Thickness-Shear and Flexural Vibrations of Rectangular Crystal Plates

Equations governing thickness-shear and flexural vibrations of crystal plates are solved for the infinite plate, the simply-supported rectangular plate and the rectangular plate with one pair of parallel edges free and the other pair simply-supported. The equations permit three types of sinusoidal waves, with sinusoidal crests, in an infinite plate. Each of these undergoes a simple reflection upon normal incidence at a simply-supported straight edge, so that the frequency spectrum of a simply-supported rectangular plate has a relatively simple character. The results of a typical computation are given for the AT-cut of quartz. At a free edge each type of incident wave gives rise, in general, to all three types of reflected wave. Consequently, the frequency spectrum of a plate with a pair of parallel, free edges exhibits an intricate coupling of three infinite systems of modes. The development of the coupling is traced continuously by means of a solution involving elastically supported edges.