Chaos of a kind of nonlinear relative rotation system based on the effect of Coulomb friction

Liu Shuang; Tian Song-Tao; Wang Zhen-Chen; Li Jian-Xiong

doi:10.7498/aps.64.064501

Abstract

Chaotic motion of a kind of nonlinear relative rotation system with load Coulomb frictional damping is investigated. Based on the Lagrange equation of a dissipative system, the dynamic equation of a kind of nonlinear relative rotation system with two pieces of mass is established, which contains a kind of nonlinear load Coulomb frictional damping. The eigenvalue of the autonomous system is discussed using Cardano formula. On this basis, the existence of homoclinic orbits is given by the undetermined coefficient method, and the chaotic motion of the system is investigated by means of Silnikov theorem. Finally the chaotic motion of the system with the known parameters is studied numerically. With the variation of Coulomb frictional damping, a route to chaos through period-doubling bifurcations is exhibited. Numerical calculation can confirm the validity of the analytical results.

Keywords:

Authors and contacts

1.
Key Laboratory of Industrial Computer Control Engineering of Hebei Province, Yanshan University, Qinhuangdao 066004, China;
2.
National Engineering Research Center for Equipment and Technology of Cold Rolling Strip, Qinhuangdao 066004, China
Funds: Project supported by the National Natural Science Foundation of China (Grant No. 61104040), the Natural Science Foundation of Hebei Province, China (Grant No. E2012203090), and University Innovation Team of Hebei Province Leading Talent Cultivation Project, China (Grant No. LJRC013).

References

[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. 16 154 (in Chinese) [罗绍凯 1996 北京理工大学学报 16 154]
[4]	Luo S K 1998 Appl. Math. Mech. 19 45
[5]	Luo S K, Chen X W, Guo Y X 2002 Chin. Phys. 11 429
[6]	Luo S K 2002 Chin. Phys. Lett. 19 449
[7]	Luo S K 2003 Chin. Phys. 12 357
[8]	Wang X Y, Wang M J 2008 Physica A 387 3751
[9]	El-Bassiouny A F 2006 Physica A 366 167
[10]	Kim T C, Rook T E, Singh R 2005 J. Sound Vib. 281 965
[11]	Wang X Y, Liang Q Y, Meng J 2008 Int. J. Mod. Phys. C 19 1389
[12]	Xu J X, Sun Z C 2001 Chin. Phys. 10 599
[13]	Wang X Y, Liang Q Y 2008 Commun. Nonlinear Sci. Numer. Simulat. 13 913
[14]	Shi P M, Han D Y, Liu B 2010 Chin. Phys. B 19 090306
[15]	Wang X Y, Luo C, Meng J 2009 Appl. Math. Comput. 207 63
[16]	Hou D X, Liu B, Shi P M 2009 Acta Phys. Sin. 58 5942 (in Chinese) [侯东晓, 刘彬, 时培明 2009 物理学报 58 5942]
[17]	Siewe Siewe M, Tchawoua C, Woafo P 2010 Mech. Res. Commun. 37 363
[18]	Wang J, Zheng J H, Yang A B 2012 Proced. Engineer. 31 563
[19]	Tang R R 2012 Acta Phys. Sin. 61 200201 (in Chinese) [唐荣荣 2012 物理学报 61 200201]
[20]	Liu S, Liu B, Shi P M 2009 Acta Phys. Sin. 58 4383 (in Chinese) [刘爽, 刘彬, 时培明 2009 物理学报 58 4383]
[21]	Thomsen J J, Fidlin A 2003 Int. J. Non-Linear Mech. 38 389
[22]	Wang X Y, Luo C 2006 Appl. Math. Comput. 183 30
[23]	Zhu S Q, Yang M, Zhang X H, Min L Q 2005 J. Beijing Sci. Technol. 27 635 (in Chinese) [朱淑芹, 杨淼, 张先华, 闵乐泉 2005 北京科技大学学报 27 635]
[24]	Zhou T S, Chen G R, Yang Q G 2004 Chaos, Soliton. Fract. 19 985
[25]	Bai Z H, Zhou Q T, Dou A M, Xu J, Wang J F 2007 Iron and Steel 42 5 (in Chinese) [白振华, 周庆田, 窦爱民, 徐俊, 王骏飞 2007 钢铁 42 5]

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. 16 154 (in Chinese) [罗绍凯 1996 北京理工大学学报 16 154]
[4]	Luo S K 1998 Appl. Math. Mech. 19 45
[5]	Luo S K, Chen X W, Guo Y X 2002 Chin. Phys. 11 429
[6]	Luo S K 2002 Chin. Phys. Lett. 19 449
[7]	Luo S K 2003 Chin. Phys. 12 357
[8]	Wang X Y, Wang M J 2008 Physica A 387 3751
[9]	El-Bassiouny A F 2006 Physica A 366 167
[10]	Kim T C, Rook T E, Singh R 2005 J. Sound Vib. 281 965
[11]	Wang X Y, Liang Q Y, Meng J 2008 Int. J. Mod. Phys. C 19 1389
[12]	Xu J X, Sun Z C 2001 Chin. Phys. 10 599
[13]	Wang X Y, Liang Q Y 2008 Commun. Nonlinear Sci. Numer. Simulat. 13 913
[14]	Shi P M, Han D Y, Liu B 2010 Chin. Phys. B 19 090306
[15]	Wang X Y, Luo C, Meng J 2009 Appl. Math. Comput. 207 63
[16]	Hou D X, Liu B, Shi P M 2009 Acta Phys. Sin. 58 5942 (in Chinese) [侯东晓, 刘彬, 时培明 2009 物理学报 58 5942]
[17]	Siewe Siewe M, Tchawoua C, Woafo P 2010 Mech. Res. Commun. 37 363
[18]	Wang J, Zheng J H, Yang A B 2012 Proced. Engineer. 31 563
[19]	Tang R R 2012 Acta Phys. Sin. 61 200201 (in Chinese) [唐荣荣 2012 物理学报 61 200201]
[20]	Liu S, Liu B, Shi P M 2009 Acta Phys. Sin. 58 4383 (in Chinese) [刘爽, 刘彬, 时培明 2009 物理学报 58 4383]
[21]	Thomsen J J, Fidlin A 2003 Int. J. Non-Linear Mech. 38 389
[22]	Wang X Y, Luo C 2006 Appl. Math. Comput. 183 30
[23]	Zhu S Q, Yang M, Zhang X H, Min L Q 2005 J. Beijing Sci. Technol. 27 635 (in Chinese) [朱淑芹, 杨淼, 张先华, 闵乐泉 2005 北京科技大学学报 27 635]
[24]	Zhou T S, Chen G R, Yang Q G 2004 Chaos, Soliton. Fract. 19 985
[25]	Bai Z H, Zhou Q T, Dou A M, Xu J, Wang J F 2007 Iron and Steel 42 5 (in Chinese) [白振华, 周庆田, 窦爱民, 徐俊, 王骏飞 2007 钢铁 42 5]

Catalog

Vol. 64, Issue 6 - 2015-03-20

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