Feedback Stabilization of Timoshenko Beam with Boundary Dissipation

Abstract

This note is concerned with nonlinear boundary feedback control to a Timoshenko beam. Under some nonlinear boundary feedback controls, first the nonlinear semigroup theory is used to show the well-posedness for the corresponding 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 and exponentially as t → ∞ respectively.