Optimal decay ratio of damped slowly rotating Timoshenko beams

Abstract

A stability analysis was performed in the problem of a rotating Timoshenko beam whose movement is controlled by the angular acceleration of the driving motor into which the beam is rigidly clamped. We introduce a damping operator with respect to a rotation angle of a cross section area of rotating Timoshenko beam model, and show the asymptotic stability of the system under certain assumptions. We find the optimal damping coefficient, maximizing the stability margin of the system. K E Y W O R D Sasymptotic stability, optimal decay, stability margin, Timoshenko beam