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

作　　者：赵晓兵 杜兴丹 陈安军 ZHAO Xiao-bing;DU Xing-dan;CHEN An-jun(Wuxi Institute of Metrology and Testing,Wuxi 214101,China;School of Mechanical Engineering,Jiangnan University,Wuxi 214122,China;China National Control and Testing Center for Packaging Quality,Wuxi 214122,China)

机构地区：[1]无锡市计量测试院,无锡214101 [2]江南大学机械工程学院,无锡214122 [3]国家轻工业包装制品质量监督检测中心,无锡214122

出　　处：《包装工程》2019年第7期46-50,共5页Packaging Engineering

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。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.

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 

分 类 号：TB485.1[一般工业技术—包装工程]