Multi-symplectic analysis of vibration of centrosymmetric thin circular plate under impact load

To preserve the local geometric properties of a dynamic system, one of the important factors for determining its dynamic response, we analyze the vibration of the centrosymmetric thin circular plate under impact load in the Hamiltonian space. Section 1 of the full paper derived Eq. (4) as the multi-symplectic symmetric form of the centrosymmetric thin circular plate and Eqs. (5), (6) and (7) for its local conservation laws. Section 2 uses the Euler Box difference discretization method to construct Eq. (8) as the multi-symplectic difference discretization scheme of the multi-symplectic symmetric form. Section 3 simulates the vibration of the centrosymmetric thin circular plate under impact load and fixed boundary conditions to analyze its dynamic response. The simulation results, given in Figs. 1 and 2, show preliminarily that our multi-symlectic algorithm can accurately keep for a long time the local geometric properties of the centrosymmetric thin circular plate under impact load, indicating that the dynamic response analysis obtained with the multi-symlectic algorithm is reliable.