Electrically forced vibration of an elastic plate with a finite piezoelectric actuator

We analyze out-of-plane vibrations of an elastic plate electrically driven by a finite piezoelectric actuator on part of the surface of the plate. The equations of linear elasticity and linear piezoelectricity are used. The mathematical problem is solved using trigonometric series. An exact solution satisfying all governing equations and boundary conditions is obtained. Basic vibration characteristics including resonant frequencies, mode shapes and electric admittance are calculated. It is shown that the vibration may be either confined to the actuator region or all over the plate, and the vibration behavior is sensitive to the parameters of the structure.