FINITE-ELEMENT MODELING OF PIEZOELECTRIC SENSORS AND ACTUATORS

A finite element formulation for vibration control of a laminated plat e with piezoelectric sensors/actuators is presented. Classical laminat e theory with the induced strain actuation and Hamilton's principle ar e used to formulate the equations of motion. The total charge develope d on the sensor layer is calculated from the direct piezoelectric equa tion. The equations of motion and the total charge are discretized wit h four-node, 12-degree-of-freedom quadrilateral plate bending elements with one electrical degree of freedom. The piezoelectric sensor is di stributed, but is also integrated since the output voltage is dependen t on the integrated strain rates over the sensor area. Also, the piezo electric actuator induces the control moments at the ends of the actua tor. Therefore, the number, size, and locations of the sensors/actuato rs are very important in the control system design. By selective assem bling of the element matrices for each electrode, responses with vario us sensor/actuator geometries can be investigated. The static response s of a piezoelectric bimorph beam are calculated. For a laminated plat e under the negative velocity feedback control, the direct time respon ses are calculated by the Newmark-beta method, and the damped frequenc ies and modal damping ratios are derived by modal state space analysis .