Electroelastic plate equations for high frequency vibrations of thermopiezoelectric materials

In relation to high frequency vibrations of ceramic materials subject to strong electric fields and large deflections, a system of plate equations is deduced from the three-dimensional equations of thermopiezoelectricity with second sound. The system of two-dimensional approximate equations is derived in differential and variational forms by means of a unified variational principle together with the series expansions of field variables, and it governs the extensional, thickness-shear and flexural as well as coupled vibrations of electroelastic plates of uniform thickness. Certain cases involving special motions, geometry and material properties are indicated and, in particular, the linearised system of plate equations is recorded and the uniqueness of its solutions is also pointed out.