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| Anti-controlling Pitchfork bifurcation on Poincaré map of a three-degree-of-freedom vibro-impact system |
| WU Xin1,2 XU Hui-dong3 WEN Gui-lin 2 WEI Ke-xiang 1 |
1. Key Laboratory of Advanced Design and Simulation Techniques for Special Equipment of Education Ministry, College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, China;
2 .School of Mechanical Engineering, Hunan Institute of Engineering , Xiangtan 411104, China;
3. College of Mechanics, Taiyuan University of Technology, Taiyuan 030024, China |
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Abstract In the premise of no change of periodic solutions of the original system and with consideration of the difficulties that 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 is studied by using linear feedback control method. Firstly, the six-dimensional Poincaré map of close-loop system is established, to overcome the difficulty that the numerical computing method can be only used to determine control gains on basis of the classical critical criteria of Pitchfork bifurcation described by the properties of eigenvalues in six-dimensional map, an explicit Pitchfork critical criterion without using eigenvalues is used to obtain the controlling parameters area of two parameters. Then, the stability of the Pitchfork bifurcation is 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 an arbitrary specified parameters point by controlling.
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Received: 28 December 2015
Published: 15 October 2016
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