Plane analysis for functionally graded magneto-electro-elastic materials via the symplectic framework

By introducing the displacements, electric potential, magnetic potential and their dual counterparts as state variables, a symplectic analysis framework is established in the Hamiltonian system to solve the plane problem of functionally graded magneto-electro-elastic materials. The material properties are assumed to vary along the length direction in an identical exponential form. The method of separation of variables along with the eigenfunction expansion technique is employed to reduce the original problem to the eigenvalue/eigensolution analysis. The particular eigensolutions corresponding to eigenvalues of zero and –α are given, which while bearing definite physical interpretations exhibit some unique characteristics. A numerical example is presented to show the influence of material inhomogeneity on the β-group solutions of the problem.