Acceleration Effect on the Thickness Vibrations of Doubly Rotated Crystal Resonators

摘要

Changes of resonance frequencies of thickness vibrations in doubly rotated circular disks of quartz due to steady accelerations as body forces are studied. The plate is of uniform thickness and supported at the edge by flexible metal ribbons with rigid contact. The initial fields of displacement, strain, and stress, caused by the reactions of the ribbon supports to the body force of arbitrary direction, are obtained by a finite element method based on Mindlin's two-dimensional, first-order equations of equilibrium for crystal plates. The frequency equation for incremental thickness vibrations superposed on the initial deformations is obtained from the previously derived two-dimensional equations of motion for incremental vibrations. In the frequency equation, the initial strain and initial deformation tensors appear as given functions of x1 and x3 of the plate. Then, by a perturbation method, changes of thickness frequencies as functions of the thickness frequencies as functions of the direction of acceleration are computed for SC-cut circular quartz resonators. The effects of plate thickness, support configurations, and support structure on the acceleration sensitivity are studied.