Exponential Stability of a Non-homogeneous Rotating Body-Beam System with Variable Coefficients

In this paper, we consider a system of a flexible beam attached to the center of a rotating rigid disk. The disk rotates freely around its axis with a non-uniform angular velocity and the motion of the beam with non-homogeneous spatial coefficients is confined to a plane perpendicular to the disk. The system can be exponentially stabilized under the boundary feedback and the torque control. Furthermore, Riesz basis property can be proved for the closed-loop system with uniform angular velocity by the method of spectral analysis.