Thickness-Shear and Flexural Vibrations of a Circular Disk

Equations governing the coupled thickness-shear and flexural vibrations of isotropic, elastic plates are solved for the case of a circular disk with free edges. The results of computations are given for the resonant frequencies analogous to those which would be excited in an AT-cut quartz disk with full electrode coating. A marked difference is observed between the frequency spectrum of the disk and the spectrum of cylindrical vibrations of a rectangular plate. The difference is due to the presence of thickness-twist modes of motion, in the disk, which, along with the thickness-shear modes, are coupled to the flexural modes.