Distortions of thickness shear mode shapes in plano-convex quartz resonators with mass perturbations

A perturbation technique for calculating the change in mode shape in a plano-convex thickness shear resonator blank due to off-center mass perturbations is developed. The perturbed shape is built as a linear combination of the familiar unperturbed modes and their anharmonics. The change in the location of the average center of the mode is calculated for different contours and different mass perturbation shapes and thicknesses. The results are used to predict changes in the acceleration sensitivity of two-point mounted 10-MHz, third SC-cut resonators when patches of metal film are deposited on the major surfaces off-center. These theoretical results are compared with published experimental results.<>