Exact electroelastic analysts of piezoelectric laminae via state space approach

In an attempt to develop an efficient analytical approach for the electromechanical analysis of laminated piezoelectric structures, an exact transfer-matrix-based methodology is presented. The state space equations for a three-dimensional piezoelectric lamina are first derived by eliminating the in-plane stresses and electric displacements from the governing equations. The transfer matrix is rendered in block form by judiciously arranging the slate variables and its property is then exploited to minimize the computational effort. Using the approach, an exact analysis of coupled electroelastic behavior of a rectangular piezoelectric plate of 6mm crystal symmetry subjected to a mechanical or electrical load is presented. A simply supported square plate made of barium titanate is analyzed as a numerical example and results are compared to those from the corresponding uncoupled analysis.