BOUNDARY FEEDBACK STABILIZATION OF A ROTATING BODY-BEAM SYSTEM

This paper deals with boundary feedback stabilization of a flexible be am clamped to a rigid body and free at the other end. The system is go verned by the beam equation nonlinearly coupled with the dynamical equ ation of the rigid body. We propose a stabilizing boundary feedback la w which suppresses the beam vibrations so that the whole structure rot ates about a fixed axis with any given smalt constant angular velocity . The stabilizing feedback law is composed of control torque applied o n the rigid body and either boundary control moment or boundary contro l force (or both of them) at the free end of the beam. It is shown tha t in any case the beam vibrations are forced to decay exponentially to zero.