Initial Stress Field and Resonance Frequencies of Incremental Vibrations in Crystal Resonators by Finite Element Method

摘要

A fine element method for numerical solutions is employed to solve the six coupled two-dimensional equations of vibrations for doubly rotated crystal plates by recasting them into a variational boundary value problem. Based on these equations two computer programs have been developed for the numerical solutions. The first program is for the purpose of calculating the initial stresses, strains, and displacements caused by the static applied forces and by the steady acceleration for the resonators with the most general crystal symmetry. The second program is to predict the resonance frequencies and mode shapes of the free, incremental vibrations in the same crystal resonators. Numerical results are obtained and compared with those from analytical or close form solutions for both isotropic and anisotropic plates and with experimental values. (Reprints)