运用同伦分析法分析一类Duffing系统

PE-HAM method on a class of Duffing equation

运用基于参数展开的同伦分析理论(PE-HAM)研究了具有五阶非线性项的保守Duffing振子ü+ω02 u+αu5=0的响应问题.在进行参数展开时,通过系统频率不同展开式分别求出了此类系统在含有小参数和不要求含有小参数情况下的近似解和近似周期.数值模拟结果说明,所得的解析近似解具有较高的精度,从而说明了同伦分析方法既适用于弱非线性系统也适用于某些强非线性系统.

A new homotopy technique based on the PE-HAM （parameter expansion homotopy analysis method） is applied to investigate the response of conservative Dulling oscillator with 5th order nonlinear term of the form u＋ω^20u＋αu^5=0. When expanded the parameters, by means of the technique of different frequency expansion, the approximate period and solution when a is a small parameter or not a small one are obtained. Then the numerical simulation proved that the analytically approximate solution obtained by this method is of high accuracy. Therefore, this technique is suitable for weakly nonlinear systems and some strongly nonlinear systems.