The investigation of three-dimensional vibration for piezoelectric rectangular parallelepipeds using the AF-ESPI method

Electronic speckle pattern interferometry (ESPI) is a powerful tool for the full-field measurement of a deformed body. In this paper, a three-dimensional vibrating block that couples the out-of-plane and in-plane motions is investigated using the amplitude-fluctuation ESPI (AF-ESPI). This method demonstrates the advantages of combining high processing speed, such as in the subtraction method, with high fringe sensitivity, such as in the time-averaged method. The optical system for AF-ESPI is then employed to analyze the volume vibration of piezoelectric material for a rectangular parallelepiped configuration. Based on the fact that fringe patterns measured by the AF-ESPI method appear as a clear picture only at the resonant frequency, both the natural frequencies and the out-of-plane and in-plane vibration mode shapes are successfully obtained in this study. Finally, the impedance analysis as well as the finite element method (FEM) with three-dimensional model are also conducted to compare with the result obtained by AF-ESPI. It is shown that the numerical calculation and the experimental result agree fairly well for both the resonant frequency and the mode shape in three-dimensional configurations.