On the in-plane acceleration sensitivity of ST-cut quartz surface-wave resonators with interior rectangular supports

Abstract

An analysis of the in-plane acceleration sensitivity of ST-cut quartz surface-wave resonators with the substrate extending beyond interior rectangular supports is performed. In the treatment the variational principle with all natural conditions is extended in such a way as to permit interior surfaces of discontinuity with spring supports at which the approximating solution functions need not satisfy the constraint-type conditions. This extension is required for the approximation procedure used in the calculation of the biasing state. The resulting extensional biasing state is employed in an existing perturbation integral along with the proper continuous representation of the acoustic-surface-wave mode shape to calculate the in-plane acceleration sensitivity. The calculated results indicate how to select the distances between the supports so as to minimize the in-plane acceleration sensitivity for a given surface-wave resonator.