It may be noted that, the spatial variation for the actuation stress and the applied voltage is the same as that of deflection. However, the variation with respect to time is different for deflection and application of electric / magnetic field. The present solution is although found out for the first mode of vibration of a simply supported beam, it should be noted that the controller is not designed individually for each mode. It is shown through the solution of transverse deflection w, that the presence of constant gain velocity feedback can suppress any mode of vibration and hence the overall vibration of the beam. Thus, the problem of 'spill-over' etc. does not arise here. The general solution of deflection shows that the damping effect of smart actuator is implicitly incorporated through the term α, such that
By controlling the control gain and thereby the term β, one can achieve the required damping. The presence of smart layer also affects the natural frequency of the beam through both damping coefficient ξ and material property constant Dn.
Congratulations! You have finished Lecture 29. | 
