Nonlinear Aerodynamic and Aeroelastic Analysis of Bridges: Frequency Domain Approach
Publication: Journal of Engineering Mechanics
Volume 140, Issue 8
Abstract
A frequency domain approach for nonlinear bridge aerodynamics and aeroelasticity, based on the Volterra series expansion, is introduced in this paper. The Volterra frequency-response functions and the associated linear equations are formulated utilizing a topological assemblage scheme and are identified utilizing an existing full-time-domain nonlinear bridge aerodynamics and aeroelasticity analysis framework. A two-dimensional sectional model of a long-span bridge is used to illustrate this approach. The results show a good comparison between the time-domain simulation and the proposed frequency-domain model. The availability of Volterra frequency-response functions enables gaining a qualitative insight into nonlinear bridge aerodynamics and aeroelasticity.
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Acknowledgments
The support of this project was made possible by National Science Foundation grant No. CMMI 09 28282.
References
Alper, P. (1965). “A consideration of discrete Volterra series.” IEEE Trans. Automat. Contr., 9(7), 322–327.
Boyd, S. P., and Chua, L. O. (1985). “Fading memory and the problem of approximating nonlinear operators with Volterra series.” IEEE Trans. Circ. Syst., 32(11), 1150–1161.
Carassale, L., and Kareem, A. (2010). “Modeling nonlinear systems by Volterra series.” J. Eng. Mech., 801–818.
Carassale, L., and Kareem, A. (2012). “Synthesis of multi-input Volterra systems by a topological assemblage scheme.” Proc., Int. Conf. on Structural Nonlinear Dynamics and Diagnosis, EDP Sciences, Les Ulis, France, 10012.
Chen, X., and Kareem, A. (2003). “Aeroelastic analysis of bridges: Effects of turbulence and aerodynamic nonlinearities.” J. Eng. Mech., 885–895.
Davenport, A. G. (1962). “Buffeting of a suspension bridge by storm winds.” J. Struct. Div., 88(3), 233–264.
Diana, G., et al. (1995). “Comparisons between wind tunnel tests on a full aeroelastic model of the proposed bridge over Stretto di Messina and numerical results.” J. Wind Eng. Ind. Aerodyn., 54–55, 101–113.
Diana, G., Bruni, S., Cigada, A., and Collina, A. (1993). “Turbulence effect on flutter velocity in long span suspended bridges.” J. Wind Eng. Ind. Aerodyn., 48(2–3), 329–342.
Donley, M. G., and Spanos, P. D. (1990). Dynamic analysis of nonlinear structures by the method of statistical quadratization, Springer, New York.
Ewen, E. J., and Weiner, D. D. (1980). “Identification of weakly non-linear systems using input and output measurements.” IEEE Trans. Circ. Syst., 27(12), 1255–1261.
Gurley, K. R., Tognarelli, M. A., and Kareem, A. (1997). “Analysis and simulation tools for wind engineering.” Probab. Eng. Mech., 12(1), 9–31.
Li, Y. and Kareem, A. (1990). “Stochastic response of a tension leg platform to wind and wave fields.” J. Wind Eng. Ind. Aerodyn., 36(12), 915–920.
Lucia, D. J., Beran, P. S., and Silva, W. A. (2004). “Reduced-order modeling: New approaches for computational physics.” Prog. Aerosp. Sci., 40(1−2), 51–117.
Næss, A. (1985). “Statistical analysis of second-order response of marine structures.” J. Ship Res., 29(4), 270–284.
Rugh, W. J. (1981). Nonlinear system theory, John Hopkins University Press, Baltimore, MA.
Scanlan, R. H., and Tomko, J. J. (1971). “Airfoil and bridge deck flutter derivatives.” J. Engrg. Mech. Div., 97(6), 1717–1737.
Schetzen, M. (1980). The Volterra and Wiener theories of nonlinear systems, Wiley, New York.
Sears, W. R. (1941). “Some aspects of non-stationary airfoil theory and its practical application.” J. Aeronaut. Sci., 8(3), 104–108.
Silva, W. A. (1997). “Discrete-time linear and nonlinear aerodynamic impulse responses for efficient CFD analyses.” Ph.D. thesis, College of William & Mary, Williamsburg, VA.
Silva, W. A. (2005). “Identification of non-linear aeroelastic systems based on the Volterra theory: Progress and opportunities.” Nonlinear Dyn., 39(1−2), 25–62.
Silva, W. A., et al. (2001). “Reduced-order modeling: Cooperative research and development at the NASA Langley Research Center.” Proc., Int. Forum on Aeroelasticity and Structural Dynamics, American Institute of Aeronautics and Astronautics (AIAA), Reno, NV, 159–174.
Tognarelli, M. A., Zhao, J., and Kareem, A. (1997). “Equivalent statistical cubicization for system and forcing nonlinearities.” J. Eng. Mech., 890–893.
Volterra, V. (1959). Theory of functionals and of integral and integro-differential equations, Dover Publications, Mineola, NY.
Wiener, N. (1942). “Response of a non-linear device to noise.” Rep. V-16S, No. 129, MIT Radiation Laboratory, Cambridge, MA.
Winterstein, S. R., Ude, T. C., and Marthinsen, T. (1994). “Volterra models of ocean structures: Extreme and fatigue reliability.” J. Eng. Mech., 1369–1385.
Wu, T., and Kareem, A. (2011). “Modeling hysteretic nonlinear behavior of bridge aerodynamics via cellular automata nested neural network.” J. Wind Eng. Ind. Aerodyn., 99(4), 378–388.
Wu, T., and Kareem, A. (2012a). “Bridge aerodynamics and aeroelasticity: A comparison of modeling schemes.” J. Fluids Struct., 43(November), 347–370.
Wu, T., and Kareem, A. (2012b). “Modelling of nonlinear bridge aerodynamics and aeroelasticity: A convolution based approach.” Proc., Int. Conf. on Structural Nonlinear Dynamics and Diagnosis, EDP Sciences, Les Ulis, France, 03004.
Wu, T., and Kareem, A. (2013a). “Simulation of nonlinear bridge aerodynamics: A sparse third-order Volterra model.” J. Sound Vib., 333(1), 178–188.
Wu, T., and Kareem, A. (2013b). “Vortex-induced vibration of bridge decks: Volterra series-based model.” J. Eng. Mech., 1831–1843.
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Published In
Journal of Engineering Mechanics
Volume 140 • Issue 8 • August 2014
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Jun 15, 2013
Accepted: Oct 18, 2013
Published online: Oct 21, 2013
Discussion open until: Jul 7, 2014
Published in print: Aug 1, 2014
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