam. We prove that the energy of the system decays exponentially or polynomially and the decay rate depends on properties of material coefficient function. The method is based on the frequency analysis and inequalities of Poincar{\'e}{\textquoteright}s and Hardy{\textquoteright}s type.",

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KW - Exponential stability

KW - Kelvin–Voigt damping

KW - Polynomial stability

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Stability of a Timoshenko system with local Kelvin–Voigt damping

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Keywords

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