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Nonlinear free vibrations of coupled spans of overhead transmission lines

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Abstract

The weakly nonlinear, freely vibrating motion of a system of coupled spans of suspended overhead transmission lines is studied. It is shown that the natural vibration is the gravity mode, of which the tension component vanishes in the first harmonic. The problem originates from a study of the phenomenon of galloping, which is a high-amplitude periodic oscillation of overhead transmission lines due to steady crosswind. Particular attention is given to an intermodal resonance, which may be interesting for galloping control.

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References

  1. den Hartog J.P. (1932). Transmission line vibration due to sleet. Trans. Amer. Inst. Electr. Eng. 51: 1074–1077

    Article  Google Scholar 

  2. Simpson A. (1983). Wind-induced vibration of overhead power transmission lines. Sci. Prog. Oxford 68: 285–308

    Google Scholar 

  3. S.W. Rienstra, Non-linear free vibrations of coupled spans of suspended cables. In: J. Manley et al. (eds.), Proceedings of the Third European Conference on Mathematics in Industry, August 27–31 1988 Glasgow. Kluwer Academic Publishers and B.G. Teubner Stuttgart (1990) pp. 133–144

  4. Chabart O. and Lilien J.L. (1998). Galloping of electrical lines in wind tunnel facilities. J. Wind Engng. Industr. Aerodyn. 74–76: 967–976

    Article  Google Scholar 

  5. Rawlins C.B. (2004). Effect of non-linearity in free large oscillations of a shallow catenary. J. Sound Vibr. 273: 857–874

    Article  ADS  Google Scholar 

  6. van der Burgh A.H.P. (1983). An asymptotic theory for the free vibrations of an iced two-conductor bundled transmission line. In: Verhulst F. (eds) Asymptotic Analysis II – Surveys and Trends. Lecture Notes in Mathematics 985. Springer-Verlag, Berlin, pp. 413–430

    Chapter  Google Scholar 

  7. Irvine H.M. and Caughey T.K. (1974). The linear theory of free vibrations of a suspended cable. Proc. R. Soc. London A341: 299–315

    ADS  Google Scholar 

  8. Hagedorn P. and Schäfer B. (1980). On non-linear free vibrations of an elastic cable. Int. J. Non-lin. Mech. 15: 333–340

    Article  MATH  Google Scholar 

  9. Landau L.D. and Lifshitz E.M. (1970). Theory of Elasticity. (2nd edition). Pergamon Press, Oxford, 165 pp

    Google Scholar 

  10. Nayfeh A.H. (1973). Perturbation Methods. John Wiley & Sons Inc., New York, 425 pp

    MATH  Google Scholar 

  11. Kevorkian J. and Cole J.D. (1996). Multiple Scale and Singular Perturbation Methods. Springer, New York, 632 pp

    MATH  Google Scholar 

  12. Nayfeh A.H. and Mook D.T. (1979). Nonlinear Oscillations. John Wiley & Sons, New York, 704pp

    MATH  Google Scholar 

  13. Simpson A. (1972). On the oscillatory motions of translating elastic cables. J. Sound. Vibr. 20: 177–189

    Article  MATH  ADS  Google Scholar 

  14. Luongo A., Rega G. and Vestroni F. (1984). Planar non-linear vibrations of an elastic cable. Int. J. Non-Lin. Mech. 19: 39–52

    Article  MATH  Google Scholar 

  15. Rega G., Vestroni F. and Benedettini F. (1984). Parametric analysis of large amplitude free vibrations of a suspended cable. Int. J. Solids Struct. 20: 95–105

    Article  MATH  Google Scholar 

  16. Benedettini F. and Rega G. (1987). Non-linear dynamics of an elastic cable under planar excitation. Int. J. Non-Lin. Mech. 22: 497–509

    Article  MATH  Google Scholar 

  17. Burgess J.J. and Triantafyllou M.S. (1988). The elastic frequencies of cables. J. Sound Vibr. 120: 153–165

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics and Computing Science, Eindhoven University of Technology, P.O. Box 513, 5600, MB, Eindhoven, The Netherlands

    Sjoerd W. Rienstra

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  1. Sjoerd W. Rienstra
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Correspondence to Sjoerd W. Rienstra.

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Rienstra, S.W. Nonlinear free vibrations of coupled spans of overhead transmission lines. J Eng Math 53, 337–348 (2005). https://doi.org/10.1007/s10665-005-9011-4

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  • DOI: https://doi.org/10.1007/s10665-005-9011-4

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