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A class of dynamical model for the nonlinear vibration of a transmission line is studied. Using the homotopy mapping method, the approximate solution with an arbitrary degree of accuracy is obtained.
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Keywords:
- transmission line /
- nonlinear vibration /
- homotopic mapping /
- approximate solution
[1] Jiang S Y, Xu J 2009 Chin. Quart. Mech. 30 33 (in Chinese)[蒋扇英、徐 鉴 2009 力学季刊 30 33]
[2] Bosdogianni A, Olivari D 1996 J. Wind Eng. Indus. Aerodyn. 64 171
[3] Wang S H, Jiang X L, Sun C X 2005 High Voltage Eng. 31 11 (in Chinese)[王少华、蒋兴良、孙才新 2005 高电压技术31 11]
[4] Lin H P,Perkins N C 1995 J. Sound Vib. 179 131
[5] Gattulli V, Alaggio R, Potenza F 2008 Int. J. Non-Linear. Mech. 43 36
[6] Xiao X W, Yang J, Jacques D, Xu Y 2003 J. Vib. Measur Diagn. 23 110 (in Chinese)[肖锡武、杨 军、Jacques D、徐 嫣 〖7] Yang Z A, Liu P F, Xi X Y 2007 Eng. Mech. 24 182 (in Chinese)[杨志安、刘鹏飞、席晓燕 2007 工程力学24 182]
[7] Li S, Liao S J 2005 Appl. Math. Comput. 169 854
[8] Mo J Q, Zhang W J, Chen X F 2007 Acta Phys. Sin. 56 6169 (in Chinese)[莫嘉琪、张伟江、陈贤峰 2007 物理学报 56 6169]
[9] Lin W T, Mo J Q 2008 Acta Phys. Sin. 57 2633 (in Chinese)[林万涛、莫嘉琪 2008 物理学报 57 2633]
[10] Mo J Q, Lin W T 2008 Acta Phys. Sin. 57 6694 (in Chinese)[莫嘉琪、林万涛 2008 物理学报 57 6694]
[11] Mo J Q 2009 Acta Phys. Sin. 58 2930 (in Chinese)[莫嘉琪 2009 物理学报 58 2930]
[12] Mo J Q, Cheng Y 2009 Acta Phys. Sin. 58 4379 (in Chinese)[莫嘉琪、程 燕 2009 物理学报 58 4379]
[13] Mo J Q, Chen X F 2010 Acta Phys. Sin. 59 1403 (in Chinese)[莫嘉琪、陈贤峰 2010 物理学报 59 1403]
[14] Wu Q K 2008 Acta Phys. Sin. 57 2654 (in Chinese)[吴钦宽 2008 物理学报 57 2654]
[15] Wu Q K 2009 J. Henan Univ. (Nat. Sci.) 39 567 (in Chinese)[吴钦宽 2009 河南大学学报(自然科学版) 39 567]
[16] Shi L F, Zhou X C 2010 Acta Phys. Sin. 59 2915 (in Chinese)[石兰芳、周先春 2010 物理学报 59 2915]
[17] Mo J Q 2009 Chin. Phys. B 18 4608
[18] Mo J Q, Lin Y H, Lin W T 2010 Chin. Phys. B 19 030202
[19] Mo J Q, Chen X F 2010 Acta Phys. Sin. 59 2919 (in Chinese)[莫嘉琪、陈贤峰 2010 物理学报 59 2919]
[20] Zhou X C, Lin W T, Lin T H, Mo J Q 2010 Acta Phys. Sin. 59 2173 (in Chinese)[周先春、林万涛、林一骅、莫嘉琪 2010 物理学报 59 2173]
[21] He J H 2002 Approxinate Nonlinear Analytical Methods in Engineering and Sciences (Zhengzhou: Henan Science and Technology Press) p113 (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)第113页] 〖23] Liao S J 2004 Beyond Perturbation: Introduction to the Homotopy Analysis Method (Yew York: CRC Press Co.) p46
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[1] Jiang S Y, Xu J 2009 Chin. Quart. Mech. 30 33 (in Chinese)[蒋扇英、徐 鉴 2009 力学季刊 30 33]
[2] Bosdogianni A, Olivari D 1996 J. Wind Eng. Indus. Aerodyn. 64 171
[3] Wang S H, Jiang X L, Sun C X 2005 High Voltage Eng. 31 11 (in Chinese)[王少华、蒋兴良、孙才新 2005 高电压技术31 11]
[4] Lin H P,Perkins N C 1995 J. Sound Vib. 179 131
[5] Gattulli V, Alaggio R, Potenza F 2008 Int. J. Non-Linear. Mech. 43 36
[6] Xiao X W, Yang J, Jacques D, Xu Y 2003 J. Vib. Measur Diagn. 23 110 (in Chinese)[肖锡武、杨 军、Jacques D、徐 嫣 〖7] Yang Z A, Liu P F, Xi X Y 2007 Eng. Mech. 24 182 (in Chinese)[杨志安、刘鹏飞、席晓燕 2007 工程力学24 182]
[7] Li S, Liao S J 2005 Appl. Math. Comput. 169 854
[8] Mo J Q, Zhang W J, Chen X F 2007 Acta Phys. Sin. 56 6169 (in Chinese)[莫嘉琪、张伟江、陈贤峰 2007 物理学报 56 6169]
[9] Lin W T, Mo J Q 2008 Acta Phys. Sin. 57 2633 (in Chinese)[林万涛、莫嘉琪 2008 物理学报 57 2633]
[10] Mo J Q, Lin W T 2008 Acta Phys. Sin. 57 6694 (in Chinese)[莫嘉琪、林万涛 2008 物理学报 57 6694]
[11] Mo J Q 2009 Acta Phys. Sin. 58 2930 (in Chinese)[莫嘉琪 2009 物理学报 58 2930]
[12] Mo J Q, Cheng Y 2009 Acta Phys. Sin. 58 4379 (in Chinese)[莫嘉琪、程 燕 2009 物理学报 58 4379]
[13] Mo J Q, Chen X F 2010 Acta Phys. Sin. 59 1403 (in Chinese)[莫嘉琪、陈贤峰 2010 物理学报 59 1403]
[14] Wu Q K 2008 Acta Phys. Sin. 57 2654 (in Chinese)[吴钦宽 2008 物理学报 57 2654]
[15] Wu Q K 2009 J. Henan Univ. (Nat. Sci.) 39 567 (in Chinese)[吴钦宽 2009 河南大学学报(自然科学版) 39 567]
[16] Shi L F, Zhou X C 2010 Acta Phys. Sin. 59 2915 (in Chinese)[石兰芳、周先春 2010 物理学报 59 2915]
[17] Mo J Q 2009 Chin. Phys. B 18 4608
[18] Mo J Q, Lin Y H, Lin W T 2010 Chin. Phys. B 19 030202
[19] Mo J Q, Chen X F 2010 Acta Phys. Sin. 59 2919 (in Chinese)[莫嘉琪、陈贤峰 2010 物理学报 59 2919]
[20] Zhou X C, Lin W T, Lin T H, Mo J Q 2010 Acta Phys. Sin. 59 2173 (in Chinese)[周先春、林万涛、林一骅、莫嘉琪 2010 物理学报 59 2173]
[21] He J H 2002 Approxinate Nonlinear Analytical Methods in Engineering and Sciences (Zhengzhou: Henan Science and Technology Press) p113 (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)第113页] 〖23] Liao S J 2004 Beyond Perturbation: Introduction to the Homotopy Analysis Method (Yew York: CRC Press Co.) p46
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