基于同伦摄动法三次型非线性系统跌落冲击响应分析

Drop Impact Response Analysis of Cubic Nonlinear System Based on Homotopic Perturbation Method

目的以典型的三次型非线性系统为研究对象,研究非线性系统跌落冲击响应的近似解析。方法研究包含复杂非线性项的保守缓冲包装系统,以三次型非线性系统为例,通过使用同伦摄动法求解运动方程,求得跌落冲击响应的一阶近似解,并使用能量法修正一阶近似解。基于最大加速度响应表达式,获取非线性系统破损边界曲面,进行系统损伤评价。结果修正后的一阶近似解的最大位移响应、最大加速度响应与龙格库塔法的数值更接近。随着产品脆值的增大,破损边界曲线逐渐上移,系统就越安全。结论同伦摄动法的应用可为后续的非线性跌落冲击分析提供简便性。

The work aims to study the approximate analysis on drop impact response of nonlinear system with typical cubic nonlinear system as the research object. The conservative buffer packing system with complex nonlinear terms was studied. Taking a cubic nonlinear system as an example, the first order approximate solution of the drop impact response was obtained by solving the motion equation with homotopic perturbation method, and the first order approximate solution was modified by energy method. Based on the expression of the maximum acceleration response, the damage boundary surface of the nonlinear system was obtained and the damage evaluation of the system was carried out. The maximum displacement response and the maximum acceleration response of the modified first order approximate solution were closer to the values of Runge Kutta method. With the increase of product brittleness value, the damage boundary curve moved up gradually and the system was more secure. The application of homotopic perturbation method can provide convenience for the subsequent nonlinear drop impact analysis.