Piezoelectric control of composite plate vibration: Effect of electric potential distribution

The paper deals with the vibration analysis of active rectangular plates. The plates considered are composites containing piezoelectric sensor/actuator layers, which operate in a velocity feedback control to achieve transverse vibration suppression. The piezoelectric layers are poled through the thickness and equipped with traditional surface electrodes. In order to satisfy the Maxwell electrostatics equation the widely used simplification of the electric potential distribution in the actuator layer (linear across the thickness) is replaced by a combination of a half-cosine and linear distribution in the transverse direction. The in-plane spatial variation of the potential instead of applying uniform distribution is determined by the solution of the coupled electromechanical governing equations with the natural boundary conditions corresponding to both the flexural and electric potential fields. The analysis is performed for simply supported plates. Two models of the plate are considered. In the first case the displacement field is based on the Kirchhoff hypothesis. For the second the Mindlin plate model is applied. The governing coupled equations describing the active plate behaviour are derived. The influence of the electric potential distribution and also the thickness of piezoelectric layers on the plate dynamics including the natural frequencies modification is numerically investigated and discussed.