非线性包装系统跌落冲击问题变分迭代法

Variational iteration method for dropping shock problem of a cubic non-linear packaging system

以三次非线性包装系统为研究对象,用变分迭代理论分析系统跌落冲击问题,获得一阶迭代近似解。为提高解的精度,与包装动力学能量分析法结合求解最大位移及加速度,修正一阶迭代近似解。算例分析表明,修正后一阶近似解在冲击持续时间、加速度峰值及冲击响应波形上与椭圆积分结果非常接近。可为非线性包装系统跌落冲击分析提供新的方法。

The variational iteration method was used to give an approximate solution to dropping shock problem of a cubic nonlinear packaging system. In order to raise the accuracy of the solution, a novel method combining the variational iteration method with the energy method was proposed. Using it, the maximum dropping shock response acceleration and displacement of the system were solved with the energy method, and the first-order iteration approximation solution was modified. The results show that the acceleration versus time and the displacement versus time curves obtained with this method are very similar to those using the elliptic integration method, and the accuracy of acceleration peak value and extended period of dropping shock obtained is satisfactory. The studying results provided a new method for dropping shock problem analysis of nonlinear packaging systems.