Coupled Vertical and Horizontal Galloping
Publication: Journal of Engineering Mechanics
Volume 118, Issue 1
Abstract
Galloping can occur when wind blows on ice‐coated conductors. In this paper, the linearized coupled vertical‐horizontal galloping equations are derived and the eigenvalues defining the motion are determined analytically. The intrinsic coupling between the vertical and horizontal equations requires that there be no vertical motion if the horizontal motion is constrained. Furthermore, vertical galloping may be initiated by a horizontal displacement or velocity. The solution of the eigenvalue equation indicates that the coupled galloping criterion may be either more or less stringent than Den Hartog's criterion. The galloping trajectory is either a straight line at a small angle to the vertical, or under more extreme conditions, defines an elliptical envelope. Solutions are obtained for four cases chosen from the literature to illustrate the effect of different combinations of values of the aerodynamic parameters.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Abramowitz, M., and Stegun, I. A. (1965). Handbook of mathematical functions. Dover Publications, New York, N.Y.
2.
Blevins, R. D., and Iwan, W. D. (1974). “The galloping response of a two‐degree‐of freedom system.” J. Appl. Mech. Trans. ASME, 41(4), 1113–1118.
3.
Burgsdorf, V. V., Liberman, A. Y., Meshkov, V. K. (1964). “Conductor vibration and dancing on E.H.V. transmission lines employing bundle conductors.” CIGRE report 219, Paris, France.
4.
Chadha, J., and Jaster, W. (1975). “Influence of turbulence on the galloping instabilityof iced conductors.” IEEE Trans. Power Apparatus Syst., 94(5), 1489–1499.
5.
Cheers, F. (1950). “A note on galloping conductors.” Report no. MT‐14, Nat. Res. Council of Canada.
6.
Den Hartog, J. P. (1932). “Transmission line vibration due to sleet.” AIEE Trans., 51(12), 1074–1076.
7.
Desai, Y. M., Popplewell, N., Havard, D. G., and Shah, A. H. (1990). “Static and dynamic behavior of mechanical components associated with electrical transmission lines—III(B).” Shock Vib. Dig., 22(3), 3–10.
8.
Edwards, A. T. (1970). “Conductor galloping.” Electra, (12) 31–48.
9.
Havard, D., and Pon, C. J. (1988). “Galloping conductor control‐Status 1988.” Proc. 4th Int. Conf. on Atmospheric Icing of Struct., Electircite de France Paris, France, 314–318.
10.
Jones, K. F., and Govoni, J. W. (1990). “Aerodynamic characteristics of natural rime ice samples.” Proc. Fifth Int. Workshop on Atmospheric Icing of Struct., Japanese Society of Snow and Ice, Tokyo, Japan, A5‐1‐(1)–A5‐1‐(6).
11.
Koutselos, L. T., and Tunstall, M. J. (1986). “Collection and reproduction of natural ice shapes on overhead line conductors and measurement of their aerodynamic characteristics.” Proc. Third Int. Workshop on Atmospheric Icing of Struct., Environment Canada, Vancouver, Canada.
12.
Koutselos, L. T., and Tunstall, M. J. (1988). “Further studies of the galloping instabilities of natural ice accretions on overhead line conductors.” Proc. Fourth Int. Conf. on Atmospheric Icing of Struct., Electricité de France, Paris, France.
13.
Mukhopadhyay, V., and Dugundji, J. (1976). “Wind excited vibration of a square section cantilever beam in a smooth flow.” J. Sound Vib., 45(3), 329–339.
14.
Nigol, O., and Buchan, P. G. (1981a). Conductor galloping part I—Den Hartog mechanism.” IEEE Trans. Power Apparatus Syst., 100(2), 699–707.
15.
Nigol, O., and Buchan, P. G. (1981b). “Conductor galloping part II—Torsional mechanism.” IEEE Trans. Power Apparatus Syst., 100(2), 708–720.
16.
Novak, M. (1969). “Aeroelastic galloping of prismatic bodies.” J. Engrg. Mech., ASCE, 95(1), 115–142.
17.
Novak, M., Davenport, A. G., and Tanaka, H. (1978). “Vibration of towers due to galloping of iced cables.” J. Engrg. Mech., ASCE 104(2), 457–473.
18.
Pohlman, I. C., and Havard, D. (1983). “Field research of the galloping of iced conductors—A status report.” Proc., 1st Int. Workshop on Atmospheric Icing of Struct., CRREL Special Report 83‐17, U.S. Army Cold Regions Res. and Engrg. Lab., Hanover, N.H.
19.
Ratkowski, J. J. (1968). “Factors relative to high amplitude galloping.” IEEE Trans. Power Apparatus Syst., 87(6), 1385–1396.
20.
Richardson, A. S. (1982). “The time line method for assessing galloping exposure.” IEEE Trans. Power Apparatus Systems, 101(8), 2885–2891.
21.
Richardson, A. S. (1988a). “Predicting galloping amplitudes.” J. of Engrg. Mech., ASCE, 114(4), 716–723.
22.
Richardson, A. S. (1988b). “Predicting Galloping Amplitudes II.” J. Engrg. Mech., ASCE, 114(11), 1945–1952.
23.
Richardson, A. S., Martuccelli, I. R., and Price, W. S. (1965). “Research study on galloping of electric power transmission lines.” Proc. First Int. Conf. on Wind Effects on Buildings and Struct., Teddington, England, 2, 611–686.
24.
Simpson, A. (1983). “Wind‐induced vibration of overhead power transmission lines.” Sci. Progress, 68, 285–308.
25.
van Horssen, W. T. (1989). “Asymptotics for a system of nonlinearly coupled wave equations with an application to the galloping oscillations of overhead transmission lines.” Q. Appl. Math., 47(2), 197–219.
26.
Wolfram, S. (1988). Mathematica, A system for doing mathematics by computer. Addison‐Wesley Publishing Co., Inc., Redwood City, Calif.
Information & Authors
Information
Published In
Copyright
Copyright © 1992 ASCE.
History
Published online: Jan 1, 1992
Published in print: Jan 1992
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.