EFFECTS OF TIME DELAYED VELOCITY FEEDBACKS ON SELF-SUSTAINED OSCILLATOR WITH EXCITATION

Applied Mathematics and Mechanics (English Edition) ›› 2004, Vol. 25 ›› Issue (5): 499-512.

EFFECTS OF TIME DELAYED VELOCITY FEEDBACKS ON SELF-SUSTAINED OSCILLATOR WITH EXCITATION

徐鉴¹, 陈予恕²

1. Key Laboratory of Solid Mechanics of MEC, Department of Engineering Mechanics and Technology, Tongji University, Shanghai 200092, P.R.China;
2. Department of Mechanics, Tianjin University, Tianjin 300072, P.R. China

收稿日期:2002-08-25 修回日期:2003-12-06 出版日期:2004-05-18 发布日期:2004-05-18
通讯作者: CHEN Yu-shu
基金资助:
the National Natural Science Foundation of China(10072039)

EFFECTS OF TIME DELAYED VELOCITY FEEDBACKS ON SELF-SUSTAINED OSCILLATOR WITH EXCITATION

XU jian¹, CHEN Yu-shu ²

1. Key Laboratory of Solid Mechanics of MEC, Department of Engineering Mechanics and Technology, Tongji University, Shanghai 200092, P.R.China;
2. Department of Mechanics, Tianjin University, Tianjin 300072, P.R. China

Received:2002-08-25 Revised:2003-12-06 Online:2004-05-18 Published:2004-05-18
Supported by:
the National Natural Science Foundation of China(10072039)

摘要/Abstract

摘要： 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 stability 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.

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 stability 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.

中图分类号:

O322
O193

徐鉴;陈予恕. EFFECTS OF TIME DELAYED VELOCITY FEEDBACKS ON SELF-SUSTAINED OSCILLATOR WITH EXCITATION[J]. Applied Mathematics and Mechanics (English Edition), 2004, 25(5): 499-512.

XU jian;CHEN Yu-shu . EFFECTS OF TIME DELAYED VELOCITY FEEDBACKS ON SELF-SUSTAINED OSCILLATOR WITH EXCITATION[J]. Applied Mathematics and Mechanics (English Edition), 2004, 25(5): 499-512.

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EFFECTS OF TIME DELAYED VELOCITY FEEDBACKS ON SELF-SUSTAINED OSCILLATOR WITH EXCITATION

EFFECTS OF TIME DELAYED VELOCITY FEEDBACKS ON SELF-SUSTAINED OSCILLATOR WITH EXCITATION

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