Galloping Analysis for Two‐Degree‐of‐Freedom Oscillator
Publication: Journal of Engineering Mechanics
Volume 116, Issue 12
Abstract
A comprehensive analysis is presented for the galloping of an oscillator that may vibrate both transversely and torsionally. Explicit solutions are given for the conditions needed to initiate galloping and also for the ensuing nonlinear periodic responses. Internal resonance as well as previously considered nonresonance responses are treated consistently by employing an averaging method. The usefulness and advantages of the analytical formulation are demonstrated by using square prismatic and bluff structural angle sections. Analytical predictions are verified by their close agreement with numerically integrated data from the original equations of motion. A variety of responses is shown to be possible for certain parameters. Moreover, it is demonstrated that the twist can be instrumental to galloping in plunge.
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References
1.
Bathe, K. J. (1982). Finite element procedures in engineering analysis. Prentice‐Hall, Inc., Englewood Cliffs, N.J.
2.
Blevins, R. D., and Iwan, W. D. (1974). “The galloping response of a two‐degree‐of‐freedom system.” J. Appl. Mech., 41, 1113–1118.
3.
Bogoliubov, N. N., and Mitropolsky, Y. A. (1961). Asymptotic methods in the theory of non‐linear oscillations. Hindustan Publishing Corp., Delhi, India.
4.
Chen, G. (1987). “Applications of a generalized Galerkin's method to non‐linear oscillations of two‐degree‐of‐freedom systems.” J. Sound Vibrations, 119(2), 225–242.
5.
Desai, Y. M., et al. (1989a). “Static and dynamic behaviour of mechanical components associated with electrical transmission lines—III: Part A: Theoretical perspective.” Shock Vib. Dig., 21(12), 3–8.
6.
Desai, Y. M., Popplewell, N., and Shah, A. H. (1989b). “Equivalence of Krylov‐Bogoliubov, Galerkin and Ritz methods for periodic autonomous systems.” Report No. ER. 89–25.100, Dept. of Mechanical Engineering, The University of Manitoba, Winnipeg, Canada.
7.
Edwards, A. T., and Madeyski, A. (1956). “Progress report on the investigation of galloping of transmission line conductors.” Transactions AIEE, 75, 666–686.
8.
Gilchrist, A. O. (1961). “The free oscillations of conservative quasilinear systems with two degrees of freedom.” Int. J. Mech. Sci., 3, 286–311.
9.
Gortemaker, P. C. M. (1984). “Galloping conductors and evaluation of the effectiveness of inspan dampers.” Kema Science and Technical Reports, Arnhem, Netherlands, 2(4), 27–39.
10.
Hagedorn, P. (1982). Non‐linear oscillations. Clarendon Press, Oxford, U.K.
11.
Klotter, K. (1952). “Non‐linear vibration problems treated by the averaging method of W. Ritz.” Proc. 1st U.S. National Cong. Applied Mech., American Society of Mechanical Engineers, New York, N.Y., 125–131.
12.
Lee, J. C. (1987). “Suppression of transmission line galloping by support compliance design,” thesis presented to the Dept. of Mechanical Engineering, Tulane University, at New Orleans, La., in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
13.
Leipholz, H. (1977). Direct variational methods and eigenvalue problems in engineering. Noordhoff International Publishing, Leyden, Netherlands.
14.
Liska, F., and Wright, S. (1979). “Computer programs for calculation of limit cycle amplitude of a two‐dimensional conductor model based on non‐linear aerodynamic coefficients.” Ontario Hydro Research Div. Report No. 79‐96‐K, Ontario Hydro., Toronto, Canada.
15.
Myerscough, C. J. (1973). “A simple model of the growth of wind‐induced oscillations in overhead lines.” J. Sound Vibrations, 28(4), 699–713.
16.
Nayfeh, A. H. (1981). “Introduction to perturbation techniques.” John Wiley and Sons, New York, N.Y.
17.
Novak, M. (1972). “Galloping oscillations of prismatic structures.” J. Engrg. Mech. Div., ASCE, 88(1), 27–45.
18.
Parkinson, G. V., and Brooks, N. P. H. (1961). “On the aeroelastic instability of bluff cylinders.” J. Appl. Mech., 83(Series E), 252–258.
19.
Parkinson, G. V., and Smith, J. D. (1964). “The square prism as an aeroelastic nonlinear oscillator.” Q. J. Mech. Appl. Math., 17(Pt. 2), 225–239.
20.
Richardson, A. S., Jr. (1981). “Dynamic analysis of lightly iced conductor galloping in two degrees of freedom.” Proc., IEE, Pt. C, 128(4), 211–218.
21.
Richardson, A. S., Jr. (1988). “Bluff body aerodynamics.” J. Struct. Engrg., ASCE, 112(7), 1723–1726.
22.
Rosenberg, R. M. (1962). “The normal modes of nonlinear n‐degree‐of‐freedom systems.” J. Appl. Mech., 84(Series E), 7–14.
23.
Sethna, P. R. (1963). “Transients in certain autonomous multiple‐degree‐of‐freedom nonlinear vibrating systems.” J. Appl. Mech., 85(Series E), 44–50.
24.
Slater, J. E. (1959). “Aeroelastic instability of a structural angle section,” thesis presented to the Dept. of Mechanical Engineering, University of British Columbia, at Vancouver, Canada, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
25.
Van der Burgh, A. H. P. (1984). “Simple aeroelastic oscillator as a model for conductor galloping.” Report No. 84‐17, Dept. of Mathematics and Informatics, Technical University of Delft, Delft, Netherlands.
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Published In
Journal of Engineering Mechanics
Volume 116 • Issue 12 • December 1990
Pages: 2583 - 2602
Copyright
Copyright © 1990 ASCE.
History
Published online: Dec 1, 1990
Published in print: Dec 1990
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