Forced vibration analysis of piezoelectric quartz plates in resonance

Quartz is a widely used piezoelectric material and quartz resonators are the primary components in many industrial applications due to the piezoelectric effect. To have a thorough understanding on the vibration characteristics of quartz plates, the experimental measurement of resonant frequencies and mode shapes is indispensable. In this paper, two experimental techniques, amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) and laser Doppler vibrometer (LDV), which are, respectively, full-field and point-wise displacement measurement methods, are used to obtain the out-of-plane vibration characteristics of AT-Cut quartz in real time. The resonant frequencies and the corresponding vibration mode shapes are successfully obtained at the same time from AF-ESPI method. However, only the resonant frequencies of the out-of-plane vibration modes are determined by the LDV. The cantilever and completely free quartz plates are used in this study and the experimental results are verified by the finite element method (FEM) analysis. The cantilever quartz plates are excited from applying voltage and acoustic waves. Furthermore, three designs of electrode for a quartz plate with free-boundary condition are studied. Excellent agreement between the measured data from the optical method and the numerical results predicted by FEM are found for both resonant frequencies and mode shapes.