具有局部非线性动力系统周期解及稳定性方法

对于具有局部非线性的多自由度动力系统，提出一种分析周期解的稳定性及其分岔的方法该方法基于模态综合技术，将线性自由度转换到模态空间中，并对其进行缩减，而非线性自由度仍保留在物理空间中在分析缩减后系统的动力特性时，基于Ｎｅｗｍａｒｋ法的预估－校正－局部迭代的求解方法，与Ｐｏｉｎｃａｒé映射法相结合，推导出一种确定周期解，并使用Ｆｌｏｑｕｅｔ乘子判定其稳定性及分岔的方法

A METHOD FOR DETERMINING THE PERIODIC SOLUTION AND ITS STABILITY OF A DYNAMIC SYSTEM WITH LOCAL NONLINEARITIES 1)

The analysis of dynamic system with many degrees of freedom can be highly complex in the presence of strong nonlinearities, but it is important to understand the mechanisms of some phenomena The fundamental response of a nonlinear nonautonomous system is periodic, other motions, such as quasi-periodic, jump, period-doubling and chaotic motion, can bifurcate from periodic motion when a system parameter is changed Therefore, determining the periodic solution and its stability are required in such case ...