An analysis of the normal acceleration sensitivity of contoured quartz resonators with simple rectangular supports

The normal acceleration sensitivity of contoured quartz resonators with the plate extending slightly beyond simple rectangular supports is analyzed. The biasing deformation fields are calculated by means of a novel variational approximation procedure that employs the variational principle with all natural conditions for anisotropic static flexure. The accompanying strains varying quadratically through the thickness are then determined recursively from the plate shearing stress resultants. The calculated biasing deformation fields are employed in an existing perturbation equation along with the equivalent trapped-energy mode shapes for the contoured resonator to calculate the normal acceleration sensitivities. Results are presented for a range of orientations and aspect ratios of the rectangular support configuration for both the AT and SC cuts