A normal mode expansion for piezoelectric plates and certain of its applications

The equations of motion of an arbitrary piezoelectric plate are represented by a set of second-order differential equations involving only the transverse spatial coordinates. This is achieved by expanding the thickness dependence in a set of basis functions derived from the solutions to the plate problem at cutoff. Techniques are presented for constructing approximate plate equations using only chosen mode amplitudes; such equations predict the true cutoff frequencies and give dispersion curves which are rigorously correct up to terms of order k(2). The coefficients in these equations can be computed analytically, and techniques for doing this are presented. Comparisons with dispersion curves calculated by partial wave analysis are given both for quartz and for lithium niobate. The theory provides a quite general basis for modeling devices such as trapped energy resonators.