Misconceptions and Generalizations of the Den Hartog Galloping Criterion
Publication: Journal of Engineering Mechanics
Volume 140, Issue 4
Abstract
Classical quasi-steady galloping analysis deals exclusively with cases of across-wind vibrations, leaving aside the more general situation where the wind and motion may not be normal. This can arise in many circumstances, such as in the motion of a power transmission cable about its equilibrium configuration that is swayed from the vertical plane as a result of the mean wind or in a tall slender structure in a skewed wind. Furthermore, the generalization to such situations, when this had been made, has only considered special issues. In this paper, the correct equations for the quasi-steady aerodynamic damping coefficients for a rotated system or wind are derived, and the differences from other variants are highlighted. Motion in two orthogonal structural planes is considered, potentially giving coupled translational galloping, for which previous analysis has often been limited or has even arrived at erroneous conclusions. For the two-degree-of-freedom case, the behavior is dependent on the structural as well as the aerodynamic parameters, in particular the orientation of the principal structural axes and the relative natural frequencies in the two planes. For the first time, the differences in the aerodynamic damping and zones of galloping instability are quantified between solutions from the correct perfectly tuned, well detuned, and classical Den Hartog equations (and also an incorrect generalization of the latter) for a variety of typical cross-sectional shapes. It is found that although the Den Hartog summation often gives a reasonable estimate for the actual aerodynamic damping, even in the rotated situation, in some circumstances the differences can be quite large.
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References
Alonso, G., Meseguer, J., and Pérez-Grande, I. (2005). “Galloping instabilities of two-dimensional triangular cross-section bodies.” Exp. Fluids, 38(6), 789–795.
Alonso, G., Valero, E., and Meseguer, J. (2009). “An analysis on the dependence on cross section geometry of galloping stability of two-dimensional bodies having either biconvex or rhomboidal cross sections.” Eur. J. Mech. B/Fluids, 28(2), 328–334.
Bearman, P., Gartshore, I., Maull, D., and Parkinson, G. (1987). “Experiments on flow-induced vibration of a square-section cylinder.” J. Fluids Struct., 1(1), 19–34.
Blevins, R. (1977). Flow-induced vibrations, 1st Ed., Van Nostrand, New York.
Blevins, R., and Iwan, W. (1974). “The galloping response of a two-degree-of-freedom system.” J. Appl. Mech., 41(4), 1113–1118.
Caracoglia, L. (2007). “Influence of weather conditions and eccentric aerodynamic loading on the large amplitude aeroelastic vibration of highway tubular poles.” Eng. Struct., 29(12), 3550–3566.
Carassale, L., Freda, A., and Piccardo, G. (2005). “Aeroelastic forces on yawed circular cylinders: Quasi-steady modeling and aerodynamic instability.” Wind Struct., 8(5), 373–388.
Davenport, A. (1966). “The treatment of wind loading on tall buildings.” Proc., Symp. on Tall Buildings, Pergamon, New York, 3–45.
Den Hartog, J. P. (1932). “Transmission line vibration due to sleet.” Trans. Am. Inst. Electr. Eng., 51(4), 1074–1086.
Den Hartog, J. P. (1947). Mechanical vibrations, 3rd Ed., McGraw Hill, New York.
Desai, Y., Shah, A., and Popplewell, N. (1990). “Galloping analysis for two-degree-of-freedom oscillatior.” J. Eng. Mech., 2583–2602.
Engineering Sciences Data Unit (ESDU). (2004). “Structural members: Mean fluid forces on members of various cross sections.” ESDU 82007, London.
Hémon, P., and Santi, F. (2002). “On the aeroelastic behaviour of rectangular cylinders in cross-flow.” J. Fluids Struct., 16(7), 855–889.
Holmes, J. (2001). Wind loading on structures, 1st Ed., Spon, New York.
Jones, K. (1992). “Coupled vertical and horizontal galloping.” J. Eng. Mech., 92–107.
Li, Q. S., Fang, J. Q., and Jeary, A. P. (1998). “Evaluation of 2D coupled galloping oscillations of slender structures.” Comput. Struct., 66(5), 513–523.
Liang, S., Li, Q., Li, G., and Qu, W. (1993). “An evaluation of the onset wind velocity for 2D coupled oscillations of tower buildings.” J. Wind Eng. Ind. Aerodyn., 50, 329–340.
Luo, S., Chew, Y., Lee, T., and Yazdani, M. (1998). “Stability to translational galloping vibration of cylinders at different mean angles of attack.” J. Sound Vib., 215(5), 1183–1194.
Luongo, A., and Piccardo, G. (2005). “Linear instability for coupled translational galloping.” J. Sound Vib., 288(4–5), 1027–1047.
Macdonald, J., Griffiths, P., and Curry, B. (2008). “Galloping analysis of stranded electricity conductors in skew winds.” Wind Struct., 11(4), 303–321.
Macdonald, J., and Larose, G. (2008a). “Two-degree-of-freedom inclined cable galloping—Part 1: General formulation and solution for perfectly tuned system.” J. Wind Eng. Ind. Aerodyn., 96(3), 291–307.
Macdonald, J., and Larose, G. (2008b). “Two-degree-of-freedom inclined cable galloping—Part 2: Analysis and prevention for arbitrary frequency ratio.” J. Wind Eng. Ind. Aerodyn., 96(3), 308–326.
McComber, P., and Paradis, A. (1998). “A cable galloping model for thin ice accretions.” Atmos. Res., 46(1–2), 13–25.
Nakamura, Y., and Hirata, K. (1964). “The aerodynamic mechanism of galloping.” Trans. Jpn. Soc. Aeronaut. Space Sci., 36(114), 257–269.
Nigol, O., and Buchan, P. (1981). “Conductor galloping part I—Den Hartog mechanism.” IEEE Trans. Power Appar. Syst., 100(2), 699–707.
Norberg, C. (1993). “Flow around rectangular cylinders: Pressure forces and wake frequencies.” J. Wind Eng. Ind. Aerodyn., 49(1–3), 187–196.
Richardson, A., and Martuccelli, J. (1965). Research study on galloping of electric power transmission lines, Vol. II, Her Majesty’s Stationary Office, London, 611–686.
Tatsuno, M., Takayama, T., Amamoto, A., and Koji, I. (1990). “On the stable posture of a triangular or a square cylinder about its central axis in a uniform flow.” Fluid Dyn. Res., 6(3-4), 201–207.
Wang, J., and Lilien, J. (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.
Weaver, D., and Veljkovic, I. (2005). “Vortex shedding and galloping of open semi-circular and parabolic cylinders in cross-flow.” J. Fluids Struct., 21(1), 65–74.
Yu, P., Desai, Y., Shah, A., and Popplewell, N. (1993). “Three-degree-of-freedom model for galloping. Part I: Formulation.” J. Eng. Mech., 2404–2425.
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© 2013 American Society of Civil Engineers.
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Received: Aug 24, 2011
Accepted: Jul 30, 2013
Discussion open until: Jul 30, 2013
Published online: Aug 1, 2013
Published in print: Apr 1, 2014
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