具有局部非线性动力系统周期解及稳定性方法

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

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。

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 A method for determining the periodic solution and its stability of a dynamic system with local nonlinearities is presented The linear degrees of freedom of components are condensed by using the mode synthesis technique, while the nonlinear degrees of freedom are still in physical space A Newmark’s scheme-based predictor-corrector algorithm is used to analyze the behaviors of the reduced system Periodic solutions are calculated efficiently by Poincaré mapping method in combination with the Newmark’s scheme-based predictor-corrector algorithm Floquet multipliers are calculated to determine the local stability of these solution and to identify local bifurcation points This method is efficient in analyzing both the stability and bifurcation of periodic motion in dynamic system mentioned above, especially for the secondary Hopf bifurcation, saddle-node bifurcation, period-doubling bifurcation, and chaotic motion Finally, a practical example, Fluid Film Bearing-Rotor Dynamic System with Squeeze Film Damper, is presented to examine the method, and it is verified that the method is efficient in analysis of large order dynamic system with local nonlinearities