VIBRATION DAMPING OF A THIN PLATE BY OPTIMAL OPEN-LOOP AND CLOSED-LOOP CONTROL FORCES

The vibrations of a rectangular plate are damped out by means of a combined open-closed-loop control mechanism. A functional involving the displacement, velocity and open-loop control function is minimized with respect to both the open-loop function and the displacement feedback parameter. The minimization is carried out subject to a constraint on the amount of feedback force that can be spent in the control process. An explicit solution of the problem is obtained and the theory is applied to the vibrating damping of an impulsively loaded plate. Numerical results are given to indicate the effectiveness of the proposed control mechanism.