Theoretical analysis and experimental measurement of flexural vibration and dynamic characteristics for piezoelectric rectangular plate

In this study, we investigate the out-of-plane vibration characteristics of a piezoelectric rectangular plate from theoretical analysis, numerical calculation and experimental measurement. The resonant frequencies and mode shapes of the piezoelectric rectangular plate with free boundary condition are analyzed in detail. The analytical solutions based on the superposition method are compared with two different techniques to confirm the validity. One is the numerical computation base on the finite element method (FEM), the other is experimental measurement. For experimental technique, two methods are used to validate the theoretical result, one is amplitude-fluctuation electronic speckle pattern interferometer (AF-ESPI) technique, and the other is laser Doppler vibrometry (LDV). This study uses a special configuration of electrodes for piezoelectric plates in experimental measurement of AF-ESPI to improve the electromechanical coupling efficiency of transverse vibration. It can be seen that specific vibration modes are easily excited by manipulating the configuration of electrodes. The superposition method is used to solve the out-of-plane displacement field and resonant frequencies for the piezoelectric plate. According to the explicit out-of-plane displacement field solution, the analytical results of mechanical and electric fields are also presented in explicit forms. It is shown that the comparison between theoretical analysis, numerical computations and experimental measurement in terms of the resonant frequencies and corresponding mode shapes are with good agreement.