多频激励软弹簧型Duffing系统中的混沌

楼京俊; 何其伟; 朱石坚

多频激励软弹簧型Duffing系统中的混沌

海军工程大学振动与噪声研究所,武汉 430033

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).

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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

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

Institute of Noise & Vibration, Naval University of Engineering, Wuhan 430033, P. R. China

摘要

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．
- 多频激励 /
- 软弹簧Duffing系统 /
- 混沌 /
- 异宿环面
Abstract: The chaotic dynamics of the softening-spring Duffing system with multi-frequency external periodic forces is studied.It is found that the mechanism for chaos is the transverse heteroclinic tori. The Poincar map,the stable and the unstable manifolds of the system under two incommensurate periodic forces were set up on a two-dimensional torus.Utilizing a global perturbation technique of Melnikov the criterion for the transverse interaction of the stable and the unstable manifolds was given. The system under more but finite incommensurate periodic forces was also studied.The Melnikov's global perturbation technique was therefore generalized to higher dimensional systems.The region in parameter space where chaotic dynamics may occur was given.It was also demonstrated that increasing the number of forcing frequencies will increase the area in parameter space where chaotic behavior can occur.
- multi-frequency excitation /
- softening Duffing system /
- chaos /
- heteroclinic torus

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参考文献(20)

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多频激励软弹簧型Duffing系统中的混沌

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).

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

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多频激励软弹簧型Duffing系统中的混沌

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).

计量

出版历程

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

计量

出版历程

目录

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).