Calculated orientations and aspect ratios of stiffened rectangular support systems of SC-cut quartz resonators which minimize the influence of fabrication imperfections on acceleration sensitivity

Existing computer programs are used in the calculation of rectangular support orientations and aspect ratios to minimize the influence of fabrication imperfections on the resultant acceleration sensitivity of stiffened rectangular support systems of SC-cut quartz resonators. Both contoured and flat-plate trapped energy resonators are treated. The shorter distance between the sidewalls is established by a criterion associated with the energy in the mode shape for each particular harmonic. Results are presented for a range of energy criteria and a number of contoured and flat-plate resonators. Although the square plate never yields good results, optimal and near-optimal results are obtained for aspect ratios considerably less than 2.0. Indeed, it is shown that an aspect ratio of 1.5 consistently yields optimum or near-optimum results. However, the orientation of the support rectangle varies significantly from one resonator to another