目的 针对单自由度无阻尼 Duffing方程， 应用何氏频率-振幅关系(HFAF)得到简单的近似解析解。 方法 以三次非线性包装系统为研究对象， 应用何氏频率-振幅（HFAF）关系分析系统跌落冲击响应， 得到跌落冲击响应的近似解；为提高解的精度， 与包装动力学分析的能量法结合， 通过能量法求解最大位移及加速度， 对近似解进行修正。 结果 修正后的近似解其位移和加速度峰值与数值分析的结果相比较，相对误差小于 0.1%，近似解解析表达简单，物理意义明确。 结论 研究结果可为非线性包装系统跌落冲击响应分析提供一种新的快速近似分析方法。

Objective Targeting at single freedom undamped Duffing equation, the He,s frequency-amplitude formulation (HFAF) was used to give approximate solutions for dropping shock response of cubic nonlinear packaging system. Methods Taking the cubic nonlinear packaging system as the study object, He’ s frequency-amplitude formulation (HFAF) was used to analyze the dropping shock response of the system, to obtain the approximate solutions of dropping shock response. In order to improve the accuracy of the solutions, a novel solution combining HFAF with energy method was proposed, the maximal dropping shock response acceleration and displacement of the system were obtained with energy method, and the approximation solution was corrected. Results The results showed that the cceleration-time and the displacement-time curve obtained by this method were very similar to that obtained by Runge-Kutta method, with relative error of < 0.1%. The HFAF method was shown to solve effectively, easily and accurately for the dropping shock problem of nonlinear packaging system with approximations converging rapidly to accurate solutions. Conclusion The results of this research provides a new simple and effective method for the analysis of dropping shock response of nonlinear packaging system.