A new symplectic approach for piezoelectric cantilever composite plates

Abstract

In the paper, an analytical method is developed to investigate piezoelectric composite plate under in-plane loads. The method based on Hamiltonian system uses both displacements and stresses as variables so that the equations so derived are variable-separable. The method of separation of variables is subsequently applied to solve the equations. The significant zero and nonzero eigensolutions are presented where the former expresses basic mechanical properties while the latter describe the localized solutions in accordance with the Saint-Venant principle. Linear combinations of them completely cover all kinds of solutions with any boundary conditions along the edges. The method shows an analytical and rational process which is different from the classical semi-inverse methods. To verify advantages of the method, some numerical examples of piezoelectric cantilever composite plates are presented. Furthermore, the boundary effects are observed. The analytical solutions can serve bench mark examples for finite element analysis.