Stability of slowly rotating Timoshenko beam with two viscoelastic damping coefficients

This paper continues the authors' previous investigations of stability of a slowly rotating Timoshenko beam whose movement is controlled by the angular acceleration of the driving motor into which the beam is rigidly clamped. We consider a viscoelastic damping operator with respect to both variables - deflection of the center line, and rotation angle of cross section area. We show that the initial unstable system becomes stable after introducing the damping.