Three-dimensional analysis of an antiparallel piezoelectric bimorph

Three-dimensional electromechanical responses of a piezoelectric bimorph ar e studied. The bimorph is antiparallel in the sense that it consists of two identical, plate-like piezoelectric elements with opposite poling directio ns. Both the top and bottom surfaces of the bimorph are fully covered with negligibly thin conductive electrodes. By introducing a small parameter and using the transfer matrix method it is shown that a three-dimensional solu tion of the problem can be readily constructed, provided the solution to a set of two-dimensional equations very similar to those in the classic plate theory is obtainable. The three-dimensional solution satisfies all the fie ld equations as well as the boundary conditions on the major surfaces and a t the interface between the two piezoelectric plates. In many special cases , the electric edge condition can be fulfilled point by point, and thus the solution is exact in Saint-Venant's sense. The formulation and new analyti cal results for a strip-shaped cantilever bimorph under the action of appli ed voltage and end moment are presented.