Design optimization for acceleration sensitivity

One of the fundamental problems faced in producing precision crystal resonators is that the acceleration sensitivity can be very sensitive to manufacturing tolerances for a particular design. The present study seeks to quantify this phenomena by using a finite element model to obtain an accurate description of the stresses and deformations in a crystal plate that has been mounted in various configurations and then combine this solution with an analytical solution of the vibration mode shape for a harmonic of thickness shear in the general perturbation procedure to obtain the frequency shift. To this end, a very powerful software tool has been created to compute the frequency shift under any applied static bias. This finite element procedure has been integrated into a general nonlinear optimization program to automate the search for good designs. Example problems of resonators of various geometries and mounting schemes are presented.