An analysis of the normal acceleration sensitivity of rotated Y-cut quartz surface transverse wave resonators simply supported along rectangular edges

An analysis of the normal acceleration sensitivity of rotated Y-cut quartz STW resonators simply supported along rectangular edges is presented. The analysis is based upon the perturbation integral formulation of Tiersten, and makes use of the previously known analytic representation of the substrate deformation for the case considered. An approximate STW mode shape which accounts for spatial variations along all three axes is employed in the perturbation integral, allowing the derivation of an analytic expression relating the normal acceleration sensitivity to such parameters as substrate length, width, thickness, and orientation, mode center offset, mode shape spatial variations, etc.