Bifurcation and chaos of some strongly nonlinear relative rotation system with time-varying clearance

Liu Bin; Zhao Hong-Xu; Hou Dong-Xiao; Liu Hao-Ran

doi:10.7498/aps.63.074501

Abstract

The dynamic equation for the relative rotation nonlinear dynamic system with time-varying clearance is investigated. Firstly, transformation parameter is deduced by using the method of MLP; the bifurcation response equations of 1/2 harmonic resonance then are generated by the method of multiple scales, while singularity analysis is employed to obtain the transition set of steady motion; further more the bifurcation characteristic and the bifurcation of the system under the situation of non-autonomy are analyzed. Finally, numerical simulation exhibits many different motions, such as periodic motion, period-doubling motion, and chaos. It is shown that the change of clearance and damp parameters may influence the motion state of the system.

Keywords:

Authors and contacts

1.
College of Electrical Engineering, YanShan University, Qinhuangdao 066004, China;
2.
Department of Control Engineering Northeastern University at Qinhuangdao, Qinhuangdao 066004, China
Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 51105324, 51005196), the Hebei Province Science and Technology Support Program, China (Grant No. 13211907D), and the Natural Science Foundation of Hebei Province, China (Grant No. E2012203194).

References

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[13]	Xu W, Sun ZH K, Yang X L 2005 Acta Phys. Sin. 54 11 (in Chinese) [徐伟, 孙中奎, 杨晓丽2005 54 11]

Cited By

[1]	Carmeli M 1985 Found. Phys. 15 175
[2]	Carmeli M 1986 Int. J. Theor. Phys. 25 89
[3]	Luo S K 1996 J. Beijing Inst. Technol. 16 (S1) 154 (in Chinese) [罗绍凯1996 北京理工大学学报16 (S1) 154]
[4]	Luo S K 1998 Appl. Math. Mech. 19 45
[5]	Lei Y M, Xu W 2008 Acta Phys. Sin. 57 6 (in Chinese)[雷佑铭, 徐伟2008 57 6]
[6]	Huang J C, Jing Zh J 2009 Chaos Solitions and Fractels 40 1449
[7]	Chen S Y, Tang J Y 2008 J. Sound Vib. 318 1109
[8]	Zhang Q C, Wang W, Liu F H 2008 Chin. Phys. B. 17 4123
[9]	Feng J J, Zhang Q C, Wang W 2011 Chin. Phys. B. 20 090202
[10]	Tang J S, Yin X B 1996 Acta Mech. Sin. 28 3 (in Chinese)[唐驾时, 尹小波1996 力学学报28 3]
[11]	Shi P M, Han D Y, Liu B 2010 Chin. Phys. B. 19 090306
[12]	Li X J, Chen X Q, Yan J 2013 Acta Phys. Sin. 62 090202 (in Chinese) [李晓静, 陈绚青, 严静2013 62 090202]
[13]	Xu W, Sun ZH K, Yang X L 2005 Acta Phys. Sin. 54 11 (in Chinese) [徐伟, 孙中奎, 杨晓丽2005 54 11]

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Catalog

Vol. 63, Issue 7 - 2014-04-05

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