Exponential stability of an active constrained layer beam actuated by a voltage source without magnetic effects

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• 作者：Chao Yang ^{chych09@163.com} ; Jun-Min Wang ; ^{jmwang@bit.edu.cn}
• 关键词：ACL beam ; Rayleigh beam ; Riesz basis ; Exponential stability
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 April 2017
• 年：2017
• 卷：448
• 期：2
• 页码：1204-1227
• 全文大小：444 K
• 卷排序：448

文摘

We study the boundary stabilization of an active constrained layer (ACL) beam consisting of a stiff layer, a viscoelastic layer and a piezoelectric layer. The piezoelectric layer is actuated by a voltage source without magnetic effects. The system is modeled as a Rayleigh beam coupled with two wave equations. By using an asymptotic technique, we present the asymptotic expressions for the eigenpairs of the system. We show that the generalized eigenfunctions form a Riesz basis in the state space, and hence the spectrum determined growth condition holds. Finally, the exponential stability of the closed-loop system is established.