New Stochastic Theory for Bridge Stability in Turbulent Flow
Publication: Journal of Engineering Mechanics
Volume 119, Issue 1
Abstract
Theoretical explanation is provided on why turbulence in the wind flow can sometimes stabilize an essentially single‐degree‐of‐freedom motion of a flexible bridge. The theory is based on a new turbulence model, which has a finite mean‐square value and a versatile spectral shape, and is capable of matching closely a target spectrum. It is shown that, without turbulence, the onset of flutter instability is associated with a critical wind velocity and an eigenvector describing a combined critical structure‐fluid mode. This particular composition strikes a balance between the energy inflow from fluid to structure, and the energy outflow from structure to fluid, so that an undamped structural motion becomes sustainable. At the introduction of turbulence, the combined structure‐fluid mode is changed continuously and randomly, and the new energy flow balance, in the sense of statistical average, renders the stabilizing or destabilizing effect of turbulence possible. Numerical results are presented for the boundary of asymptotic sample stability for a bridge model undergoing a single‐degree‐of‐freedom torsional motion.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Béliveau, J.‐G., Vaicaitis, R., and Shinozuka, M. (1977). “Motion of suspension bridge subject to wind loads.” J. Struct. Div., ASCE, 103(6), 1189–1205.
2.
Bogoliubov, N. N., and Mitropolsky, Y. A. (1961). Asymptotic methods in the theory of non‐linear oscillations. Gordon & Breach, New York, N.Y.
3.
Bucher, C. G., and Lin, Y. K. (1988). “Stochastic stability of bridges considering coupled modes.” J. Engrg. Mech., ASCE, 114(12), 2055–2071.
4.
Bucher, C. G., and Lin, Y. K. (1989). “Stochastic stability of bridges considering coupled modes: II.” J. Engrg. Mech., ASCE, 115(2), 384+400.
5.
Dimentberg, M. F. (1988). Statistical dynamics of nonlinear and time‐varying systems. Res. Studies Press, Latchwork, England, U.K.
6.
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.
7.
Huston, D. R. (1986). “The effect of upstream gusting on the aeroelastic behavior of long suspended‐span bridges,” Ph.D. thesis, Princeton University, Princeton, N.J.
8.
Irwin, H. P. A. H., and Schuyler, G. D. (1978). “Wind effects on a full aeroelastic bridge model.” ASCE Spring Convention and Exhibit, Pittsburgh, Penn., Apr. 24–28.
9.
Itô, K. (1951). “On a formula concerning stochastic differentials.” Nagoya Math. J., Japan, 3, 55–65.
10.
Kozin, F. (1969). “A survey of stability of stochastic systems.” Automatica, 5, 95–112.
11.
Kozin, F., and Sugimoto, S. (1977). “Relations between sample and moment stability for linear stochastic differential equations.” Proc., Conf. Stochastic Differential Eqs., D. Mason, ed., Academic Press, New York, N.Y., 145–162.
12.
Lin, Y. K., and Ariaratnam, S. T. (1980). “Stability of bridge motion in turbulent winds.” J. Struct. Mech., ASCE, 8(1), 1–15.
13.
Sabzevari, A., and Scanlan, R. H. (1968). “Aerodynamic instability of suspension bridges.” J. Engrg. Mech. Div., ASCE, 94(2), 489–519.
14.
Scanlan, R. H. (1981). “State‐of‐the‐art methods for calculating flutter, vortex‐induced, and buffeting response of bridge structures.” Report No. FHWA/RD‐80/050, Fed. Highway Admin., Office of Res. and Dev., Struct. and Appl. Mech. Div., Washington, D.C., Apr.
15.
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.
16.
Scanlan, R. H., and Tomko, J. J. (1971). “Airfoil and bridge flutter derivatives.” J. Engrg. Mech. Div., ASCE, 97(6), 1717–1737.
17.
Simiu, E., and Scanlan, R. H. (1986). Wind effects on structures: An introduction to wind engineering. John Wiley and Sons, New York, N.Y.
18.
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.
19.
Stratonovich, R. L. (1967). Topics in the theory of random noises II. Gordon & Breach, New York, N.Y.
20.
von Kármán, T. (1948). “Progress in the statistical theory of turbulence.” Proc. Nat. Acad. Sci., Washington, D.C., 530–539.
21.
Wedig, W. V. (1989). “Analysis and simulation of nonlinear stochastic system” Nonlinear dynamics in engineering systems, W. Schiehlen, ed., Springer‐Verlag, Berlin, Germany, 337–344.
Information & Authors
Information
Published In
Copyright
Copyright © 1993 American Society of Civil Engineers.
History
Received: May 7, 1992
Published online: Jan 1, 1993
Published in print: Jan 1993
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.