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多频激励软弹簧型Duffing系统中的混沌

楼京俊 何其伟 朱石坚

楼京俊, 何其伟, 朱石坚. 多频激励软弹簧型Duffing系统中的混沌[J]. 应用数学和力学, 2004, 25(12): 1299-1304.
引用本文: 楼京俊, 何其伟, 朱石坚. 多频激励软弹簧型Duffing系统中的混沌[J]. 应用数学和力学, 2004, 25(12): 1299-1304.
LOU Jing-jun, HE Qi-wei, ZHU Shi-jian. Chaos in the Softening Duffing System Under Multi-Frequency Periodic Forces[J]. Applied Mathematics and Mechanics, 2004, 25(12): 1299-1304.
Citation: LOU Jing-jun, HE Qi-wei, ZHU Shi-jian. Chaos in the Softening Duffing System Under Multi-Frequency Periodic Forces[J]. Applied Mathematics and Mechanics, 2004, 25(12): 1299-1304.

多频激励软弹簧型Duffing系统中的混沌

详细信息
    作者简介:

    楼京俊(1976- ),男,浙江义乌人,博士研究生(E-mail:jingjun-lou@hotmail.com);朱石坚,教授,硕士(联系人.Tel:+86-27-83443991;Fax:+86-27-83443990;E-mail:zhushj@public.wh.hb.cn).

  • 中图分类号: O322

Chaos in the Softening Duffing System Under Multi-Frequency Periodic Forces

  • 摘要: 研究了多频激励下的软弹簧型Duffing系统的混沌动力学,发现混沌产生的根本原因是系统相空间中横截异宿环面的存在.建立了双频激励情况下二维环面上的Poincaré映射、稳定流形和不稳定流形,应用Melnikov方法给出了稳定流形和不稳定流形横截相交的条件,并将此方法推广到激励包含有限多个频率的情形.推广了Melnikov方法在高维系统中的应用,给出了Smale马蹄意义下混沌存在的判据.同时证明,激励频率数目的增加扩大了参数空间上的混沌区域.
  • [1] 刘曾荣.混沌的微扰判据[M].上海:上海科技教育出版社,1994: 7—10.
    [2] Moon F C, Holmes W T.Double Poincare sections of a quasi-periodically forced, chaotic attractor[J].Physics Letters A,1985,111(4):157—160. doi: 10.1016/0375-9601(85)90565-1
    [3] Wiggins S.Chaos in the quasiperiodically forced Duffing oscillator[J]. Physics Letters A,1987,124(3):138—142. doi: 10.1016/0375-9601(87)90240-4
    [4] Wiggins S.Global Bifurcations and Chaos—Analytical Methods[M].New York: Springer-Verlag, 1988: 313—333.
    [5] Kayo IDE, Wiggins S.The bifurcation to homoclinic tori in the quasiperiodically forced Duffing oscillator[J].Physica D,1989,34(1):169—182. doi: 10.1016/0167-2789(89)90232-7
    [6] Heagy J, Ditto W L.Dynamics of a two-frequency parametrically driven Duffing oscillator[J].Journal of Nonlinear Science,1991,1(2):423—455. doi: 10.1007/BF02429848
    [7] LU Qi-shao.Principle resonance of a nonlinear system with two-frequency parametric and self-excitations[J].Nonlinear Dynamics,1991,2(6):419—444. doi: 10.1007/BF00045437
    [8] 陆启韶、黄克累.非线性动力学、分岔和混沌[A].见:黄文虎,陈滨,王照林 编.一般力学(动力学、振动与控制)最新进展[C].北京:科学出版社,1994, 11—18.
    [9] Yagasaki K, Sakata M,Kimura K.Dynamics of weakly nonlinear system subjected to combined parametric and external excitation [J].Trans ASME,Journal of Applied Mechanics,1990,57(1):209—217. doi: 10.1115/1.2888306
    [10] Yagasaki K.Chaos in weakly nonlinear oscillator with parametric and external resonance[J].Trans ASME,Journal of Applied Mechanics,1991,58(1):244—250. doi: 10.1115/1.2897158
    [11] Yagasaki K.Chaotic dynamics of a quasi-periodically forced beam[J].Trans ASME,Journal of Applied Mechanics,1992,59(1): 161—167. doi: 10.1115/1.2899422
    [12] 陈予恕,王德石.轴向激励下梁的混沌运动[J].非线性动力学学报,1993,1(2):124—135.
    [13] Kapitaniak T.Combined bifurcations and transition to chaos in a nonlinear oscillator with two external periodic forces[J].Journal of Sound and Vibration,1988,121(2):259—268. doi: 10.1016/S0022-460X(88)80028-2
    [14] Kapitaniak T.Chaotic distribution of nonlinear systems perturbed by random noise[J].Physical Letters A,1986,116(6):251—254. doi: 10.1016/0375-9601(86)90588-8
    [15] Kapitaniak T.A property of a stochastic response with bifurcation to nonlinear system[J].Journal of Sound and Vibration,1986,107(1):177—180. doi: 10.1016/0022-460X(86)90292-0
    [16] 毕勤胜,陈予恕,吴志强.多频激励Duffing系统的分岔和混沌[J].应用数学和力学,1998,19(2):113—120.
    [17] Leung A Y T, Fung C.Construction of chaotic regions [J].Journal of Sound and Vibration,1989,131(3): 445—455. doi: 10.1016/0022-460X(89)91004-3
    [18] Stupnicka S,Bajkowski. The 1/2 subharmonic resonance its transition to chaos motion in a nonlinear oscillator[J].IFTR Reports,1986,4(1):67—72.
    [19] Dooren R V.On the transition from regular to chaotic behaviour in the Duffing oscillator[J].Journal of Sound and Vibration,1988,123(2):327—339. doi: 10.1016/S0022-460X(88)80115-9
    [20] Yagasaki K.Homoclinic tangles,phase locking,and chaos in a two-frequency perturbation of Duffing equation[J].Journal of Nonlinear Science,1999,9(1):131—148. doi: 10.1007/s003329900066
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出版历程
  • 收稿日期:  2002-12-30
  • 修回日期:  2004-05-31
  • 刊出日期:  2004-12-15

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