Modeling of multiple layered piezoelectric actuators in active structural control

Abstract

The design and analysis of finite length, multiple layered, induced strain actuators is investigated. A model of an arbitrary multiple layered actuator is utilized to predict the applied force and moment from the ith layer onto a structure. The transverse equations of motion of a simply supported beam are derived using Timoshenko beam theory. This approach accounts for shear deformation and allows the actuator-applied moments to be directly incorporated into the equations of motion without further approximation. The model is cast in state space form and an assumed mode method is used to solve for the forced response of a nonuniform beam. Experiments are performed verifying the developed analytical model. The first experiment characterizes the dynamic properties of five different actuator/substructure configurations. Results indicate the system natural frequencies decreased and the structural damping increased with more attached actuators. Analytical predictions are shown to be in good agreement with the experimental results.