Analysis of beams with piezoelectric stack by using finite element method and impedance method

Piezoelectric structures achieve structural control by using electromechanical coupling characteristics, therefore, their design and analysis involve interaction between mechanical system and circuit system inevitably. Based on the analogy between governing equations of mechanical system and circuit system, equivalent relation is established in the paper. Using the analogy relations, the piezoelectric stacks are equivalently modeled as one spring-mass-damping system and the electrical impedances are also included. The parameters are determined by analyzing the impedance matrix of the piezoelectric stack for the SMD system. Consequently, the impedance and mass elements in commercial FEM software will be used to simulate the electromechanical impedances in the coupling problem. Sensoring and actuation of a cantilever beam with piezoelectric stack support are analyzed by using the proposed method. Dynamic response of the system is analyzed when the piezoelectric stack is used as actuator or sensor respectively. The frequency response curves which are consistent with the existing results are obtained. As the advantages of the proposed method, the external circuit electrical impedance can be brought into the finite element model in the numerical examples. The results show that external circuit impedance has less impact on the frequency characteristics of structural system, but greater impact on the amplitude of electrical response. The other advantages of the proposed hybrid use of FEM and electromechanical impedance matrix are also discussed.