强非线性多自由度自治系统的内共振

基于改进的KBM法,研究了强非线性多自由度自治系统的内共振.求出了极限环的振幅和近似解的表达式.与KBM法比较,该方法的特点是:近似解中包含项中的不再是时间的线性函数,而是时间的非线性函数,它能提高近似解的精度,且应用更广.最后给出一个具体实例,得到了近似解以及相图.和数值结果比较,本文方法具有较高的精度.

Internal resonance of strongly nonlinear autonomous systems with multi-degrees of freedom

The internal resonance of strongly non-linear autonomous systems with multi-degrees of freedom was analyzed on the basis of modifying the KBM method,and the amplitude of limit cycles and the approximate solution were obtained.Compared with KBM method,the characteristic of the present method was that the term included in the approximate solution was a nonlinear function of time instead of a linear function,which could increase the accuracy and be used extensively.An example was given,whose approximate solution and phase-space trajectories were obtained.The results computed by this method were in pretty good agreement with the numerical results,and the accuracy of the present method was very good.