On the normal acceleration sensitivity of ST-cut quartz surface wave resonators supported along rectangular edges

An analysis of the normal acceleration sensitivity of grooved ST-cut quartz surface wave resonators supported along the edges is performed. Both the simply supported and rigidly supported cases are treated. The variational principle with all natural conditions for anisotropic flexure, which is required for the new approximation procedure used in the calculation of the flexural biasing state for the case of rigid supports, is presented. The flexural biasing states are employed in an existing perturbation equation along with the proper continuous representation of the acoustic surface wave mode shape for arrays of reflecting grooves to calculate the normal acceleration sensitivity. It is shown that by appropriate selection of the planar aspect ratio of an ST-cut quartz substrate the normal acceleration sensitivity can be made to vanish.