Size optimization of a piezoelectric actuator on a clamped elastic plate

We determine by a theoretical analysis the optimal dimension of a piezoelectric actuator attached to a multilayered elastic plate clamped at both ends. The dimension is optimal in the sense of producing maximal plate center flexural displacement. The first-order theory for laminated piezoelectric plates is used. A theoretical solution is obtained. Numerical results calculated from the solution show that when the actuator length takes a particular value, the center flexural displacement of the elastic plate reaches a maximum. For PZT4 and PZT5A actuators this happens when the actuator length is about 55% of the plate length. Basic vibration characteristics of the structure at the first resonance near the optimal actuator length are also calculated. It is found that the admittance is also maximal when the electrode length is optimal.