TRANSVERSELY VARYING THICKNESS MODES IN QUARTZ RESONATORS WITH BEVELED CYLINDRICAL EDGES

The equation for transversely varying thickness modes in doubly rotate d quartz resonators is applied in the analysis of trapped energy reson ators with beveled cylindrical edges. The coefficients appearing in th e planar differential operator are written as a sum of a mean or isotr opic part plus a deviation. Asymptotic eigensolutions for the nearby i sotropic 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 resul ts are presented for a few beveled AT- and SC-cut quartz resonators an d the influence of the radius of curvature of the contour is exhibited . (C) 1994 American Institute of Physics.