Stabilization of the uniform Timoshenko beam by one locally distributed feedback

被引：31

作者：

Wehbe, Ali ^{[1
]}

Youssef, Wael ^{[2
]}

机构：

[1] Univ Libanaise, Fac Sci, Dept Math, Hadath, Beyrouth, Lebanon

[2] Univ Metz Ile Saulcy, Dept Math, F-57045 Metz 01, France

来源：

APPLICABLE ANALYSIS | 2009年 / 88卷 / 07期

关键词：

Timoshenko system; locally distributed feedback; exponential and polynomial stability; frequency domain conditions; DECAY-RATE; ENERGY;

D O I：

10.1080/00036810903156149

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we study the energy decay rate for an elastic Timoshenko system. This system consists of two coupled wave equations. Only the equation about the rotation angle is damped by one locally distributed feedback at the neighbourhood of the boundary. The equation for the transverse displacement of the beam is only indirectly damped through the coupling. First, we establish an exponential energy decay rate in the case of the same speed of propagation. Next, when the wave speeds are different, a polynomial-type decay rate is obtained. These results are proved by verifying the frequency domain conditions.

引用

页码：1067 / 1078

页数：12

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