Active Vibration Control of Piezolaminated Composite Plates Considering Strong Electric Field Nonlinearity

Abstract

A theoretical framework is presented for modeling active vibration control of smart multilayered plates integrated with piezoceramic sensors and actuators, considering their constitutive nonlinearity under a strong electric field. The application of an electric field beyond the linear threshold limit of piezoelectric materials is often necessary to achieve high actuation authority. A recently developed efficient layerwise theory, for which the computational efficiency and accuracy have been well established for linear electromechanical response, is employed for the laminate mechanics. The nonlinear finite element model for dynamic response is developed consistently using a variational principle, considering a rotationally invariant second-order constitutive relationship for piezoelectric materials. The nonlinear system is transformed to an equivalent linear system using the feedback linearization approach, through control input transformation. The linear quadratic Gaussian controller is adopted for control of the equivalent system. Results are presented for a smart sandwich plate under step, impulse, and sinusoidal excitations. It is revealed that, using the piezoelectric nonlinearity, the vibration control can be achieved at a much lower actuation potential than predicted by the linear model. While in the linear model, the control voltage is almost independent of the actuator thickness, and its nonlinear prediction reduces significantly with the decrease in the actuator thickness.