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

A perturbation technique is developed for calculating the change in mode shape in a plano-convex thickness shear resonator blank due to off-center mass perturbations. The perturbed shape is built as a linear combination of the usual unperturbed modes and their anharmonics. The change in the center location of the mode is used to predict experimentally observed changes in the acceleration sensitivity of two-point mounted 10 MHz, 3rd, SC-cut resonators when patches of metal film are deposited on the major surfaces off-center