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基于Lyapunov运动稳定性理论,经过推导可知,一个单自由度的某一个受迫振动的特解的运动稳定性问题等价于这个单自由度系统自由振动的稳定问题.对于复杂非线性系统的动力稳定性问题,直接应用Lyapunov理论进行系统的动力稳定性判定比较困难,考虑大跨度拱型结构的变形特征,提出一种简洁、实用且适合数值计算的动力稳定性判别方法——位移时程变化法.运用该方法计算结构在承受一般动荷载类型和不同计算条件下的动力稳定性,验证此方法的实用性及正确性.
Based on the theory of Lyapunov stability, we know that the stability problem of a particular solution of a forced one-degree-of-freedom vibration is equivalent to the stability problem of the free vibration of a one-degree-of-freedom system. For the dynamics of complex nonlinear systems It is difficult to directly apply the Lyapunov theory to determine the dynamic stability of the system. Considering the deformation characteristics of the long-span arch structure, a simple, practical and suitable numerical method to determine the dynamic stability of the dynamic stability of the system is proposed The method is used to calculate the dynamic stability of the structure subjected to general dynamic load types and different calculation conditions, and to verify the practicability and correctness of this method.