Thickness-field excitation of doubly-rotated piezoelectric crystal

Two-dimensional equations of motion of piezoelectric crystal plates, developed previously from the three-dimensional series of the thickness coordinate of the plate, are used to study the vibrations driven by the thickness electric field applied to the major surfaces of doubly-rotated quartz strips. Straight-crested vibrational solutions in closed form are obtained for the first eight coupled equations which constitute the two-dimensional, first-order approximate equations of motion of piezoelectric crystal plates. Dispersion curves, the frequency spectrum for electrically shorted and traction-free surface conditions, and mode shapes at different resonances and for various width-to-thickness ratios of the plate are computed and plotted for SC-cut quartz strips