ANZIAM J.
44 (2002), 205220

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



DeXing Feng
Laboratory of Systems and Control
Institute of Systems Science
Academy of Mathematics and Systems Science
Chinese Academy of Sciences
Beijing 100080
China
dxfeng@iss03.iss.ac.cn



Abstract

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.

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