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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.
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Keywords:
- relatively rotation /
- time-varying clearance /
- strongly nonlinear /
- chaos
[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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[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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