Symplectic superposition method for vibration problems of orthotropic rectangular thin plates with four corners point-supported

This paper presents a series expansion solution for the vibration question of an orthotropic rectangular thin plate (RTP) with four corners point-supported based on the superposition method and the separation variable method in the Hamiltonian system. First, the original vibration question is decomposed into two sub-vibration questions by analyzing the boundary conditions. After that, the separation variable method in the Hamiltonian system is used to calculate the general solutions for the two sub-vibration questions. Then, these two general solutions are superimposed to obtain the symplectic superposition solution for the original vibration question. Finally, the gained symplectic superposition solution is applied to calculate the vibration questions of isotropic and orthotropic RTPs with four corners point-supported, and the convergence analysis is conducted for the calculation of the orthotropic RTPs using the symplectic superposition solution.