| Stability for the Timoshenko Beam System with Local Kelvin-Voigt Damping |
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| 作者姓名： | Hong Liang ZHAO Kang Sheng LIU Chun Guo ZHANG |
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| 作者单位： | [1]Department of Mathematics, Zhejiang University, Hangzhou 310027, P. R. China [2]Department of Mathematics, Northeast Normal University, Changchun 130024, P. R. China |
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| 基金项目： | This project is supported partially by the National Natural Science Foundation of China Grants 69874034 and 10271111 |
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| 摘 要： | In this paper, we consider a vibrating beam with one segment made of viscoelastic material of a Kelvin-Voigt （shorted as K-V） type and other parts made of elastic material by means of the Timoshenko model. We have deduced mathematical equations modelling its vibration and studied the stability of the semigroup associated with the equation system. We obtain the exponential stability under certain hypotheses of the smoothness and structural condition of the coefficients of the system, and obtain the strong asymptotic stability under weaker hypotheses of the coefficients.
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| 关 键 词： | Timoshenko波束系统 Kelvin-Voigt衰减 稳定性 黏弹性材料 数学方程 |
| 收稿时间： | 2002-04-08 |
| 修稿时间： | 2002-04-082002-11-26 |
Stability for the Timoshenko Beam System
with Local Kelvin–Voigt Damping |
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| Hong Liang ZHAO Kang Sheng LIU Chun Guo ZHANG.Stability for the Timoshenko Beam System with Local Kelvin-Voigt Damping[J].Acta Mathematica Sinica,2005,21(3):655-666. |
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| Authors: | Hong Liang Zhao Kang Sheng Liu Chun Guo Zhang |
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| Institution: | (1) Department of Mathematics, Zhejiang University, Hangzhou 310027, P. R. China;(2) Department of Mathematics, Northeast Normal University, Changchun 130024, P. R. China;(3) Department of Mathematics, Zhejiang University, Hangzhou 310027, P. R. China |
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| Abstract: | In this paper, we consider a vibrating beam with one segment made of viscoelastic material
of a Kelvin–Voigt (shorted as K–V) type and other parts made of elastic material by means of the
Timoshenko model. We have deduced mathematical equations modelling its vibration and studied the
stability of the semigroup associated with the equation system. We obtain the exponential stability
under certain hypotheses of the smoothness and structural condition of the coefficients of the system,
and obtain the strong asymptotic stability under weaker hypotheses of the coefficients.
This project is supported partially by the National Natural Science Foundation of China Grants 69874034 and
10271111 |
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| Keywords: | Timoshenko beam Kelvin-Voigt damping Semigroup Stability |
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