正切型非线性包装系统跌落冲击响应分析的同伦摄动法与修正

Correction of the homotopy perturbation method for analyzing dropping shock response of a tangent nonlinear packaging system

以正切型非线性包装系统为例,对系统跌落冲击的响应进行理论分析,以得到包装系统跌落冲击响应的近似解析解。采用解决普遍非线性振动问题的同伦摄动法,并结合包装工程中的能量法对跌落冲击动态方程的求解进行了算法修正。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1%。该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。

Aimsing at analyzing the accuracy of approximate analytical solutions for dropping shock responses of a tangent nonlinear packaging system without damping, dropping shock dynamic equations were established and the first-order approximate solutions were obtained by applying the homotopy perturbation method which is often adopted to solve general nonlinear vibration problems. The results were further modified by the energy method usually used in the packaging engineering. The corrected maximum displacement responses, the maximum acceleration responses and the system response periods are very close to the Runge-Kutta numerical solutions. The relative error is less than 1%. The research provides an effective and scientific method for the analysis of dropping shock responses of nonlinear packaging systems.