Abstract
The equation for transversely varying thickness modes in doubly rotated quartz resonators is applied in the analysis of trapped energy resonators with beveled cylindrical edges. The coefficients appearing in the planar differential operator are written as a sum of a mean or isotropic part plus a deviation. Asymptotic eigensolutions for the nearby isotropic case are obtained for the cylindrical beveled resonator. The resonant frequencies for the actual anisotropic case are obtained from an equation for the perturbation in eigenfrequency from the isotropic solution. A lumped parameter representation of the admittance, which is valid in the vicinity of a resonance, is obtained. Calculated results are presented for a few beveled AT- and SC-cut quartz resonators and the influence of the radius of curvature of the contour is exhibited.
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