Finite element modeling of piezoelectric sensors and actuators

Abstract

A finite element formulation for vibration control of a laminated plate with piezoelectric sensors/actuators is presented. Classical laminate theory with the induced strain actuation and Hamilton's principle are used to formulate the equations of motion. The total charge developed on the sensor layer is calculated from the direct piezoelectric equation. The equations of motion and the total charge are discretized with four-node, 12-degree-of-freedom quadrilateral plate bending elements with one electrical degree of freedom. The piezoelectric sensor is distributed, but is also integrated since the output voltage is dependent on the integrated strain rates over the sensor area. Also, the piezoelectric actuator induces the control moments at the ends of the actuator. Therefore, the number, size, and locations of the sensors/actuators are very important in the control system design. By selective assembling of the element matrices for each electrode, responses with various sensor/actuator geometries can be investigated. The static responses of a piezoelectric bimorph beam are calculated. For a laminated plate under the negative velocity feedback control, the direct time responses are calculated by the Newmark-beta method, and the damped frequencies and modal damping ratios are derived by modal state space analysis.