Duffing简谐振子同伦分析法求解

冯少东; 陈立群

doi:10.3879/j.issn.1000-0887.2009.09.002

Duffing简谐振子同伦分析法求解

doi: 10.3879/j.issn.1000-0887.2009.09.002

冯少东¹,
陈立群^1,2

1.
上海大学上海市应用数学和力学研究所,上海 200072;2.上海大学力学系,上海 200444

基金项目: 国家杰出青年科学基金资助项目(10725209);国家自然科学基金资助项目(10672092);上海市优秀学科带头人计划资助项目(09XD1401700);上海市重点学科建设资助项目(Y0103)

详细信息

作者简介:
冯少东(1984- ),男,浙江宁波人,硕士生(E-mail:shaodong6819@163.com);陈立群(1960- ),博士生导师(联系人.Tel:+86-21-66136905;E-mail:lqchen@shu.edu.cn).

中图分类号: O241.7; O322
计量
- 文章访问数: 1581
- HTML全文浏览量: 157
- PDF下载量: 1251
- 被引次数: 0
出版历程
- 收稿日期: 2009-01-13
- 修回日期: 2009-07-20
- 刊出日期: 2009-09-15

Homotopy Analysis Approach to the Duffing-Harmonic Oscillator

FENG Shao-dong¹,
CHEN Li-qun^1,2

1.
Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P. R. China;

摘要

摘要: 利用同伦分析方法求解了Duffing简谐振子，数值确定了变形方程中的辅助参数，得到了一族响应和频率的近似周期解，该解与精确解符合很好．结果表明，同伦分析法在求解强非线性振子时，仍然是一种行之有效的方法．
- Duffing简谐振子 /
- 同伦分析法 /
- 近似解
Abstract: The homotopy analysis is performed for the Duffing-harmonic oscillator.The auxiliary parameter in the deformation equation was numerically determined.The response and the frequency of the Duffing-harmonic oscillator were calculated.The analytical results are validated by the direct numerical simulations.
- Duffing-harmonic oscillator /
- homotopy analysis method /
- approximate solution

HTML全文

参考文献(15)

[1]	Mickens R E.Mathematical and numerical study of the Duffing-harmonic oscillator[J].J Sound Vibration,2001,244(3):563-567. doi: 10.1006/jsvi.2000.3502
[2]	Lim C W,Wu B S.A new analytical approach to the Duffing-harmonic oscillator[J].Phys Lett A,2003,311(5):365-377. doi: 10.1016/S0375-9601(03)00513-9
[3]	Tiwari S B,Rao B N,Swamy N S,et al.Analytical study on a Duffing-harmonic oscillator[J].J Sound Vibration,2005,285(4):1217-1222. doi: 10.1016/j.jsv.2004.11.001
[4]	Hu H,Tang J H.Solution of a Duffing-harmonic oscillator by the method of harmonic balance[J].J Sound Vibration,2006,294(3):637-639. doi: 10.1016/j.jsv.2005.12.025
[5]	Lim C W,Wu B S,Sun W P.Higher accuracy analytical approximations to the Duffing-harmonic oscillator[J].J Sound Vibration,2006,296(4):1039-1045. doi: 10.1016/j.jsv.2006.02.020
[6]	Hu H.Solutions of the Duffing-harmonic oscillator by an iteration procedure[J].J Sound Vibration,2006,298(1):446-452. doi: 10.1016/j.jsv.2006.05.023
[7]	Murdock J A.Perturbations:Theory and Methods[M].New York:Wiley,1991.
[8]	Nayfeh A H.Perturbation Methods[M].New York:Wiley,2000.
[9]	Liao S J.The proposed homotopy analysis technique for the solution of nonlinear problems[D].PhD thesis.Shanghai:Shanghai Jiao Tong University,1992.
[10]	Liao S J.Beyond Perturbation:Introduction to the Homotopy Analysis Method[M].Boca Raton:Chapman & Hall/CRC Press,2003.
[11]	Liao S J,Tan Y.A general approach to obtain series solutions of nonlinear differential equations[J].Studies Appl Math,2007,119(4):297-354. doi: 10.1111/j.1467-9590.2007.00387.x
[12]	廖世俊.超越摄动：同伦分析方法基本思想及其应用[J].力学进展,2008,38(1):1-34.
[13]	Liao S J.An approximate solution technique not depending on small parameters:a special example[J].Int J Non-Linear Mech,1995,30(3):371-380. doi: 10.1016/0020-7462(94)00054-E
[14]	Liao S J,Chwang A T.Application of homotopy analysis method in nonlinear oscillations[J].ASME,J Appl Mech,1998,65(4):914-922. doi: 10.1115/1.2791935
[15]	Pirbodaghi T,Hoseini S H,Ahmadian M T,et al.Duffing equations with cubic and quintic nonlinearities[J].Comput Math Appl,2009,57(3):500-506. doi: 10.1016/j.camwa.2008.10.082