Wave Propagation in an Infinite Piezoelectric Plate

The problem of wave propagation in an infinite piezoelectric plate belonging to crystallographic class C6v, situated between shorted electrodes, is rigorously analyzed for two special orientations of the sixfold axis. The solution is derived using the linear piezoelectric equations. The analysis shows that for a given frequency and wave number in the propagation direction there are three independent solutions of the differential equations, and, furthermore, that these three solutions couple at the traction-free boundaries of the plate. The dispersion curves can be calculated from the resulting transcendental equations. It has previously been shown that the resonant frequencies at infinite wavelength of a plate, in which the electromechanical coupling factors are high, deviate considerably from those of the purely elastic solution. Thus the dispersion spectrum calculated from this analysis will deviate considerably from that of the purely elastic analysis. It is shown in an appendix that the solution for the plate of infinite width is also applicable in the case of the plate of infinitesimal width.