New Stochastic Theory for Bridge Stability in Turbulent Flow. II
Publication: Journal of Engineering Mechanics
Volume 121, Issue 1
Abstract
Motion stability of a long-span bridge in turbulent wind is studied. The bridge motion is represented by a torsional mode and a bending mode, and the new wind turbulence model proposed in an earlier paper is used in the analysis. This turbulence model is capable of matching closely a target spectral density, such as the well-known von-Kármán or Dryden spectrum. It is shown that the presence of turbulence changes the combined structure-fluid critical mode and results in a new energy balance. The asymptotic behavior of the combined structure-fluid system is determined by the largest Lyapunov exponent, and the motion is asymptotically stable if the largest Lyapunov exponent is negative. In this sense, the turbulence has a stabilizing or a destabilizing effect, depending on whether it increases or decreases the critical mean wind velocity at which the largest Lyapunov exponent vanishes. For a particular bridge model investigated, it is found that the peak location of the spectral density of the turbulence is crucial to the stability condition. By changing the peak location of the spectrum, a stabilizing turbulence can become destabilizing, even when the mean-square value remains the same.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Bogoliubov, N. N., and Mitropolsky, Y. A. (1961). Asymptotic methods in the theory of non-linear oscillations . Gordon & Breach, New York, N.Y.
2.
Bucher, C. G., and Lin, Y. K.(1988). “Stochastic stability of bridges considering coupled modes.”J. Engrg. Mech., ASCE, 114(12), 2055–2071.
3.
Bucher, C. G., and Lin, Y. K.(1989a). “Stochastic stability of bridges considering coupled modes: II.”J. Engrg. Mech., ASCE, 115(2), 384–400.
4.
Bucher, C. G., and Lin, Y. K.(1989b). “Effect of spanwise correlation of turbulence field on the motion stability of long-span bridges.”J. Fluids and Struct., 2, 237–251.
5.
Dryden, H. L. (1961). “A review of the statistical theory of turbulence.”Turbulence, S. K. Friedlander and L. Topper, eds., Interscience, New York, N.Y., 115–150.
6.
Itô, K.(1951a). “On stochastic differential equations.”Memoirs of Am. Math. Soc., 4, 289–302.
7.
Itô, K.(1951b). “On a formula concerning stochastic differentials.”Nagoya Math. J., 4, 55–65.
8.
Khaz'minskii, R. Z.(1966). “A limit theorem for the solution of differential equations with random right hand sides.”Theory of probability and applications, 11, 340–406.
9.
Kozin, F.(1969). “A survey of stability of stochastic systems.”Automatica, 5, 95–112.
10.
Lin, Y. K. (1967). Probabilistic theory of structural dynamics, McGraw-Hill, New York, N.Y., reprinted by Krieger Publishing Co., Melbourne, Fla.
11.
Lin, Y. K., and Ariaratnam, S. T.(1980). “Stability of bridge motion in turbulent winds.”J. Struct. Mech., 8, 1–15.
12.
Lin, Y. K., and Li, Q. C.(1993). “New stochastic theory for bridge stability in turbulent flow.”J. Engrg. Mech., ASCE, 119(1), 113–127.
13.
Scanlan, R. H., and Tomko, J. J.(1971). “Airfoil and bridge flutter derivatives.”J. Engrg. Mech. Div., ASCE, 97(6), 1717–1737.
14.
Scanlan, R. H., Béliveau, J. G., and Budlong, K. S.(1974). “Indicial aerodynamic functions for bridge decks.”J. Engrg. Mech. Div., ASCE, 100(4), 657–672.
15.
Sri Namachchivaya, N., and Lin, Y. K.(1988). “Application of stochastic averaging for nonlinear systems with high damping.”Probabilistic Engrg. Mech., 3(3), 159–167.
16.
Stratonovich, R. L. (1967). Topics in the theory of random noise I & II, R. L. Silverman, translator, Gordon and Breach, New York, N.Y.
17.
von Kármán, T. (1948). “Progress in the statistical theory of turbulence.”Proc., Nat. Acad. Sci., National Academy of Science, Washington, D.C., 530–539.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 121 • Issue 1 • January 1995
Pages: 102 - 116
Copyright
Copyright © 1995 American Society of Civil Engineers.
History
Published online: Jan 1, 1995
Published in print: Jan 1995
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.