Analysis of plate piezoelectric unimorphs

Two-dimensional (2-D) equations for coupled extensional and flexural motions of a two-layered, elastic-piezoelectric plate (unimorph) are derived systematically from the 3-D equations of linear piezoelectricity. For static problems, the equations are simplified by the introduction of a stress function. The equations are used to analyze two problems of a circular disk unimorph under a uniform mechanical load and a voltage, and a concentrated load and a voltage. Analytical solutions are obtained and examined.