Boundary feedback stabilization of Timoshenko beam with boundary dissipation

Abstract

Nonlinear boundary feedback control to a Timoshenko beam is studied. Under some nonlinear boundary feedback controls, the nonlinear semi-group theory is used to show the well-posedness for the correspnding closed loop system. Then by using the energy perturbed method, it is proved that the vibration of the beam under the proposed control actions decays asymptotically or exponentially as t→∞.