【摘要】 通过非线性时间变换，利用系统的功能关系，结合小参数法，求出了强非线性振动系统主共振解和１／３亚谐解。利用转迁特性求得Ｄｕｆｉｎｇ方程从主共振到１／３亚谐共振解分叉转迁集的解析表达式，与ＩＨＢ（ＩｎｃｒｅｍｅｎｔａｌＨａｒｍｏｎｉｃＢａｌａｎｃｅ）方法的结果比较表明，两者吻合良好更多还原

【Abstract】 By introducing nonlinear time transformation, using the work energy relationship of the system and combining the method of small parameter, the primary resonant solution and 1/3 subharmonic resonant solution of the strongly nonlinear vibrating system are obtained. By studing the transition characteristics, the analytic expresses of the transition boundaries from 1/3 subharmonic solution to primary resonant solution of Duffings Equation are also obtained. The results by our method are in good agreement with those by Incremental Harmonic Balance method.更多还原