Attractor migration control of a two-degree-of-freedom nonlinear vibration isolation system

PDF(2236 KB)

Journal of Vibration and Shock ›› 2018, Vol. 37 ›› Issue (22) : 10-16.

CHAI Kai1,2,LOU Jingjun2,ZHU Shijian2,YU Xiang2,WU Haiping2

Author information +

History +

Abstract

A migration control strategy for a nonlinear vibration isolation system with multiple coexistent attractors was investigated.First, a global bifurcation analysis was carried out and the multiple coexistent attractors were obtained.Then, several control methods were adopted to accomplish the migration of different attractors.The umerical simulations show that the open-plus-nonlinear-closed-loop (OPNCL) control has the global controlling basin property, compared with the open loop, linear feedback and open-plus-closed-loop (OPCL) controls.The results providea novel approach for the line spectrum reduction in the low frequency band of submarine radiated underwater noises.

Key words

nonlinear vibration isolation system / global bifurcation / multiple coexistent attractors / migration control / open-plus-nonlinear-closed loop control

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations

CHAI Kai1,2,LOU Jingjun2,ZHU Shijian2,YU Xiang2,WU Haiping2. Attractor migration control of a two-degree-of-freedom nonlinear vibration isolation system[J]. Journal of Vibration and Shock, 2018, 37(22): 10-16

References

[1] 俞孟萨，黄国荣，伏同先．潜艇机械噪声控制技术的现状及发展概述[J]．船舶力学，2003，7(4)：110-120．
Yu Mengsa, Huang Guorong, Fu Tongxian. Development review on mechanical noise control for submarine [J]. Journal of Ship Mechanics, 2003, 7(4): 110-120.
[2] P. R. Fenstermacher, H. L. Swinney, J. P. Gollub. Dynamical instabilities and transition to chaotic Taylor vortex flow [J]. Journal of Fluid Mechanics, 1979, 94: 103-128.
[3] E. Atlee Jackson. The OPCL control method for entrainment, model-resonance, and migration actions on multiple-attractor systems [J]. American Institute of Physics, 1997, 7(4): 550-559.
[4] L. Q. Chen, Y. Z. Liu. An open plus closed loop control approach to synchronization of chaotic and hyper-chaotic maps [J]. International Journal of bifurcation and Chaos, 2002, 12(5): 1219-1225.
[5] E. Atlee Jackson, I. Grosu. An open-plus-closed-loop (OPCL) control of complex dynamic systems [J]. Physica D, 1995, 85(1): 1-9.
[6] Song Yun-Zhong. The open-plus-closed-loop (OPCL) method for chaotic systems with multiple strange attractors [J]. Chinese Physics, 2007, 16(7): 1918-05.
[7] Jian-he Shen, Shu-hui Chen. An open-plus-closed- loop control for chaotic Mathieu-Duffing oscillator [J]. Applied Mathematics and Mechanics (English Edition), 2009, 30(1): 19-21.
[8] Tong-Chun Hu, Yong-Qing Wu, Shi-Xing Li. Lag synchronization between two coupled networks via open-plus-closed-loop and adaptive controls[J]. Communications in Theoretical Physics, 2016, 65(1): 33-38.
[9] Wang Jie, Wang Xiaohong. A global control of polynomial chaotic system [J]. International Journal of Control, 1999, 72(10): 911-918.
[10] 王杰，田沛，陈陈．连续多项式混沌系统的全局控制[J]．控制与决策，2000，15(3)：309-313．
Wang Jie, Tian Pei, Chen Chen. Global control of continuous polynomial chaotic system [J]. Journal of Control and Decision, 2000, 15(3): 309-313.
[11] L. Q. Chen. An open plus nonlinear closed loop control of chaotic oscillators [J]. Chinese Physics, 2002, 11(9): 900-904.
[12] Yu-Chu Tian, Moses O. Tadé, Jin-Yu Tang. Nonlinear open-plus-closed-loop (NOPCL) control of dynamic systems [J]. Chaos, Solitons and Fractals, 2000, 11: 1029-1035.
[13] 徐伟，孙春艳，孙建桥，等．胞映射方法的研究和进展[J]．力学进展，2013，43(1)：91-100．
Xu Wei, Sun Chunyan, Sun Jianqiao, et al. Development and study on cell mapping methods [J]. Advances in Mechanics, 2013, 43(1): 91-100.
[14] 俞翔，朱石坚，刘树勇．PMUCR方法在高维非线性动力学系统中的应用[J]．应用力学学报，2006，23(2)：232-236．
Yu Xiang, Zhu Shijan, Liu Shuyong. PMUCR method with applications to high-dimensional nonlinear system [J]. Chinese Journal of Applied Mechanics, 2006, 23(2): 232-236.