YAN Bo, LIU Xiao-hui, ZHAO Li, ZHOU Lin-shu. Nonlinear Galloping of Iced Quad-Bundle Conductors With Internal Resonances[J]. Applied Mathematics and Mechanics, 2014, 35(1): 39-49. doi: 10.3879/j.issn.1000-0887.2014.01.005
 Citation: YAN Bo, LIU Xiao-hui, ZHAO Li, ZHOU Lin-shu. Nonlinear Galloping of Iced Quad-Bundle Conductors With Internal Resonances[J]. Applied Mathematics and Mechanics, 2014, 35(1): 39-49.

# Nonlinear Galloping of Iced Quad-Bundle Conductors With Internal Resonances

##### doi: 10.3879/j.issn.1000-0887.2014.01.005
Funds:  The National Natural Science Foundation of China(51277168； 51308570)
• Rev Recd Date: 2013-11-27
• Publish Date: 2014-01-15
• Galloping of iced quad-bundle conductors with internal resonance was numerically investigated by means of nonlinear finite element method. Based on the numerical simulation of galloping processes of the typical iced quad-bundle conductor lines in both the steady and the stochastic wind fields, galloping characteristics of the iced conductor line with the ratio of the frequency of the first symmetric in-plane mode to the frequency of the out-of-plane mode being 2∶1 were discussed. It is shown that energy continuously interchanges between the vertical motion and transverse horizontal motion as internal resonance exists, which is apparently different from those of the line without internal resonance. The result provides a theoretical basis for the understanding of the coupling mechanism of galloping.
•  [1] EPRI Transmission Line Reference Book. Wind-Induced Conductor Motion [M]. 2nd Ed. Palo Alto, California: Electric Power Research Institute, 2009, 1018554. [2] Nayfeh A H, Mook D T. Nonlinear Oscillation [M]. New York: Wiley , 1979. [3] Lee C L, Perkins N C. Nonlinear oscillations of suspended cables containing a two-to-one internal resonance[J]. Nonlinear Dynamics,1992,3(6): 465-490. [4] Rega G, Lacarbonara W, Nayfeh A H, Chin C M. Multiple resonances in suspended cables: direct versus reduced-order models[J]. International Journal of Non-Linear Mechanics , 1999,34(5): 901-924. [5] Nayfeh A H, Arafat H N. Multimode interactions in suspended cables[J]. Journal of Vibration and Control,2002,8(3): 337-387. [6] Luongo A, Piccardo G. Non-linear galloping of sagged cables in 1∶2 internal resonance[J]. Journal of Sound and Vibration,1998,214(5): 915-940. [7] Luongo A, Zulli D, Piccardo G. Analytical and numerical approaches to nonlinear galloping of internally resonant suspended cables[J]. Journal of Sound and Vibration,2008,315(3): 375-393. [8] 刘小会, 严波, 张宏雁, 周松. 覆冰导线舞动非线性数值模拟方法[J]. 应用数学和力学, 2009,30(4): 457-468.(LIU Xiao-hui, YAN Bo, ZHANG Hong-yan, ZHOU Song. Nonlinear numerical simulation method for galloping of iced conductor[J]. Applied Mathematics and Mechanics,2009,30(4): 457-468.(in Chinese)) [9] Desai Y M, Yu P, Popplewell N, Shah A H. Finite element modeling of transmission line galloping[J]. Computers & Structures,1995,57(3): 407-420. [10] Zhang Q, Popplewell N, Shah A H. Galloping of bundle conductor[J]. Journal of Sound and Vibration , 2000,234(1): 115-134. [11] 刘小会, 严波, 张宏雁, 周松, 唐杰. 分裂导线舞动非线性有限元分析方法[J]. 振动与冲击, 2010,29(6): 129-133.(LIU Xiao-hui, YAN Bo, ZHANG Hong-yan, ZHOU Song, TANG Jie. Nonlinear finite element method for bundle conductors[J]. Journal of Vibration and Shock , 2010,29(6): 129-133.(in Chinese)) [12] Hu J, Yan B, Zhou S, Zhang H. Numerical investigation on galloping of iced quad bundle conductors[J]. IEEE Transactions on Power Delivery,2012,27(2): 784-792. [13] Irvine H M, Caughey T K. The linear theory of free vibrations of a suspended cable[J].Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences,1974,341(1626): 299-315. [14] 张宏雁, 严波, 周松, 胡景, 刘小会. 覆冰四分裂导线静态气动力特性试验研究[J]. 空气动力学学报, 2011,29(2): 23-27.(ZHANG Hong-yan, YAN Bo, ZHOU Song, HU Jing, LIU Xiao-hui. Static test on aerodynamics of iced quad bundle conductors[J]. Acta Aerodynamica Sinica,2011,29(2): 23-27.(in Chinese)) [15] Simiu E, Scanlan R H. Wind Effects on Structures[M]. 2nd ed. New York: John Wiley & Sons,1986. [16] Yan B, Lin X, Luo W, Chen Z, Liu Z. Numerical study on dynamic swing of suspension insulator string in overhead transmission line under wind load[J]. IEEE Transactions on Power Delivery,2010,25(1): 248-259. [17] 刘小会, 严波, 张宏雁, 周松. 随机风场中覆冰四分裂导线舞动数值模拟[J]. 振动与冲击, 2012,31(13): 16-21.(LIU Xiao-hui, YAN Bo, ZHANG Hong-yan, ZHOU Song. Numerical investigation on galloping of iced quad bundle conductor in stochastic wind field[J]. Journal of Vibration and Shock , 2012,31(13): 16-21.(in Chinese))

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