Exponential Stability of Non-uniform Timoshenko Beam With Indefinite Damping Under Boundary Control

Abstract

In this paper we study the stabilization of a non-uniform Timoshenko beam with indefinite damping terms under boundary control and prove how the damping terms can affect the decay rate asymptotically. Using the theory of perturbed problems, we obtain the stability and establish the spectrum determined growth condition for the problem. Moreover, when the two damping terms are indefinite, we provide a condition to obtain  the exponential stability.