Dynamic boundary stabilization of Euler-Bernoulli beam through a Kelvin-Voigt damped wave equation
In this paper, we study the stability of a one-dimentional Euler-Bernoulli beam coupled with a Kelvin- Voigt damped wave equation, where the wave equation acts as a dynamic boundary feedback controller to exponentially stabilize the Euler-Bernoulli beam. Remarkably, the resolvent of the closed-loop system operator is not compact anymore. By a detailed spectral analysis, we show that the residual spectrum is empty and the continuous spectrum contains only one point. Moreover, we verify that the generalized eigenfunctions of the system forms a Riesz basis for the energy state space. It then follows that the C0-semigroup generated by the system operator satisfies the spectrum-determined growth assumption. Finally, the exponential stability and Gevrey regularity of the system are established.
Euler-Bernoulli equation Kelvin-Voigt damping spectrum asymptotic analysis Riesz basis stability
Lu Lu Jun-Min Wang
School of Mathematics, Beijing Institute of Technology, Beijing 100081, P.R. China
国际会议
长沙
英文
223-228
2014-05-31（万方平台首次上网日期，不代表论文的发表时间）