目的 分析得到三次非线性包装系统跌落冲击的近似解析解， 修正提高解的精度， 以达到工程要求。方法 采用解决普遍非线性振动问题的何氏参数展开法， 并针对跌落冲击动态方程的求解进行算法修正， 选取三次非线性包装系统跌落冲击模型为算例， 求解得到一阶近似解； 与包装工程中的能量法结合， 对近似解进行修正。结果 修正后的最大位移响应、 最大加速度响应、 系统响应周期与Runge-Kutta数值解非常接近， 相对误差小于0.05%。结论 为非线性包装系统跌落冲击响应分析提供了一种新的科学有效的近似分析方法。

This study analyzed and obtained the approximate analytical solutions for dropping shock response of cubic nonlinear packaging system and improved the accuracy of the solutions and achieved engineering requirements by correction. He′ s parameter-expanding method (PEM) was applied to solve general nonlinear vibration problems. Taking the dropping shock model of cubic nonlinear packaging system as an example, the dropping shock dynamic equations were solved, the algorithm was modified and the first-order approximate solutions were obtained. A novel solution combining PEM with energy method was proposed and the approximation solution was corrected. The results after modification showed that the maximum displacement response, the maximum acceleration response of the system and the period of the response were very similar to those by Runge-Kutta method, with the relative error of < 0.05%. This study provided a new scientific and effective method for the analysis of dropping shock response of nonlinear packaging system.