Symplectic analysis of vibration, buckling, and bending of 2D decagonal quasicrystal plates on a two-parameter elastic foundation

This paper presents a unified analytical framework for the free vibration, buckling, and bending of two-dimensional (2D) decagonal quasicrystal (QC) plates on two-parameter elastic foundations. The governing equations are derived based on Mindlin plate theory, reformulated as a Hamiltonian system, and solved analytically using the symplectic approach (SA). In contrast to traditional semi-inverse methods, the SA introduces dual variables to convert the higher-order differential equations into an equivalent first-order Hamiltonian form, eliminating the need for additional potential functions and simplifying the analytical procedure. The effects of elastic foundations, boundary conditions, geometric parameters, and phason-phonon coupling constants on the mechanical responses are systematically examined. The results show that the phonon field predominantly governs the plate behavior, while the elastic foundation markedly enhances structural stiffness. Boundary conditions and geometric parameters also exert significant influences on vibration frequencies, buckling stability, and bending deflections. These findings provide valuable guidance for the design and performance regulation of QC plates, and the SA employed in this study offers a general framework applicable to plate and shell structures made of other types of QCs.