摘要
针对典型双曲正切缓冲包装系统,跌落冲击条件下讨论系统近似解析解。将系统简化为三次-五次非线性系统,引入无量纲参数推导无量纲动力学方程,应用牛顿谐波平衡法获得系统响应一阶、二阶、三阶近似解析解。算例分析表明,牛顿谐波平衡法获得的三阶近似解与龙格-库塔法的数值解最为接近,位移响应最大值、加速度响应最大值以及跌落冲击时间的相对误差控制在1%以内。为双曲正切型非线性系统跌落冲击响应分析提供了一种新的近似分析方法。
For a typical hyperbolic tangential buffering packaging system,the approximate analytical solution of the system was discussed under the condition of drop impact.The hyperbolic tangent system was simplified to the cubic-quintic nonlinear system,and the dimensionless dynamic equation was obtained by introducing dimensionless parameters.The first-order,second-order and third-order approximate analytical solutions of the system response were obtained by the Newton-harmonic balancing method.Compared with the fourth-order Runge-Kutta numerical solution,the example analysis showed that the third-order approximate solution of the Newton-harmonic balancing method was the closest to the Runge-Kutta numerical solution,and the relative errors of the maximum displacement response,maximum acceleration response and dropping shock duration were controlled within 1%.A new approximate analysis method was provided for the drop impact response analysis of hyperbolic tangential nonlinear packaging system.
作者
赵晓兵
杜兴丹
陈安军
ZHAO Xiaobing;DU Xingdan;CHEN Anjun(Wuxi Institute of Metrology and Testing,Wuxi Jiangsu 214101,China;School of Mechanical Engineering,Jiangnan University,Wuxi Jiangsu 214122,China;China National Control and Testing Center for Packaging Quality,Wuxi Jiangsu 214122,China)
出处
《包装学报》
2019年第3期82-87,共6页
Packaging Journal
关键词
双曲正切型非线性系统
牛顿谐波平衡法
近似解
位移最大值
加速度最大值
跌落冲击时间
hyperbolic tangent nonlinear system
newton-harmonic balancing
approximate analytical solution
maximum displacement
maximum acceleration
dropping shock duration
