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

The in-plane acceleration sensitivity of ST-cut quartz surface-wave resonators with the substrate extending beyond interior rectangular supports is analyzed. In the treatment the variational principle with all conditions appearing as 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. The resulting extensional biasing state is used in the existing perturbation integral along with the proper continuous representation of the acoustic surface wave mode shape to calculate the in-plane acceleration sensitivity for this support configuration. Results are presented as a function of planar aspect ratio for a number of overhand configurations