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一类多频激励相对转动非线性动力学模型的重正规化解

唐荣荣

引用本文:
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一类多频激励相对转动非线性动力学模型的重正规化解

唐荣荣

The renormalization solution for a class of relative rotation nonlinear dynamic model with multi-frequency excitation

Tang Rong-Rong
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  • 用摄动理论研究了一类多频激励下具有非线性弹性力和摩阻力的相对转动非线性动力学模型. 探讨了各种组合频率之间的关系,给出了使多种类型共振同时发生的条件, 并用重正规化方法得出了模型在各相应条件下解的渐近表达式.
    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.
    • 基金项目: 国家自然科学基金(批准号: 11071205)和浙江省自然科学基金(批准号: Y6090164)资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11071205) and the Natural Science Foundation of Zhejiang Province, China (Grant No. Y6090164).
    [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 物理学报 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 物理学报 57 4675]

    [4]

    Meng Z, Liu B 2008 Acta Phys. Sin. 57 1329 (in Chinese) [孟宗, 刘彬 2008 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 59 4403]

    [16]

    Ji Y, Bi Q S 2009 Acta Phys. Sin. 58 4431 (in Chinese) [季颖, 毕勤胜 2009 物理学报 58 4431]

    [17]

    Tang R R 2008 Acta Math. Sci. 28 546 (in Chinese) [唐荣荣 2008 数学物理学报 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 物理学报 55 494]

    [20]

    Tang R R 2008 Acta Math. Sci. 28 1128 (in Chinese) [唐荣荣 2008 数学物理学报 28 1128]

  • [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 物理学报 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 物理学报 57 4675]

    [4]

    Meng Z, Liu B 2008 Acta Phys. Sin. 57 1329 (in Chinese) [孟宗, 刘彬 2008 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 59 4403]

    [16]

    Ji Y, Bi Q S 2009 Acta Phys. Sin. 58 4431 (in Chinese) [季颖, 毕勤胜 2009 物理学报 58 4431]

    [17]

    Tang R R 2008 Acta Math. Sci. 28 546 (in Chinese) [唐荣荣 2008 数学物理学报 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 物理学报 55 494]

    [20]

    Tang R R 2008 Acta Math. Sci. 28 1128 (in Chinese) [唐荣荣 2008 数学物理学报 28 1128]

计量
  • 文章访问数:  5605
  • PDF下载量:  730
  • 被引次数: 0
出版历程
  • 收稿日期:  2012-03-07
  • 修回日期:  2012-03-31
  • 刊出日期:  2012-10-05

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