冲击荷载作用下中心对称薄圆板振动的多辛分析

摘要

基于Bridges建立的多辛理论，构造了中心对称薄圆板振动方程的多辛对称形式及其多种局部守恒律，针对振动方程的多辛形式，采用Euler Box差分离散方法构造其多辛格式，利用计算机模拟，研究了冲击荷载作用下中心对称薄圆板的振动问题，并在模拟过程中重点关注多辛算法是否精确保持振动系统的局部几何性质，该研究结果为薄板振动问题提供了新的数值研究途径。%To preserve the local geometric properties of a dynamic system , one of the important factors for determi-ning 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 re-sults, 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 .