A Study of Displacement Distribution in a Piezoelectric Heterogeneous Bimorph

Piezoelectric heterogeneous bimorphs have extensive applications in the MEMS area. In order to formulate their displacement distribution more conveniently, a concise analytical solution is described herein. This solution integrates all of the important influence factors, such as geometry and material properties, into a single expression. Secondary effects such as shear, residual stress induced curvature, and electrostiction, are not considered, but they are found to be minimally important based on the accuracy of the predicted results. The expression is verified using the finite element method, and shown to be straightforward compared to the more complicated couple-field FEM analysis for a specific range of materials and thicknesses. The method is subsequently shown to be capable of quickly estimating the displacement in a bimorph beam, making it a useful tool for designing piezoelectric structures.