Symplectic Elasticity Approach for the Anti-Plane Problem of One-Dimensional Hexagonal Piezoelectric Quasicrystal Plates

This paper presents the analytical solutions for the anti-plane problem in one-dimensional hexagonal piezoelectric quasicrystal plates using the symplectic elasticity approach. The equilibrium equations with body forces are transformed into the Hamiltonian system using the variational principle, and then the corresponding Hamiltonian operator matrix is derived. Furthermore, the completeness of the eigenfunction system of the operator is proved, and the general solutions to the problem are given by utilizing the symplectic orthogonality. As an application, the numerical results are obtained for the rectangular plates under the lateral concentrated load.