研究强非线性振动系统同宿分岔问题的规范形方法

以改进的规范形理论为基础，采用强非线性振动问题的分析方法，拓展了原有弱非线性振动系统同宿分岔判据的适用范围.首先在复规范形求解过程中引入待定固有频率，计算了一类单自由度强非线性振动系统的周期解.然后分别依据系统的待定固有频率趋于零和周期轨道趋近于鞍点两条途径获得了强非线性振动条件下系统同宿分岔的解析判据.最后通过与原有解析结果和数值结果相比较验证了本文方法的有效性.关键词：规范形同宿分岔强非线性周期解

Homoclinic bifurcation of the strongly nonlinear oscillation system by the normal form method

The available range of the homoclinic bifurcation criterions are extended from the weakly nonlinear oscillation system to the strongly nonlinear oscillation system. It combines the analysis method of the strongly nonlinear oscillation system with the former criterions based on the improved complex normal form method. The periodic solution of this kind of system with a single degree of freedom is obtained by introducing the fundamental frequency under determination into the complex normal form computation. Then two different analytical criteria to predict the critical values of homoclinic bifurcation are adapted to the new system. It includes the undertermined fundamental frequency approaching zero and the collision of the periodic orbit with the saddle point. The results derived from different methods are compared in the specific systems with numerical simulation to testify the correctness and efficiency of the theoretical results.