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Using the perturbation theory, a class of relative rotation nonlinear dynamical model possessing nonlinear elastic force, friction force and multi-frequency excitation is investigated. The relations for the frequency syntheses are investigated, and the conditions under which multi-typical resonance happens at the same time are given. Using the renormalization method, the asymptotic expansions for the solutions of the model under corresponding conditions are obtained.
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Keywords:
- relative rotation /
- dynamic model /
- renormalization method /
- asymptotic expansions
[1] Hu H Y 2000 Applied Nonlinear Dynamics (Beijing: Aviation Industry Press) (in Chinese) [胡海岩 2000 应用非线性动力学(北京:航空工业出版社)]
[2] Shi P M, Liu B 2007 Acta Phys. Sin. 56 3678 (in Chinese) [时培明, 刘彬 2007 56 3678]
[3] Shi P M, Liu B, Liu S 2008 Acta Phys. Sin. 57 4675 (in Chinese) [时培明, 刘彬, 刘爽 2008 57 4675]
[4] Meng Z, Liu B 2008 Acta Phys. Sin. 57 1329 (in Chinese) [孟宗, 刘彬 2008 57 1329]
[5] Yang S P, Yuan X R 1998 Acta Nonlinear Dynamical Sin. 3 223 (in Chinese) [杨绍普, 袁向荣 1998 非线性动力学学报 3 223]
[6] Mo J Q, Cheng R J, Ge H X 2011 Acta Phys. Sin. 60 040203 (in Chinese) [莫嘉琪, 程荣军, 葛红霞 2011 60 040203]
[7] Shi P M, Liu B, Hou D X 2008 Acta Phys. Sin. 57 1321 (in Chinese) [时培明, 刘彬, 侯东晓 2008 57 1321]
[8] Wang K, Guan X P, Qiao J M 2010 Acta Phys. Sin. 59 3648 (in Chinese) [王坤, 关新平, 乔杰敏 2010 59 3648]
[9] Barbu L, Morosanu G 2007 Singularly Perturbed Boundary-Value Problems (Basel: Birkhauserm Verlag AG)
[10] de Jager E M, Jiang F R 1996 The Theory of Singular Pertubation (Amsterdamm: North-Holland Publishing Co.)
[11] Hovhannisyanm G, Vulanovic R 2008 Nonlinear Stud. 15 297
[12] Barbu L, Cosma E 2009 J. Math. Anal. Appl. 351 392
[13] Xu Y H, Yao J S, Mo J Q 2012 Acta Phys. Sin. 61 020202 (in Chinese) [许永红, 姚静荪, 莫嘉琪 2012 61 020202]
[14] Xu H, Chen L H, Mo J Q 2011 Acta Phys. Sin. 60 100201 (in Chinese) [徐惠, 陈丽华, 莫嘉琪 2011 60 100201]
[15] Mo J Q, Liu S D, Tang R R 2010 Acta Phys. Sin. 59 4403 (in Chinese) [莫嘉琪, 刘树德, 唐荣荣 2010 59 4403]
[16] Ji Y, Bi Q S 2009 Acta Phys. Sin. 58 4431 (in Chinese) [季颖, 毕勤胜 2009 58 4431]
[17] Tang R R 2008 Acta Math. Sci. 28 546 (in Chinese) [唐荣荣 2008 数学 28 546]
[18] Tang R R 2008 Appl. Math. J. 31 232 (in Chinese) [唐荣荣 2008 应用数学学报 31 232]
[19] Tang R R 2006 Acta Phys. Sin. 55 494 (in Chinese) [唐荣荣 2006 55 494]
[20] Tang R R 2008 Acta Math. Sci. 28 1128 (in Chinese) [唐荣荣 2008 数学 28 1128]
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[1] Hu H Y 2000 Applied Nonlinear Dynamics (Beijing: Aviation Industry Press) (in Chinese) [胡海岩 2000 应用非线性动力学(北京:航空工业出版社)]
[2] Shi P M, Liu B 2007 Acta Phys. Sin. 56 3678 (in Chinese) [时培明, 刘彬 2007 56 3678]
[3] Shi P M, Liu B, Liu S 2008 Acta Phys. Sin. 57 4675 (in Chinese) [时培明, 刘彬, 刘爽 2008 57 4675]
[4] Meng Z, Liu B 2008 Acta Phys. Sin. 57 1329 (in Chinese) [孟宗, 刘彬 2008 57 1329]
[5] Yang S P, Yuan X R 1998 Acta Nonlinear Dynamical Sin. 3 223 (in Chinese) [杨绍普, 袁向荣 1998 非线性动力学学报 3 223]
[6] Mo J Q, Cheng R J, Ge H X 2011 Acta Phys. Sin. 60 040203 (in Chinese) [莫嘉琪, 程荣军, 葛红霞 2011 60 040203]
[7] Shi P M, Liu B, Hou D X 2008 Acta Phys. Sin. 57 1321 (in Chinese) [时培明, 刘彬, 侯东晓 2008 57 1321]
[8] Wang K, Guan X P, Qiao J M 2010 Acta Phys. Sin. 59 3648 (in Chinese) [王坤, 关新平, 乔杰敏 2010 59 3648]
[9] Barbu L, Morosanu G 2007 Singularly Perturbed Boundary-Value Problems (Basel: Birkhauserm Verlag AG)
[10] de Jager E M, Jiang F R 1996 The Theory of Singular Pertubation (Amsterdamm: North-Holland Publishing Co.)
[11] Hovhannisyanm G, Vulanovic R 2008 Nonlinear Stud. 15 297
[12] Barbu L, Cosma E 2009 J. Math. Anal. Appl. 351 392
[13] Xu Y H, Yao J S, Mo J Q 2012 Acta Phys. Sin. 61 020202 (in Chinese) [许永红, 姚静荪, 莫嘉琪 2012 61 020202]
[14] Xu H, Chen L H, Mo J Q 2011 Acta Phys. Sin. 60 100201 (in Chinese) [徐惠, 陈丽华, 莫嘉琪 2011 60 100201]
[15] Mo J Q, Liu S D, Tang R R 2010 Acta Phys. Sin. 59 4403 (in Chinese) [莫嘉琪, 刘树德, 唐荣荣 2010 59 4403]
[16] Ji Y, Bi Q S 2009 Acta Phys. Sin. 58 4431 (in Chinese) [季颖, 毕勤胜 2009 58 4431]
[17] Tang R R 2008 Acta Math. Sci. 28 546 (in Chinese) [唐荣荣 2008 数学 28 546]
[18] Tang R R 2008 Appl. Math. J. 31 232 (in Chinese) [唐荣荣 2008 应用数学学报 31 232]
[19] Tang R R 2006 Acta Phys. Sin. 55 494 (in Chinese) [唐荣荣 2006 55 494]
[20] Tang R R 2008 Acta Math. Sci. 28 1128 (in Chinese) [唐荣荣 2008 数学 28 1128]
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