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Exponential decay rate of the energy of a Timoshenko beam with locally distributed feedback

Published online by Cambridge University Press:  17 February 2009

Dong-Hua Shi  and
De-Xing Feng
Dong-Hua Shi
Affiliation:
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China; e-mail: dhshi@math.tsinghua.edu.cn.
De-Xing Feng
Affiliation:
Laboratory of Systems and Control, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences Beijing 100080, China; e-mail: dxfeng@iss03.iss.ac.cn.
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Abstract

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The problem of the energy exponential decay rate of a Timoshenko beam with locally distributed controls is investigated. Consider the case in which the beam is nonuniform and the two wave speeds are different. Then, using Huang's theorem and Birkhoff's asymptotic expansion method, it is shown that, under some locally distributed controls, the energy exponential decay rate is identical to the supremum of the real part of the spectrum of the closed loop system. Furthermore, explicit asymptotic locations of eigenfrequencies are derived.

Type
Research Article
Information
The ANZIAM Journal , Volume 44 , Issue 2 , October 2002 , pp. 205 - 220
Copyright
Copyright © Australian Mathematical Society 2002

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