时滞速度反馈对强迫自持系统动力学行为的影响

徐鉴; 陈予恕

时滞速度反馈对强迫自持系统动力学行为的影响

徐鉴¹,
陈予恕²

1.
教育部固体力学重点实验室,同济大学力学系,上海 200092;2.天津大学力学系,天津 300072

基金项目: 国家自然科学基金资助项目(10072039)

详细信息

作者简介:
徐鉴(1961- ),男,浙江人,教授,博士导师,博士(联系人.Tel:+86-21-65985364;Fax:+86-2l-65981138;E-mail:xujian@mail.tongji.edu.cn).

中图分类号: O322；O193
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- 文章访问数: 3225
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出版历程
- 收稿日期: 2002-08-25
- 修回日期: 2003-12-06
- 刊出日期: 2004-05-15

Effects of Time Delayed Velocity Feedbacks on Self-Sustained Oscillator With Excitation

XU Jian¹,
CHEN Yu-shu²

1.
Key Laboratory of Solid Mechanics of MEC, Department of Engineering Mechanics and Technology, Tongji University, Shanghai 200092, P. R. China;

摘要

摘要: 研究强迫自持振动系统因时滞反馈产生的主共振解及其分岔．通过对强迫非自治系统的时滞反馈控制，得到所要研究的数学模型．讨论对应的线性化系统使平凡平衡态失稳出现周期解的稳定性临界条件．特别关注主共振及分岔．结果表明，稳定的主共振解随着时滞的变化周期性地出现在系统中．同时，也给出了不稳定的主共振关于时滞变化的区域，在理论方面给出了系统出现概周期运动的时滞区域．数据模拟证实了理论结果．
- 非线性动力学 /
- 时滞微分方程 /
- 分岔
Abstract: Both the primary resonant solutions and their bifurcations due to time delayed velocity feedbacks used in a self-sustained oscillator with excitation were further investigated. A model was proposed by adding linear and nonlinear time delayed feedbacks to a representative non-autonomous system(with external forcing). The stablity condition of the linearized system at trivial equilibrium was discussed, which leads to a critical stability boundary where periodic solutions may occur. The main attention was focused on bifurcations from the primary resonant solutions. It is found that the stable primary resonant solution may appear periodically in the time delay. Meanwhile, the unstable regions for such solutions are also obtained, predicting the occurrence of quasi-periodic motions.
- nonlinear dynamics /
- delayed differential equation /
- bifurcation

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参考文献(19)

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时滞速度反馈对强迫自持系统动力学行为的影响

作者简介:
徐鉴(1961- ),男,浙江人,教授,博士导师,博士(联系人.Tel:+86-21-65985364;Fax:+86-2l-65981138;E-mail:xujian@mail.tongji.edu.cn).

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Effects of Time Delayed Velocity Feedbacks on Self-Sustained Oscillator With Excitation

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时滞速度反馈对强迫自持系统动力学行为的影响

作者简介: 徐鉴(1961- ),男,浙江人,教授,博士导师,博士(联系人.Tel:+86-21-65985364;Fax:+86-2l-65981138;E-mail:xujian@mail.tongji.edu.cn).

计量

出版历程

Effects of Time Delayed Velocity Feedbacks on Self-Sustained Oscillator With Excitation

计量

出版历程

目录

作者简介:
徐鉴(1961- ),男,浙江人,教授,博士导师,博士(联系人.Tel:+86-21-65985364;Fax:+86-2l-65981138;E-mail:xujian@mail.tongji.edu.cn).