Structural Engineering and Mechanics

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The nonlinear galloping of iced transmission conductor under uniform and turbulence wind

  • Liu, Zhonghua (School of Architecture and Civil Engineering, Xiamen University) ;
  • Ding, Chenhui (School of Architecture and Civil Engineering, Xiamen University) ;
  • Qin, Jian (School of Architecture and Civil Engineering, Xiamen University) ;
  • Lei, Ying (School of Architecture and Civil Engineering, Xiamen University)
  • Received : 2019.12.12
  • Accepted : 2020.02.20
  • Published : 2020.08.25
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Abstract

The analytical approach for stability and response of iced conductor under uniform wind or turbulent wind is presented in this study. A nonlinear dynamic model is established to describe the motion of iced conductor galloping. In the case of uniform wind, the stability condition is derived by analyzing the eigenvalue associated with linearized matrix; The first order and second order approximation of galloping amplitude are obtained using multi-scale method. However, real wind has random characteristics essentially. To accurately evaluate the performance of the galloping iced conductor, turbulence wind should be described by random processes. In the case of turbulence wind, the Lyapunov exponent is conducted to judge the stability condition; The probability density of displacement is obtained by using the path integral method to predict galloping amplitude. An example is proposed to verify the effectiveness of the previous methods. It is shown that the fluctuating component of wind has little influence on the stability of iced conductor, but it can increase galloping amplitude. The analytical results on stability and response are also verified by numerical time stepping method.

Keywords

Acknowledgement

The research described in this paper was financially supported by National Key R&D Program of China (Grant No. 2017YFC0803300) and the National Natural Science Foundation of China (Grant No. 11772277).

References

  1. Cai, G.Q. and Zhu, W.Q. (2017), Elements of Stochastic Dynamics, World Scientific Co. Pte. Ltd., Singapore.
  2. Chadha, J. and Jaster, W. (1975), "Influence of turbulence on the galloping instability of iced conductors", IEEE Trans. Power App. Syst., 94(5),1489-1499. https://doi.org/10.1109/T-PAS.1975.31991.
  3. Choi, E.Y., Cho, J.R., Cho, Y.U., Jeong, W.B., Lee, S.B., Hong, S.P. and Chun, H.H. (2015), "Numerical and experimental study on dynamic response of moored spar-type scale platform for floating offshore wind turbine", Struct. Eng. Mech., 54(5), 909-922. https://doi.org/10.1109/T-PAS.1975.31991.
  4. Den Hartog, J.P. (1932). "Transmission line vibration due to sleet", AIEE Tran., 51(4), 1074-1086. https://doi.org/10.1109/T-AIEE.1932.5056223.
  5. Desai, Y.M., Yu, P., Popplewell, N., and Shah, A.H. (1995). "Finite element modeling of transmission line galloping", Comput. Struct., 57(3), 407-420. https://doi.org/10.1016/0045-7949(94)00630-L.
  6. Irvine, H.M., and Caughey, T.K. (1974). "The linear theory of free vibration of a suspended cable", Philos. T R Soc. A., 641, 299-315. https://doi.org/10.1098/rspa.1974.0189.
  7. Kim, J.W. and Sohn, J.H. (2018), "Galloping simulation and of the power transmission line under the fluctuating wind", Int. J. Precis. Eng. Manuf., 19(9), 1393-1398. https://doi.org/10.1007/s12541-018-0164-2.
  8. Lin L., Ang A.H.S., Xia D.D., Hu H. T., Wang H.F. and He F.Q. (2017), "Fluctuating wind field analysis based on random Fourier spectrum for wind induced response of high-rise structures", Struct. Eng. Mech., 63(6), 837-846. https://doi.org/10.12989/sem.2017.63.6.837.
  9. Lin, Y.K. and Cai G.Q. (1995), Probabilistic Structural Dynamics, McGraw-Hill Inc., New York, NY, USA.
  10. Lou, W.J., Yang L. Huang M.F. and Yang X.H. (2014), "Two-parameter bifurcation and stability analysis for nonlinear galloping of Iced transmission lines", J. Eng. Mech., 140(11), 04014081. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000795.
  11. Macdonald J., Larose G. (2006), "A unified approach to aerodynamic damping and drag/lift instabilities and its application to dry inclined cable galloping", J. Fluid. Struct., 22(2), 229-252. https://doi.org/10.1016/j.jfluidstructs.2005.10.002.
  12. Naess A. and Moe V. (2000), "Efficient path integration methods for nonlinear dynamic systems", Probabilistic Eng. Mech., 15, 221-231. https://doi.org/10.1016/S0266-8920(99)00031-4.
  13. Nayfeh, A.H., and Mook D.T. (1995), Nonlinear Oscillations, John Wiley Sons Inc., New York, NY, USA.
  14. Nayfeh, A.H., Arafat, H.N., Chin, C.M., and Lacarbonara, W. (2002), "Multimode interactions in suspended cables", J. Vib. Control, 8(3), 337-387. https://doi.org/10.1177/107754602023687.
  15. Nigol, O. and Buchan, P.G. (1981), "Conductor Galloping 2: Torsional mechanism", IEEE Trans. Power App. Syst., 100(2), 708-720. https://doi.org/10.1109/TPAS.1981.316922.
  16. Petrini F., Olmati P. and Bontempi (2019), "Coupling effects between wind and train transit induced fatigue damage in suspension bridges", Struct. Eng. Mech., 70(3), 311-324. https://doi.org/10.12989/sem.2019.70.3.311.
  17. Sun J.Q. (2006), Stochastic Dynamics and Control, Elsevier, Amsterdam, The Netherlands.
  18. Van Dyke, P., and Laneville, A. (2008). "Galloping of a single conductor covered with a D-Section on a high-voltage overhead test line", J. Wind Eng. Ind. Aerodyn, 96(6-7), 1141-1151. https://doi.org/10.1016/j.jweia.2007.06.036.
  19. Wang, J. and Lilien, J.L. (1998). "Overhead electrical transmission line galloping: A full multi-span 3-DOF model, some applications and design recommendations", IEEE Trans. Power Deliv., 13(3), 909-916. https://doi.org/10.1109/61.686992.
  20. Yu, P., Shah, A. H. and Popplewell, N. (1992), "Inertially coupled galloping of iced conductors", J. Appl. Mech., 59(1), 140-145. https://doi.org/10.1115/1.2899419.
  21. Yu, P., Desai, Y. M., Popplewell, N. and Shah, A. H. (1993), "Three-degree-of-freedom model for galloping. Part II: Solutions", J. Eng. Mech., https://doi.org/10.1061/(ASCE)0733-9399(1993)119:12(2426), 2426-2448.
  22. Zhang, J.F., Liu, Q.S., Ge, Y.J. and Zhao, L. (2019), "Studies on the influence factors of wind dynamic responses on hyperbolic cooling tower shells", Struct. Eng. Mech., 72(5), 541-555. https://doi.org/10.12989/sem.2019.72.5.541.
  23. Zhi L.H., Chen B. and Fang M.X. (2015), "Wind load estimation of super-tall buildings based on response data", Struct. Eng. Mech., 56(4), 625-648. https://doi.org/10.12989/sem.2015.56.4.625.

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