An analysis of the in-plane acceleration sensitivity of contoured quartz resonators rigidly supported along the edges

The in-plane acceleration sensitivity of contoured AT- and SC-cut quartz crystal resonators with the same support configuration is performed. The extensional biasing deformation field is determined by means of the variational approximation procedure using the variational principle in which all conditions appear as natural conditions. The resulting extensional biasing state is used in the existing perturbation equation along with the mode shapes of the contoured resonators to calculate the in-plane acceleration sensitivities. Results are presented as a function of the planar aspect ratio and orientation of the rectangle.<>