Boundary stabilization of nonuniform Timoshenko beam

Abstract

In this paper, the boundary stabilization of the Timoshenko equation of a nonuniform beam, with clamped boundary condition at one end and with bending moment and shear force controls at the other end, is considered. It is proved that the system is exponentially stabilizable when the bending moment and shear force controls are simultaneously applied. The frequency domain method and the multiplier technique are used.