Equivalent electric circuits of thin plates with two-dimensional piezoelectric actuators

Electrical equivalent circuits with impedance elements modeling the electromechanical behavior of a thin plate with piezoelectric actuators are presented. The dynamic characteristics of a two-dimensional piezoelectric force actuator are represented by a 5×5 impedance matrix, which is equivalent to a five-port electric network. When the dual piezoelectric actuators are assumed to produce average bending moments for a unit length along the edge at the interfacial surfaces, a 5×5 impedance matrix for these actuators is obtained. While the dual actuators are assumed to produce average bending moments for a unit area at the interfacial surfaces between the plate and the actuators, a 3×5 impedance matrix is presented. According to the theory of thin plates, the impedance of a rectangle thin plate with four simply supported edges is related with vibration amplitude of the plate. The continuity conditions between the actuators and the plates are established by using two approximate hypotheses we proposed. The system impedances are finally obtained by solving the impedance equations of the piezoelectric actuators and the plate. Four numerical examples are analyzed to illustrate the application of this modeling method, and the results agree well with the results obtained by other methods. Equivalent electric circuits of thin plates with piezoelectric actuators are capable of dynamically analyzing of such complex electromechanical system with 2D piezoelectric actuators.