Hamiltonian System for Three-Dimensional Problem of Two-Dimensional Decagonal Piezoelectric Quasicrystals and Its Symplectic Analytical Solutions

A Hamiltonian system is developed for the three-dimensional (3D) problem of two-dimensional (2D) decagonal piezoelectric quasicrystals via the variational principle. Based on the full state vector and the properties of the Hamiltonian operator matrix, the superposition principle of solutions obtains the symplectic analytical solutions of the problem under simply supported boundary conditions. Numerical examples are illustrated to display the effects of the stacking sequences and material constants on the stresses, displacements, electric potential, and electric displacements under the mechanical and electric displacement loadings. The symplectic analytical solutions presented in the article can be used as a reference for further numerical research.