Coupled Vibration Analysis for a Piezoelectric Array Element Using Superposition Method

The coupled vibration was analyzed for a piezoelectric array element of two-dimensional structure whose vibration can be described by two coupled differential equations with coupled boundary conditions. The exact solutions satisfying both equations of motion and boundary conditions are not available. Therefore, the approximate solutions were obtained using the superposition method suggested for accurate vibration analysis of the elastic structures. To this end, the mechanical and electrical boundary conditions were satisfied approximately by summing the stress and the electric potential obtained from the displacements. The frequency spectrum and the electromechanical coupling factor of the element varying the width/thickness ratio were calculated and compared with the results of the finite element analysis and experiment. As the ratio of thickness to with increases, the fundamental frequency and the electromechanical coupling factor of the array element increase. The theoretically calculated results has shown good agreement with the results of the finite element analysis. The superposition method was verified to provide the accurate analysis for a piezoelectric array element.