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

XU Jian; CHEN Yu-shu

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XU Jian, CHEN Yu-shu. Effects of Time Delayed Velocity Feedbacks on Self-Sustained Oscillator With Excitation[J]. Applied Mathematics and Mechanics, 2004, 25(5): 455-466.

Citation:

XU Jian, CHEN Yu-shu. Effects of Time Delayed Velocity Feedbacks on Self-Sustained Oscillator With Excitation[J]. Applied Mathematics and Mechanics, 2004, 25(5): 455-466.

Citation:

XU Jian, CHEN Yu-shu. Effects of Time Delayed Velocity Feedbacks on Self-Sustained Oscillator With Excitation[J]. Applied Mathematics and Mechanics, 2004, 25(5): 455-466.

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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;

Received Date: 2002-08-25
Rev Recd Date: 2003-12-06
Publish Date: 2004-05-15

Abstract

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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References(19)

References

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