Coupled Thickness Shear and Flexure Displacements in Rectangular <scp>AT</scp> Quartz Plates

Abstract

The length variation of the thickness-shear and thickness-flexure modes in rectangular AT quartz plates are computed from Mindlin's first order theory, which assumes particular thickness variation. These curves are compared with the mode shapes determined experimentally by measuring the x-ray intensity diffracted from vibrating quartz plates. The diffracted x-ray intensity is proportional to the curvature, a combination of strain-gradient terms of the Bragg planes, which may be approximated from the first-order theory. The approximation for the curvature is quite good for modes that are essentially thickness shear. When the mode has a large flexure component, the approximation used to determine the curvature of the Bragg planes is not as accurate.