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Approximate solution for a class of relative rotation nonlinear dynamic model

Mo Jia-Qi Ge Hong-Xia Cheng Rong-Jun

Approximate solution for a class of relative rotation nonlinear dynamic model

Mo Jia-Qi, Ge Hong-Xia, Cheng Rong-Jun
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  • A class of relative rotation nonlinear dynamical model with nonlinear damping force and forcing periodic force is investigated. First, a homotopic mapping is constructed, and then the initial approximate solution is determined. Finally, using the homotopic mapping method, the arbitrarily degree approximation for corresponding model is found.
    • Funds:
    [1]

    Fu J L, Chen L Q, Xue Y 2003 Acta Phys. Sin. 52 256 (in Chinese) [傅景礼、 陈立群、 薛 纭 2003 物理学报 52 256]

    [2]

    Zhang K, Feng J 2005 Acta Phys. Sin. 54 2985 (in Chinese) [张 凯、 冯 俊 2005 物理学报 54 2985]

    [3]

    Wang K, 2005 Acta Phys. Sin. 54 5530 (in Chinese) [王 坤 2005 物理学报 54 5530]

    [4]

    Zhao W, Liu B, Shi P M, Jiang J S 2006 Acta Phys. Sin. 55 3852 (in Chinese)[赵 武、 刘 彬、 时培明、 将金水 2006 物理学报 55 3852]

    [5]

    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]

    [6]

    Shi P M, Liu, 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]

    [7]

    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]

    [8]

    de Jager E M Jiang F R 1996 The Theory of Singular Pertubation, (Amsterdamm, North-Holland Publishing Co)

    [9]

    Sagon G 2008 Nonlinearity 21 1183

    [10]

    Hovhannisyanm G, Vulanovic R 2008 Nonlinear Stud. 15 297

    [11]

    Barbu L, Cosma E 2009 J. Math. Anal. Appl. 351 392

    [12]

    Ramos M 2009 J. Math. Anal. Appl. 352 246

    [13]

    Mo J Q 2009 Adv. Math. 38 227

    [14]

    Mo J Q 2009 Science in China Ser. G 52 1007

    [15]

    Mo J Q, Lin W T 2008 J, Sys. Sci. & Complexity 20 119

    [16]

    Mo J Q 2009 Chin. Phys. Lett. 26 010204

    [17]

    Mo J Q 2009 Chin. Phys. Lett. 26 060202

    [18]

    Mo J Q 2010 Commun. Theor. Phys. 53 440

    [19]

    Mo J Q, Lin W T 2004 Acta Phys. Sin. 53 996 (in Chinese) [莫嘉琪、 林万涛 2004 物理学报 53 996]

    [20]

    Mo J Q Lin Y H, Lin W 2009 Acta Phys. Sin. 58 6692 (in Chinese) [莫嘉琪、 林一骅、 林万涛 2009 物理学报 58 6692]

    [21]

    Mo J Q 2010 Chin. Phys. B 19 010203

    [22]

    Mo J Q, Lin Y H, Lin W T 2010 Chin. Phys. B 19 030202

    [23]

    Mo J Q, Lin W T, Lin Y H 2009 Chin. Phys. B 18 3624

    [24]

    Mo J Q 2010 Chin. Phys. B 19 010203

    [25]

    He J H 2002 Approximate Nonlinear Analytical Methods in Engineering and Sciences (Zhengzhou: Henan Science and Technology Press) (in Chinese) [何吉欢 2002 工程和科学计算中的近似非线性分析方法 (郑州 河南科学技术出版社)]

    [26]

    Liao Shijun 2004 Beyond Perturbation: Introduction to the Homotopy Analysis Method, (New York, CRC Press Co)

  • [1]

    Fu J L, Chen L Q, Xue Y 2003 Acta Phys. Sin. 52 256 (in Chinese) [傅景礼、 陈立群、 薛 纭 2003 物理学报 52 256]

    [2]

    Zhang K, Feng J 2005 Acta Phys. Sin. 54 2985 (in Chinese) [张 凯、 冯 俊 2005 物理学报 54 2985]

    [3]

    Wang K, 2005 Acta Phys. Sin. 54 5530 (in Chinese) [王 坤 2005 物理学报 54 5530]

    [4]

    Zhao W, Liu B, Shi P M, Jiang J S 2006 Acta Phys. Sin. 55 3852 (in Chinese)[赵 武、 刘 彬、 时培明、 将金水 2006 物理学报 55 3852]

    [5]

    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]

    [6]

    Shi P M, Liu, 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]

    [7]

    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]

    [8]

    de Jager E M Jiang F R 1996 The Theory of Singular Pertubation, (Amsterdamm, North-Holland Publishing Co)

    [9]

    Sagon G 2008 Nonlinearity 21 1183

    [10]

    Hovhannisyanm G, Vulanovic R 2008 Nonlinear Stud. 15 297

    [11]

    Barbu L, Cosma E 2009 J. Math. Anal. Appl. 351 392

    [12]

    Ramos M 2009 J. Math. Anal. Appl. 352 246

    [13]

    Mo J Q 2009 Adv. Math. 38 227

    [14]

    Mo J Q 2009 Science in China Ser. G 52 1007

    [15]

    Mo J Q, Lin W T 2008 J, Sys. Sci. & Complexity 20 119

    [16]

    Mo J Q 2009 Chin. Phys. Lett. 26 010204

    [17]

    Mo J Q 2009 Chin. Phys. Lett. 26 060202

    [18]

    Mo J Q 2010 Commun. Theor. Phys. 53 440

    [19]

    Mo J Q, Lin W T 2004 Acta Phys. Sin. 53 996 (in Chinese) [莫嘉琪、 林万涛 2004 物理学报 53 996]

    [20]

    Mo J Q Lin Y H, Lin W 2009 Acta Phys. Sin. 58 6692 (in Chinese) [莫嘉琪、 林一骅、 林万涛 2009 物理学报 58 6692]

    [21]

    Mo J Q 2010 Chin. Phys. B 19 010203

    [22]

    Mo J Q, Lin Y H, Lin W T 2010 Chin. Phys. B 19 030202

    [23]

    Mo J Q, Lin W T, Lin Y H 2009 Chin. Phys. B 18 3624

    [24]

    Mo J Q 2010 Chin. Phys. B 19 010203

    [25]

    He J H 2002 Approximate Nonlinear Analytical Methods in Engineering and Sciences (Zhengzhou: Henan Science and Technology Press) (in Chinese) [何吉欢 2002 工程和科学计算中的近似非线性分析方法 (郑州 河南科学技术出版社)]

    [26]

    Liao Shijun 2004 Beyond Perturbation: Introduction to the Homotopy Analysis Method, (New York, CRC Press Co)

  • [1] Shi Pei-Ming, Liu Bin. Stability of nonlinear dynamical system of relative rotation and approximate solution under forced excitation. Acta Physica Sinica, 2007, 56(7): 3678-3682. doi: 10.7498/aps.56.3678
    [2] Shi Pei-Ming, Liu Bin, Liu Shuang. Stability and approximate solution of a relative-rotation nonlinear dynamical system under harmonic excitation. Acta Physica Sinica, 2008, 57(8): 4675-4684. doi: 10.7498/aps.57.4675
    [3] Meng Zong, Liu Bin. Stability of equilibrium state of a kind of nonlinear relative rotation dynamic system and associated harmonic approximate solution. Acta Physica Sinica, 2008, 57(3): 1329-1334. doi: 10.7498/aps.57.1329
    [4] Li Xiao-Jing, Chen Xuan-Qing. Periodic solution of relative rotation nonlinear dynamic model with commonly damped force and forcing periodic force. Acta Physica Sinica, 2012, 61(21): 210201. doi: 10.7498/aps.61.210201
    [5] Li Xiao-Jing, Yan Jing, Chen Xuan-Qing, Cao Yi. The periodic solution problem of a relative rotation nonlinear system with nonlinear elastic force and generalized damping force. Acta Physica Sinica, 2014, 63(20): 200202. doi: 10.7498/aps.63.200202
    [6] Shi Pei-Ming, Liu Bin, Hou Dong-Xiao. Chaotic motion of some relative rotation nonlinear dynamic system. Acta Physica Sinica, 2008, 57(3): 1321-1328. doi: 10.7498/aps.57.1321
    [7] Shi Pei-Ming, Jiang Jin-Shui, Liu Bin. Stability and approximate solution of a relative-rotation nonlinear dynamical system with coupled terms. Acta Physica Sinica, 2009, 58(4): 2147-2154. doi: 10.7498/aps.58.2147
    [8] Hou Dong-Xiao, Liu Bin, Shi Pei-Ming. The bifurcation of a kind of relative rotational dynamic equation with hysteresis and its approximate solution. Acta Physica Sinica, 2009, 58(9): 5942-5949. doi: 10.7498/aps.58.5942
    [9] Liu Bin, Zhang Ye-Kuan, Liu Shuang, Wen Yan. Hopf bifurcation and stability of periodic solutions in a nonlinear relative rotation dynamical system with time delay. Acta Physica Sinica, 2010, 59(1): 38-43. doi: 10.7498/aps.59.38
    [10] Guan Xin-Ping, Qiao Jie-Min, Wang Kun. Precise periodic solutions and uniqueness of periodic solutions of some relative rotation nonlinear dynamic system. Acta Physica Sinica, 2010, 59(6): 3648-3653. doi: 10.7498/aps.59.3648
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  • Received Date:  28 June 2010
  • Accepted Date:  16 July 2010
  • Published Online:  15 April 2011

Approximate solution for a class of relative rotation nonlinear dynamic model

  • 1. (1)Department of Mathematics, Anhui Normal University, Wuhu 241003, China; (2)Faculty of Science, Ningbo University, Ningbo 315211, China; (3)Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China

Abstract: A class of relative rotation nonlinear dynamical model with nonlinear damping force and forcing periodic force is investigated. First, a homotopic mapping is constructed, and then the initial approximate solution is determined. Finally, using the homotopic mapping method, the arbitrarily degree approximation for corresponding model is found.

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