Parametric study of acceleration insensitivity of doubly rotated circular quartz resonators

The purpose of the study was to search for potentially acceleration-insensitive circular quartz resonators by computing the combined effect from various resonator parameters in order to reduce or minimize acceleration sensitivity. Initial displacement gradients and strains that were caused by the steady acceleration of an arbitrary direction acting on a crystal disk are calculated from the finite-element solution of Mindlin´s two-dimensional first-order equations of equilibrium of crystal plates. These initial displacement gradients and strains are then taken into account as known functions in the frequency equation of incremental thickness vibrations which is, in turn, solved for frequency changes by a perturbation method