Self-Excited Travelling Waves as a Model of Cable Galloping

Abstract:

In the paper the galloping phenomenon is modelled by self-excited waves travelling along the cable. The critical conditions of air flow and corresponding changes in the lift coefficient are presented. The motion of the cable was described in relation to equilibrium configuration. Since the wavelengths are small with reference to considered distances and additionally the tension and curvature of equilibrium line of the cable are slowly varying functions of the arc co-ordinate, the problems concerning the travelling waves can be solved using the Wentzel-Kramers-Brillouin (WKB) method. Using this method the equations describing wave numbers and amplitudes of waves were derived. The results of the calculations of amplitudes are presented in the form of plots.

• Periodical: Solid State Phenomena (Volume 177)
• Pages: 135-142
• DOI: https://doi.org/10.4028/www.scientific.net/SSP.177.135
• Online since: July 2011
• Authors: Jacek Snamina
• Keywords: Coupled Wave, Galloping, Long Cable, Wind Induced Vibration

References

[1] J.J. Burgess, M.S. Triantafyllou, The elastic frequencies of cables, Journal of Sound and Vibration, 120 (1988) 153-165.

DOI: 10.1016/0022-460x(88)90340-9

[2] Y.M. Desai, P. Yu, N. Popplewell, A.H. Shah, Finite element modeling of transmission line galloping, Computers and Structures, 53, 3 (1995) 407-420.

DOI: 10.1016/0045-7949(94)00630-l

[3] C.J. Myerscough, A simple model of the growth of wind-induced oscillations in overhead lines, Journal of Sound and Vibration, 28 (1973) 699-713.

DOI: 10.1016/s0022-460x(73)80144-0

[4] C.J. Myerscough, Further studies of the growth of wind-induced oscillations in overhead lines, Journal of Sound and Vibration, 28 (1974) 503-517.

DOI: 10.1016/s0022-460x(75)80030-7

[5] N.C. Perkins, C.D. Mote, Three-dimensional vibration of travelling elastic cables, Journal of Sound and Vibration, 114 (1987) 325-340.

DOI: 10.1016/s0022-460x(87)80157-8

[6] N.C. Perkins, M. Behbahani-Nejad, Freely propagating waves in elastic cables, Journal of Sound and Vibration, 2 (1996) 189-202.

DOI: 10.1006/jsvi.1996.0476

[7] J. Snamina, The properties of coupled waves propagating in long suspended cables, Journal of Theoretical and Applied Mechanics, 46 (2008) 973-992.

[8] H. Sockel, Wind-excited vibrations of structures, Springer Verlag, (1994).

[9] N. Srinil, G. Rega, S. Chucheepsakul, Three-dimensional non-linear coupling and dynamic tension in the large-amplitude free vibrations of arbitrarily sagged cables, Journal of Sound and Vibration, 269 (2004) 823-852.

DOI: 10.1016/s0022-460x(03)00137-8

[10] H. Yang, Wave Packets and their Bifurcations in Geophysical Fluid Dynamics, Springer Verlag, (1990).

[11] G.B. Whitham, Linear and Nonlinear Waves, John Wiley and Sons Inc., New York (1999).