窄带随机噪声作用下非线性系统的响应

戎海武; 王向东; 孟光; 徐伟; 方同

窄带随机噪声作用下非线性系统的响应

戎海武^1,2,
王向东¹,
孟光²,
徐伟³,
方同³

1.
佛山科学技术学院数学系, 广东佛山 528000;
2.
上海交通大学振动冲击噪声国家重点实验室, 上海 200030;
3.
西北工业大学应用数学系, 西安 710072

基金项目: 国家自然科学基金资助项目(10072049,19972054);广东省自然科学基金资助项目(000017);上海交通大学振动、冲击、噪声国家重点实验室开放基金(VSN-2002-04)

详细信息

作者简介:
戎海武(1966- ),男,浙江宁波人,副教授,博士(E-mail:ronghw@foshan.net).

中图分类号: O324
计量
- 文章访问数: 2881
- HTML全文浏览量: 259
- PDF下载量: 727
- 被引次数: 0
出版历程
- 收稿日期: 2000-08-30
- 修回日期: 2002-12-01
- 刊出日期: 2003-07-15

Response of Nonlinear Oscillator Under Narrow-Band Random Excitation

1.
Department of Mathematics, Foshan University, Foshan, Guangdong 528000, P. R. China;
2.
The State Key Laboratory of Vibration, Shock and Noise, Shanghai Jiaotong University, Shanghai 200030, P. R. China;
3.
Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, P. R. China

摘要

摘要: 研究了Duffing振子在窄带随机噪声激励下的主共振响应和稳定性问题.用多尺度法分离了系统的快变项,讨论了系统的阻尼项、随机项等对系统响应的影响.在一定条件下,系统具有两个均方响应值.数值模拟表明方法是有效的.
- Duffing振子 /
- 主共振 /
- 多尺度法
Abstract: The principal resonance of Duffing oscillator to narrow-band random parametric excitation was investigated.The method of multiple scales was used to determine the equations of modulation of amplitude and phase.The behavior,stability and bifurcation of steady state response were studied by means of qualitative analyses.The effects of damping,detuning,bandwidth and magnitudes of deterministic and random excitations were analyzed.The theoretical analyses were verified by numerical results.Theoretical analyses and numerical simulations show that when the intensity of the random excitation increases,the nontrivial steady state solution may change from a limit cycle to a diffused limit cycle.Under some conditions the system may have two steady state solutions.
- principal resonance /
- Duffing oscillator /
- multiple scale method

HTML全文

参考文献(17)

[1]	Den Hartog J P.Mechanical Vibrations[M].forth edition.New York:McGraw-Hill,1956.
[2]	Lyon R H,Heckl M,Hazelgrove C B.Response of hard-spring oscillator to narrow-band excitation[J].Journal of the Acoustical Society of America,1961,33(4):1404-1411.
[3]	Richard K,Anand G V.Nonlinear resonance in suings under narrow band random excitation-part Ⅰ:planar response and stability[J].Journal of Sound and Vibration,1983,86(8):85-98.
[4]	Davies H G,Nandall D.Phase plane for narrow band random excitation of a Duffing oscillator[J].Journal of Sound and Vibration,1986,104(2):277-283.
[5]	Iyengar R N.Response of nonlinear systems to narrow-band excitation[J].Structural Safety,1989,6(2):177-185.
[6]	Lennox W C,Kuak Y C.Narrow band excitation of a nonlinear oscillator[J].Journal of Applied Mechanics,1976,43(2):340-344.
[7]	Grigoriu M.Probabilistic analysis of response of Duffing oscillator to narrow band stationary Gaussian excitation[A].In:E H Dowell Ed.Proceedings of First Pan-American Congress of Applied Mechantics[C].Rio de Janeiro:Brazil,1989.
[8]	Davis H G,Liu Q.The response probability density function of a Duffing oscillator with random narrow band excitation[J].Journal of Sound and Vibration,1990,139(1):1-8.
[9]	Kapitaniak T.Stochastic response with bifurcations to non-linear Duffing's oscillator[J].Journal of Sound and Vibration,1985,102(3):440-441.
[10]	FangT,Dowell E H.Numerical simulations of jump phenomena in stable Duffing systems[J].International Journal of Nonlinear Mechanics,1987,22(2):267-274.
[11]	Zhu W Q,Lu M Q,Wu Q T.Stochastic jump and bifurcation of a Duffing oscillator under narrowband excitation[J].Journal of Sound and Vibration,1993,165(2):285-304.
[12]	Wedig W V.Invariant measures and Lyapunov exponents for generalized parameter fluctuations[J].Structural Safety,1990,8(1):13-25.
[13]	Nayfeh A H.Introduction to Perturbation Techniques[M].New York:Wiley,1981.
[14]	Rajan S,Davies H G.Multiple time scaling of the response of a Duffing oscillator to narrow-band excitations[J].Journal of Sound and Vibration,1988,123(3):497-506.
[15]	Nayfeh A H,Serhan S J.Response statistics of nonlinear systems to combined deterministic and random excitations[J].International Journal of Nonlinear Mechanics,1990,25(5):493-509.
[16]	RONG Hai-wu,XU Wei,FANG Tong.Principal response of Duffing oscillator to combined deterministic and narrow-band random parametric excitation[J].Journal of Sound and Vibration,1998,210(4):483-515.
[17]	朱位秋.随机振动[M].北京:科学出版社,1992.