An analysis of the normal acceleration sensitivity of contoured quartz resonators rigidly supported along the edges

The authors perform an analysis of the normal acceleration sensitivity of contoured quartz resonators rigidly supported along rectangular edges. Calculated biasing deformation fields are used in an existing perturbation equation along with the equivalent trapped energy mode shapes for the contoured resonator to calculate the normal acceleration sensitivities. It is shown that the normal acceleration sensitivity vanishes for certain values of the planar aspect ratio for all modes considered in both the AT and SC cuts. In addition, the sensitivity has been calculated as a function of the orientation of the rectangle with respect to the nodal lines of the anharmonics of the contoured resonator for the case of square AT- and SC-cut plates. The calculations reveal that the SC cut has zero-crossings for this case while the AT cut does not and that the sensitivity is consistently lower for the square SC cut than the AT cut