Anti-controlling pitchfork bifurcation on Poincaré map of a three-degree-of-freedom vibro-impact system

被引：0

作者：

Wu X. ^{[1
,2
]}

Xu H. ^{[3
]}

Wen G. ^{[2
]}

Wei K. ^{[1
]}

机构：

[1] School of Mechanical Engineering, Hunan Institute of Engineering, Xiangtan

[2] Key Laboratory of Advanced Design and Simulation Techniques for Special Equipment of Education Ministry, Hunan University, Changsha

[3] College of Mechanics, Taiyuan University of Technology, Taiyuan

来源：

Zhendong yu Chongji/Journal of Vibration and Shock | 2016年 / 35卷 / 20期

关键词：

Anti-controlling bifurcation; Pitchfork bifurcation; Stability; Vibro-impact system;

D O I：

10.13465/j.cnki.jvs.2016.20.004

中图分类号：

学科分类号：

摘要：

In the premise of not changing periodic solutions of the original system and with considering the difficulties that are given by the implicit Poincaré map of the vibro-impact system, anti-control of Pitchfork bifurcation on Poincaré map of a three-degree-of-freedom vibro-impact system was studied by using the linear feedback control method. Firstly, the six-dimensional Poincaré map of a close-loop system was established. To overcome the difficulty that the numerical computing method can only be used to determine control gains on the basis of the classical critical criteria of Pitchfork bifurcation described by the properties of eigenvalues in the six-dimensional map, an explicit pitchfork critical criterion without using eigenvalues was used to obtain the controlling parameters area of two parameters. Then, the stability of the pitchfork bifurcation was further analyzed by utilizing the center manifold and normal formal theory. Finally, the numerical experiments verify that the stable pitchfork bifurcation solutions can be generated at arbitrary specified parameters. © 2016, Editorial Office of Journal of Vibration and Shock. All right reserved.

引用

页码：24 / 29

页数：5

共 17 条

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