中文摘要：

对称破缺是复杂动力学系统的本质属性，决定着系统诸多非线性性质。关注荷载不对称性和结构耗散这两类引起对称破缺的因素，采用广义多辛分析方法研究了偏心冲击荷载作用下阻尼薄圆板振动问题。在哈密顿体系下，建立偏心冲击荷载作用下阻尼薄圆板振动问题的动力学控制方程，构造其广义多辛近似对称形式，研究由于以上因素引起的守恒律误差。随后采用显式中点差分离散方法构造其广义多辛格式，并用于研究圆板阻尼和冲击荷载偏心对振动过程的影响。研究思路为进一步探索动力学系统的对称性与耗散效应之间的内在联系奠定基础。

英文摘要：

Symmetry breaking is one of important properties of the complex dynamic system that affect the nonlinear characteristics of the dynamic systems. Focusing on the two typical symmetry case, including the asymmetry of the load as well as the dissipation effect, the vibration problem on the thin damping circular plate under the eccentric impact load is investigated by the generalized multi-symplectic method. Firstly, the control equation of the plate is established and the generalized multi-symplectic form is deduced for the control equation. And then, the errors of the conservation laws are given in the formwork of the generalized multi-symplectic theory. Finally, a generalized multi-symplectic scheme is constructed to simulate the vibration of the plate and the effects from the symmetry breaking are analyzed from the simulation results. The results obtained in this paper lay the foundation of the investigation on the relationship between the symmetry and the dissipation effect.