多频激励Duffing系统的分岔和混沌<sup>*</sup>

毕勤胜; 陈予恕; 吴志强

多频激励Duffing系统的分岔和混沌^*

天津大学力学与工程测试系, 天津 300072

基金项目: *国家自然科学基金;博士点基金

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出版历程
- 收稿日期: 1995-04-15
- 修回日期: 1996-06-30
- 刊出日期: 1998-02-15

Bifurcation in a Nonlinear Duffing System with Multi-Frequency External Periodic Forces

Department of Mechanics, Tianjing University, Tianjin 300072, P. R. China

摘要

摘要: 本文通过引入非线性频率,利用Floquet理论及解通过转迁集时的特性,研究了不可通约两周期激励作用下的Dufing方程在一次近似下的各种分岔模式及其转迁集,并指出其通向混沌可能的途径.
- 非线性频率 /
- Floquet理论 /
- 分岔 /
- 混沌 /
- 多频激励Duffing系统
Abstract: By introducing nonlinear frequency,using Floquel theory and referring to the characteristics of the solution when it passes through the transition bounaries all kinds of bifurcation modes and their transition boundaries of Duffing equation with two periodic excitatins as well as the possible ways to chaos are studied in this paper.
- nonlinear frequency /
- Floquet theory /
- bifrucation /
- chaos /
- Duffing system with multi-frequency external periodic forces

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参考文献(18)

[1]	W.H.Steeb.W.Erig and A,Kunick.Chaotic behaviour and limit cycle behaviour ofanharmonic systems with periodic external perturbations,Physics Letters A,93,6(1983),267-270.
[2]	S.Sato,M.Sano and Y.Sawada,Universal scaling property in bifurcation structure ofDuffing's and generalized Duffing 's equation,Physical Review A,28,3(1983),1654-1658.
[3]	Y.Ueda and N.Slamatsu,Chaotically transitional phenomena in the forced negativeresistance oscillator,Institute of Electrical Engineers Transactions on Circuits System,CAS-28,2(1981),217-223.
[4]	Q.S.Lu and C.W.S.To,Principle resonance of a nonlinear system with two-frequencyparametric and self-excitations,Nonlinear Dynamics,2,6(1991),419-444.
[5]	陆启韶、黄克累、非线性动力学、分岔和混沌,全国一般力学发展与展望会议,哈尔滨(1993),11-18.
[6]	K.Yagasaki,M.Sakata and K.Kimura,Dynamics of weakly nonlinear system subjectedto combined parametric and external excitation,Trans.ASME,J.Appl.Mech.,57,1(1990),209-217.
[7]	K.Yagasaki,Chaos in weakly nonlinear oscillator with parametric and externalresonance,Trans.ASME,J.Appl.Mech.58.1(1991),244-250.
[8]	K.Yagasaki,Chaotic dynamics of a quasi-periodically forced beam,Trans.ASME.J.Appl.Mech.,59.1(1992),161-167.
[9]	陈予恕、王德石,轴向激励下梁的混沌运动,非线性动力学学报,1(2)(1993),124-135.
[10]	A.Y.T.Leung and T.C.Fung,Construction of chaotic regions,J.Sound Vib.,131,3(1989),445-455.
[11]	Szemplinska-Stupnicka and Bajkowski.The 1/2 subharmonic resonance its transition tochaos motion in a nonlinear oscillator,IFTR Reports 4,1(1986),67-72.
[12]	R.Van Dooren.On the transition from regular to chaotic behaviour in the Duffingoscillator.J.Sound Vib.,123.2(1988).327-339.
[13]	T.Kapitaniak,Combined bifurcations and transition to chaos in a nonlinear oscillatorwith two external periodic forees.J.Sound Vib.121,2(1988),259-268.
[14]	T.Kapitaniak.Chaotic distribution of nonlinear systems perturbed by random noise.Physical Lefters A.116,6(1986).251-254.
[15]	T.Kapitaniak,A property of a stochastic response with bifurcation to nonlinear system.J.Sound Vib.,107.1(1986).177-180.
[16]	V.I.Arnold,Ordinary Differential Equation.M.I.T.Press(1973),22-26,48-52.
[17]	A.H.Nayfeh and D.T.Mook.Perturbation Methods.John Wiley & Sons,New York(1979),300-313.
[18]	R.Raty and J.Von Boehm,Absence of inversion-symmetric limit cycles of even periodand chaotic motion of Duffing oscillator.Physics Letters A.103,6(1984),288-292.