Stabilization of variable coefficients Euler-Bernoulli beam equation with a tip mass controlled by combined feedback forces

Abstract

In this paper, we consider stability of a vibrating beam system clamped at one end, controlled by combined forces, with a mass attached at the other end. By adopting the Riesz basis approach, it is shown that the closed-loop system is a Riesz spectral system. Consequently, the exponential stability, spectrum-determined growth condition, and optimal decay rate are obtained. A numerical simulation of the spectrum is also presented.