Boundary feedback stabilization of the undamped Timoshenko beam with both ends free ✩

In this paper, we study a boundary feedback system of a class of nonuniform undamped Timoshenko beam with both ends free.We give some sufficient conditions and some necessary conditions for the system to have exponential stability. Our method is based on the operator semigroup technique, the multiplier technique, and the contradiction argument of the frequency domain method. © 2006 Elsevier Inc. All rights reserved