Thickness-shear vibrations of circular quartz crystal plates

Abstract eng:
The thickness-shear vibrations of quartz crystal plates are of interests in the analysis and design of quartz crystal resonators which usually have complications because of structural configuration. Due to the material anisotropy, vibrations of circular plates of quartz crystal are no longer axisymmetric and solutions are not available from analytical solutions. By approximating the equations for the thickness-shear vibrations with the reduced couplings with the flexural mode only, we obtained the simplified equations of the only fundamental harmonics terms of angular dependence. The differential equations are solved by the Frobenius method with solutions in infinite power series for the thickness-shear and flexural mode shapes and frequency spectra.

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