正切型非线性包装系统跌落冲击响应分析的同伦摄动法与修正

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摘要目的本文以正切型非线性包装系统为例，对系统跌落冲击的响应进行理论分析，以得到包装系统跌落冲击响应的近似解析解。方法采用解决普遍非线性振动问题的同伦摄动法，并结合包装工程中的能量法对跌落冲击动态方程的求解进行了算法修正。结果修正后的最大位移响应、最大加速度响应、系统响应周期与Runge-Kutta数值解非常接近，相对误差小于1%。结论该研究为非线性包装系统跌落冲击响应分析提供了一种新的科学有效的近似分析方法。

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	郭蓓蓓1
	王军1
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关键词 ：跌落冲击, 同伦摄动法, 位移响应, 加速度响应 , 跌落冲击时间

Abstract：Aimsing at analyzing the accuracy of approximate analytical solutions for dropping shock responses of a tangent nonlinear packaging system without damping, dropping shock dynamic equations were established and the first-order approximate solutions were obtained by applying the homotopy perturbation method which is often adopted to solve general nonlinear vibration problems.The results were further modified by the energy method usually used in the packaging engineering.The corrected maximum displacement responses, the maximum acceleration responses and the system response periods are very close to the Runge-Kutta numerical solutions.The relative error is less than 1%.The research provides an effective and scientific method for the analysis of dropping shock responses of nonlinear packaging systems.

Key words： dropping shock the homotopy perturbation displacement response acceleration response dropping shock duration

收稿日期: 2017-06-12 出版日期: 2018-11-15

引用本文:

郭蓓蓓1, 王军1，2. 正切型非线性包装系统跌落冲击响应分析的同伦摄动法与修正[J]. 振动与冲击, 2018, 37(22): 111-114.
Guo Beibei1,Wang Jun1,2. Correction of the homotopy perturbation method for analyzing dropping shock response of a tangent nonlinear packaging system. JOURNAL OF VIBRATION AND SHOCK, 2018, 37(22): 111-114.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2018/V37/I22/111

[1] 胡海岩. 应用非线性动力学.北京：航空工业出版社.2000
Hu Hai yan. Application of nonlinear dynamics. BeiJing: Aviation industry press.2000.
[2] He Jihuan, Wu Xuhong. Variational iteration method: New development and applications [J]. Computers and Mathematics with Applications, 2007, 54: 881―894.
[3] 陈安军. 非线性包装系统跌落冲击问题变分迭代法[J]. 振动与冲击, 2013, 32（18）：105—107.
CHEN An-jun. Variational Iteration Method for Dropping Shock Problem of a Cubic Non-linear Packaging System[J].Journal of Vibration and Shock，2013，32（18）：105—107.
[4] Nayfeh A H. Perturbation methods [M]. New York: John Wiley & Sons, 2008:18―29.
[5] 李秀梅, 吴锋, 张克实. 结构动力微分方程的一种高精度摄动解[J].工程力学, 2013, 30(5): 8―12.
Li Xiumei, Wu Feng, Zhang Keshi. A high-precision perturbation solution for structure dynamic differential equations[J]. Engineering Mechanics, 2013, 30(5): 8―12.
[6] 陈鸣, 陈安军. 非线性包装系统跌落冲击响应分析的HFAF法[J]. 包装工程, 2014, 35（15）：40—43.
CHEN Ming，CHEN An-jun. He′s Frequency-amplitude For-mulation Method for Analyzing Dropping Shock Response of Cubic Nonlinear Packaging System[J]. Packaging Engineering, 2014, 35（15）：40—43.
[7] HE Jihuan. Comment on He′s Frequency Formulation for Nonlinear Oscillators[J]. European Journal of Physics, 2008, 29（4）：1—4.
[8] Liao Shijun. Notes on the homotopy analysis method: Some definitions and theorems[J].Communications in Nonlinear Science and Numerical Simulation, 2009, 14(4): 983―997.
[9]Shou D H, He Jihuan. Application of parameter-expanding method to strongly nonlinear oscillators [J]. International Journal of Nonlinear Sciences and Numerical Simulation, 2007, 8(1): 121―124.
[10] 陈乃立, 薛子光, 张治权, 赵明, 蔡先进, 白振国. 正切非线性包装系统的缓冲分析[J]. 包装工程,2002,04:106-108.
Chen Nai-li.Xue Ziguang.Zhang Zhiquan.Analysis of Cushioning Properties on Product Packaging System with TangenNonlinearity[J].Packaging Engineering.2002,04:106-108.
[11] 张刚, 梁爱锋. 具有正切非线性转动包装系统跌落冲击研究[J]. 包装工程,2010,15:58-61.
Zhang Gang, Liang Ai-feng. Research on Drop Shock of Packaging System with Tangent Nonlinear Rotation[J].Packaging Engineering.2010,15:58-61.
[12] 王军, 王志伟. 考虑易损件的正切型包装系统冲击破损边界曲面研究[J]. 振动与冲击, 2008, 27（2）：166—167.
WANG Jun，WANG Zhi-wei. Damage Boundary Surface of a Tangent Nonlinear Packaging System with Critical Component[J]. Journal of Vibration and Shock，2008，27（2）：166—167.
[13] 姜兆敏, 曹毅. 一类二阶非线性振动方程的同伦摄动近似解[J]. 江苏技术师范学院学报,2011,10:50-53.
JIANG Zhao-min, CAO Yi. Approximations for a Quadratic Nonlinear Oscillator by Homotopy Perturbation Method[J].Journal of Jiangsu Teachers University of Technology,2011,10:50-53.
[14] 何吉欢. 应用一种新的摄动方法求解数学摆的近似解析解[J].上海理工大学学报, 1998, 20(4): 325- 329.
He Ji-huan.A new Perturbation technique and its application to a mathematical pendulum[J].Journal of Shanghai for Science and Technology.1998, 20(4): 325- 329.
[15] 胡云佳, 李海洋, 王廷廷. 非线性振动方程的同伦摄动法求解[J]. 辽宁科技大学学报,2012,01:25-29.
Hu Yun-jia Li Hai-yang,Wang Tingting.Homotopy perturbation method solution for nonlinear oscilltion equation [J].Journal of Liaoning University of Science and Technology .2012,01:25-29.
[16] 蔡萍. 一个改进的同伦摄动法的修正[J]. 重庆文理学院学报(自然科学版),2010,(06):21-23.
Cai Ping.A mendment of a modified homotopy perturbation method [J]. Journal of Chongqing University of Arts and Sciences,2010,(06):21-23.
[17] He J H. homotopy perturbation method for solving boundary value problems[J].Physics Letter A ,2006,35(9):87-88
[18] He J H. Comparison of homotopy perturbation method and homotopy analysis method[J]. Applied Mathematics and Computation,2004,15(6):27-39