Active vibration suppression of moderately thick rectangular plates

In the present work, active vibration suppression of moderately thick rectangular plates by means of piezoelectric actuators is investigated. Based on Lagrange energy method, a finite element formulation is presented for mathematical modeling of the system. Using modal controllability criterion, a simple method is offered for optimal placement of the piezoelectric actuator. For a cantilevered plate with specific characteristics, the optimal position of a piezoelectric patch is investigated. Then, for suppression of plate vibrations, an active damping controller is designed using modal velocity feedbacks. Numerical simulations are then performed for studying the performance of the designed controller. Presented simulations indicate the feasibility of vibration control of moderately thick plates by means of high voltage piezoelectric actuators. These simulations also show that, for a specific excitation force, the maximum required voltage for vibration suppression approaches to an asymptotic value as the values of modal feedback gains increase. This conclusion is of high importance in practical controller design.