Stability of variable coefficients Rayleigh beam with indefinite damping under a force control in position and velocity

Abstract

In this paper we study the exponential stability of a damped variable coefficients Rayleigh beam, that is clamped at one end and is free at the other. This is a continuation of the work of Wang et al in \cite{wangyung}. To stabilize the system, we apply a leaner boundary control in position and velocity at the free end of the beam. Using the modern spectral analysis approach, we obtain the Riesz basis property and the exponential stability.