目的 分析得到正切型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PEM， 并针对跌落冲击动态方程的求解进行了算法修正， 选取正切型非线性包装系统跌落冲击模型为算例， 求解得到了一阶近似解； 与包装工程中的能量法结合， 对近似解进行了修正。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4%。结论 研究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。

The aim of this work was to analyze and get the approximate analytical solutions for dropping shock response of tangent nonlinear packaging system and to improve the accuracy of the solutions by correction, in order to satisfy engineering requirements. He′ s parameter-expanding method (PEM) that is applied to solve general nonlinear vibration problems was used. Taking tangent nonlinear packaging system dropping shock model as an example, the algorithm was modified for solving the dropping shock dynamic equations 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 showed that the maximum displacement response, the maximum acceleration response of the system and the period of the response after correction were very similar to those obtained with Runge-Kutta method, with a relative error of <4%. This research provides a new scientific and effective method for the approximate analysis of dropping shock response of nonlinear packaging system.