Vibration analysis of thin plate actuated by piezoelectric element using finite element method and impedance method

The impedance is often used as a measurement to represent the dynamics of an intelligent material system. This study attempts to combine the theoretical analysis and the finite element method to establish relationships between input efforts and output effect at the boundaries of a piezoelectric membrane. At first, vibration analysis of a piezoelectric membrane under harmonic excitation is conducted, and a 5×5 impedance matrix is theoretically obtained to represent the dynamics of the piezoelectric element. The exciting forces and equivalent impedances of the piezoelectric membrane are worked out by analyzing the elements of the impedance matrix. Then, the forces and the equivalent impedances are set up in finite element models, in order to model the interaction between the elastic plate and the piezoelectric patches, and the dynamic response of piezoelectric patches driving plates is obtained finally by using commercial FEM software. A thin steel plate actuated by PVDF at three different pasting positions is taken as examples, and the dynamic responses are predicted by using the proposed method. The results are compared with the results from the other theoretical and experimental methods. It indicates that the results from this paper are in good agreement with the other results. It is shown that the proposed model and method is effective in analyzing vibration of smart structures with two-dimensional piezoelectric patches. Because of the advantages of finite element method, the proposed method is naturally suitable and more convenient for dynamic analysis of complex structures.