赵晓兵,杜兴丹,陈安军.正切型缓冲系统跌落冲击响应分析的NHB方法[J].包装工程,2019,40(7):46-50.
ZHAO Xiao-bing,DU Xing-dan,CHEN An-jun.NHB Method for Analyzing Dropping Shock Response of Cushion Packaging System with Tangent Nonlinearity[J].Packaging Engineering,2019,40(7):46-50. |
| 正切型缓冲系统跌落冲击响应分析的NHB方法 |
| NHB Method for Analyzing Dropping Shock Response of Cushion Packaging System with Tangent Nonlinearity |
| 投稿时间：2018-12-06 修订日期：2019-04-10 |
| DOI：10.19554/j.cnki.1001-3563.2019.07.007 |
| 中文关键词: 牛顿谐波平衡 非线性 分析解 位移最大值 加速度最大值 跌落冲击时间 |
| 英文关键词: newton-harmonic balancing nonlinear analytical solution maximum displacement maximum acceleration dropping shock duration |
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| 中文摘要: |
| 目的 为了获得正切型缓冲系统跌落冲击响应的近似解析解。方法 将正切型系统简化为3次、5次非线性系统，经无量纲处理后获得无量纲动力学方程，应用牛顿谐波平衡法求解系统无量纲动力学方程，得到跌落冲击响应一阶、二阶近似解析解，并获得系统位移响应最大值、加速度响应最大值以及跌落冲击持续时间等重要参数的解析表达式。结果 通过算例分析表明，牛顿谐波平衡法二阶近似解与龙格-库塔数值解接近，相对误差控制在2%以内。结论 牛顿谐波平衡法为非线性缓冲系统跌落冲击响应分析提供了一种新的有效解析方法。 |
| 英文摘要: |
| The aim of this work is to analyze and get the approximate analytical solutions for dropping shock response of cushion packaging system with tangent nonlinearity. The tangent system was simplified to the cubic-quintic nonlinear system to obtain the dimensionless dynamic equation after dimensionless treatment. The Newton-harmonic balancing method was used to obtain the first-order and the second-order analytical solutions of dropping shock response to the non-dimensional dynamic equation, and the analytical expressions of important parameters including the maximum displacement, the maximum acceleration of the system response and the dropping shock duration. The example analysis showed that the second order approximate solutions of the NHB method were very similar to those obtained from the Runge-Kutta method. The relative error was controlled within 2%. The newton-harmonic balancing method provides a new effective solution method for dropping shock response analysis of nonlinear packaging system. |
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