Piezoelectric Control of Composite Plate Vibration: Effect of Electric Field 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 closed loop control acting to suppress transverse vibration. PVDF polymeric materials characterized by a relatively low stiffness are used for the sensors while the actuators are made of PZT ceramics because of their high electromechanical efficiency. The piezoelectric layers are poled in the transverse direction and equipped with traditional electrodes on both surfaces. 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 non-linear potential term, which relates to shortly connected electrodes and a uniform bending moment applied, was analysed in [

1

] and [

2

] among others. 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 assumed potential distribution improves the model of interaction between the actuator layer and the main structure. The analysis is performed for simply supported plates. The plats are modelled as laminate or sandwich structures. In the first case the displacement field is based on the Kirchhoff hypothesis. For the sandwich plates the Mindlin model with the effect of shear and rotary inertia is applied. External load acting in the transverse direction is distributed over the limited or total area of the plate surface. The steady-state behaviour of the plate is considered. Therefore, the loading is assumed to be harmonic in time single frequency function. The velocity feedback strategy is applied to reduce the plate transverse vibration. 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 frequency modification is numerically investigated and discussed.