In-plane accelerations and forces on frequency changes in doubly rotated quartz plates

Two-dimensional equations of motion of doubly rotated quartz plates for the thickness-shear, flexure, and extensional vibrations under in-plane initial stresses are employed to predict changes in the fundamental thickness-shear frequencies due to initial stresses. Two types of initial stresses are considered: (1) stresses due to a pair of diametral forces, and (2) stresses due to steady accelerations for a three-point ‘‘T’’-shaped mount and a four point ‘‘+’’-shaped mount configurations. Force sensitivity and acceleration sensitivity coefficients are computed and compared with experimental data and existing computed results. For both ‘‘T’’- and ‘‘+’’-shaped mount configurations, mount orientations corresponding to the maximum and minimum of acceleration sensitivity are predicted.