Exponential stabilization of timoshenko beam with locally distributed feedback *

Abstract

Abstract The problem of exponential stabilization of Timoshenko beam with locally distributed controls is investigated in this paper. In the case that the beam is non-uniform and the two wave speeds are different, first it is shown, under some locally distributed controls, that the vibration of the beam decays exponentially by using Huang's theorem and Birkhoff's asymptotic expansion method. Then explicit asymptotic locations of eigeufrequencies are also derived. When the two wave speeds are same, by using Chen's theorem, the exponential decay is established as well for a uniform beam.