Wind-Induced Buffeting Vibration of Long-Span Bridge Considering Geometric and Aerodynamic Nonlinearity Based on Reduced-Order Modeling
Publication: Journal of Structural Engineering
Volume 149, Issue 11
Abstract
Aeroelastic instability and buffeting are two wind-induced phenomena for long-span bridges. In the traditional method, aeroelastic instability and buffeting are analyzed separately. If geometric and aerodynamic nonlinearity are required, aeroelastic instability is normally calculated based on finite-element methods, and buffeting is carried out based on linearization of structural and aerodynamic nonlinearity. Then, the standard frequency-domain methods are utilized on the eigenvalue decomposition. However, for ultralong-span bridges, aerostatic deformation, aeroelasticity, and buffeting are strongly coupled. During buffeting, the bridge deck pitching will change both structural stiffness and aerodynamic loads; therefore, the nonlinearity should be included in the long-span bridge buffeting analysis. This paper establishes a reduced-order modeling procedure to simulate the wind-induced buffeting vibration for long-span bridges including the nonlinear aeroelasticity and buffeting force. First, the mode-based vibration formulas are derived to consider both structural and aerodynamic nonlinearity through polynomial expansion. Next, the numerically simulated turbulence is imported into the vibration governing equation, and the structural response can be calculated using the time-domain integration method.
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Data Availability Statement
All data, models, and code generated or used during the study appear in the published article.
Acknowledgments
The authors gratefully acknowledge the support of National Natural Science Foundation of China (52008314 and 52078383). Any opinions, findings and conclusions or recommendations are those of the authors and do not necessarily reflect the views of the aforementioned agencies.
References
Amman, O. H., T. von Kármán, and G. B. Woodruff. 1941. The failure of the Tacoma Narrows Bridge. Washington, DC: Federal Works Agency.
Arena, A., and W. Lacarbonara. 2012. “Nonlinear parametric modeling of suspension bridges under aeroelastic forces: Torsional divergence and flutter.” Nonlinear Dyn. 70 (4): 2487–2510. https://doi.org/10.1007/s11071-012-0636-3.
Barni, N., O. Øiseth, and C. Mannini. 2021. “Time-variant self-excited force model based on 2D rational function approximation.” J. Wind Eng. Ind. Aerodyn. 211 (Apr): 104523. https://doi.org/10.1016/j.jweia.2021.104523.
Borri, C., and C. Costa. 2004. “Quasi-steady analysis of a two-dimensional bridge deck element.” Comput. Struct. 82 (13–14): 993–1006. https://doi.org/10.1016/j.compstruc.2004.03.019.
Cao, S., Y. Tamura, N. Kikuchi, M. Saito, I. Nakayama, and Y. Matsuzaki. 2009. “Wind characteristics of a strong typhoon.” J. Wind Eng. Ind. Aerodyn. 97 (1): 11–21. https://doi.org/10.1016/j.jweia.2008.10.002.
Chen, X., M. Matsumoto, and A. Kareem. 2000. “Time domain flutter and buffeting response analysis of bridges.” J. Eng. Mech. 126 (1): 7–16. https://doi.org/10.1061/(ASCE)0733-9399(2000)126:1(7).
Cheng, J., J.-J. Jiang, R.-C. Xiao, and H.-F. Xiang. 2002. “Nonlinear aerostatic stability analysis of Jiang Yin Suspension Bridge.” Eng. Struct. 24 (6): 773–781. https://doi.org/10.1016/S0141-0296(02)00006-8.
Costa, C., C. Borri, O. Flamand, and G. Grillaud. 2007. “Time-domain buffeting simulations for wind–bridge interaction.” J. Wind Eng. Ind. Aerodyn. 95 (9–11): 991–1006. https://doi.org/10.1016/j.jweia.2007.01.026.
Cui, W., and L. Caracoglia. 2018a. “A fully-coupled generalized model for multi-directional wind loads on tall buildings: A development of the quasi-steady theory.” J. Fluids Struct. 78 (Apr): 52–68. https://doi.org/10.1016/j.jfluidstructs.2017.12.008.
Cui, W., and L. Caracoglia. 2018b. “A unified framework for performance-based wind engineering of tall buildings in hurricane-prone regions based on lifetime intervention-cost estimation.” Struct. Saf. 73 (Jul): 75–86. https://doi.org/10.1016/j.strusafe.2018.02.003.
Davenport, A. G. 1962. “Buffeting of a suspension bridge by storm winds.” J. Struct. Div. 88 (3): 233–270. https://doi.org/10.1061/JSDEAG.0000773.
Deodatis, G. 1996. “Simulation of ergodic multivariate stochastic processes.” J. Eng. Mech. 122 (8): 778–787. https://doi.org/10.1061/(ASCE)0733-9399(1996)122:8(778).
Diana, G., D. Rocchi, T. Argentini, and S. Muggiasca. 2010. “Aerodynamic instability of a bridge deck section model: Linear and nonlinear approach to force modeling.” J. Wind Eng. Ind. Aerodyn. 98 (6–7): 363–374. https://doi.org/10.1016/j.jweia.2010.01.003.
Gao, G., L. Zhu, W. Han, and J. Li. 2018. “Nonlinear post-flutter behavior and self-excited force model of a twin-side-girder bridge deck.” J. Wind Eng. Ind. Aerodyn. 177 (Jun): 227–241. https://doi.org/10.1016/j.jweia.2017.12.007.
Gao, G., L. Zhu, J. Li, and W. Han. 2020. “Application of a new empirical model of nonlinear self-excited force to torsional vortex-induced vibration and nonlinear flutter of bluff bridge sections.” J. Wind Eng. Ind. Aerodyn. 205 (Oct): 104313. https://doi.org/10.1016/j.jweia.2020.104313.
Ge, Y., J. Xia, L. Zhao, and S. Zhao. 2018. “Full aeroelastic model testing for examining wind-induced vibration of a 5,000 m spanned suspension bridge.” Front. Built Environ. 4 (Apr): 20. https://doi.org/10.3389/fbuil.2018.00020.
Hollkamp, J. J., R. W. Gordon, and S. M. Spottswood. 2005. “Nonlinear modal models for sonic fatigue response prediction: A comparison of methods.” J. Sound Vib. 284 (3–5): 1145–1163. https://doi.org/10.1016/j.jsv.2004.08.036.
Jones, N. P., and R. H. Scanlan. 2001. “Theory and full-bridge modeling of wind response of cable-supported bridges.” J. Bridge Eng. 6 (6): 365–375. https://doi.org/10.1061/(ASCE)1084-0702(2001)6:6(365).
Kaps, P., and P. Rentrop. 1979. “Generalized runge-kutta methods of order four with stepsize control for stiff ordinary differential equations.” Numer. Math. 33 (1): 55–68. https://doi.org/10.1007/BF01396495.
Ko, J., S. Xue, and Y. Xu. 1998. “Modal analysis of suspension bridge deck units in erection stage.” Eng. Struct. 20 (12): 1102–1112. https://doi.org/10.1016/S0141-0296(97)00207-1.
Leahu-Aluas, I., and F. Abed-Meraim. 2011. “A proposed set of popular limit-point buckling benchmark problems.” Struct. Eng. Mech. 38 (6): 767–802. https://doi.org/10.12989/sem.2011.38.6.767.
Li, K., Y. Han, C. Cai, P. Hu, and C. Li. 2021. “Experimental investigation on post-flutter characteristics of a typical steel-truss suspension bridge deck.” J. Wind Eng. Ind. Aerodyn. 216 (Sep): 104724. https://doi.org/10.1016/j.jweia.2021.104724.
Liu, S., L. Zhao, G. Fang, C. Hu, and Y. Ge. 2022. “Nonlinear aerodynamic characteristics and modeling of a quasi-flat plate at torsional vibration: Effects of angle of attack and vibration amplitude.” Nonlinear Dyn. 107 (Feb): 1–25.
Mignolet, M. P., A. Przekop, S. A. Rizzi, and S. M. Spottswood. 2013. “A review of indirect/non-intrusive reduced order modeling of nonlinear geometric structures.” J. Sound Vib. 332 (10): 2437–2460. https://doi.org/10.1016/j.jsv.2012.10.017.
Muravyov, A. A., and S. A. Rizzi. 2003. “Determination of nonlinear stiffness with application to random vibration of geometrically nonlinear structures.” Comput. Struct. 81 (15): 1513–1523. https://doi.org/10.1016/S0045-7949(03)00145-7.
Przekop, A., M. S. Azzouz, X. Guo, C. Mei, and L. Azrar. 2004. “Finite element multiple-mode approach to nonlinear free vibrations of shallow shells.” AIAA J. 42 (11): 2373–2381. https://doi.org/10.2514/1.483.
Shinozuka, M. 1974. “Digital simulation of random processes in engineering mechanics with the aid of FFT technique (fast Fourier transformation).” In Stochastic problems in mechanics, 277–286. Berlin: Springer.
Strogatz, S. H. 2018. Nonlinear dynamics and chaos: With applications to physics, biology, chemistry, and engineering. Boca Raton, FL: CRC Press.
Vickery, P. J., F. J. Masters, M. D. Powell, and D. Wadhera. 2009. “Hurricane hazard modeling: The past, present, and future.” J. Wind Eng. Ind. Aerodyn. 97 (7): 392–405. https://doi.org/10.1016/j.jweia.2009.05.005.
Wang, H., T. Wu, T. Tao, A. Li, and A. Kareem. 2016. “Measurements and analysis of non-stationary wind characteristics at Sutong Bridge in Typhoon Damrey.” J. Wind Eng. Ind. Aerodyn. 151 (Apr): 100–106. https://doi.org/10.1016/j.jweia.2016.02.001.
Wang, J., S. Cao, W. Pang, and J. Cao. 2017. “Experimental study on effects of ground roughness on flow characteristics of tornado-like vortices.” Bound.-Layer Meteorol. 162 (2): 319–339. https://doi.org/10.1007/s10546-016-0201-6.
Wu, B., X. Chen, Q. Wang, H. Liao, and J. Dong. 2020. “Characterization of vibration amplitude of nonlinear bridge flutter from section model test to full bridge estimation.” J. Wind Eng. Ind. Aerodyn. 197 (Feb): 104048. https://doi.org/10.1016/j.jweia.2019.104048.
Xia, J., K. Li, and Y. Ge. 2021. “Wind tunnel testing and frequency domain buffeting analysis of a 5000 m suspension bridge.” Adv. Struct. Eng. 24 (7): 1326–1342. https://doi.org/10.1177/1369433220975568.
Xiang, H., and Y. Ge. 2002. “Refinements on aerodynamic stability analysis of super long-span bridges.” J. Wind Eng. Ind. Aerodyn. 90 (12–15): 1493–1515. https://doi.org/10.1016/S0167-6105(02)00266-0.
Zhang, M., F. Xu, Z. Zhang, and X. Ying. 2019. “Energy budget analysis and engineering modeling of post-flutter limit cycle oscillation of a bridge deck.” J. Wind Eng. Ind. Aerodyn. 188 (May): 410–420. https://doi.org/10.1016/j.jweia.2019.03.010.
Zhang, R., Z. Liu, L. Wang, and Z. Chen. 2021. “A practical method for predicting post-flutter behavior of a rectangular section.” J. Wind Eng. Ind. Aerodyn. 216 (Sep): 104707. https://doi.org/10.1016/j.jweia.2021.104707.
Zhao, L., W. Cui, and Y. Ge. 2019. “Measurement, modeling and simulation of wind turbulence in typhoon outer region.” J. Wind Eng. Ind. Aerodyn. 195 (Dec): 104021. https://doi.org/10.1016/j.jweia.2019.104021.
Zhao, L., T. Ma, W. Cui, and Y. Ge. 2023. “Finite element based study on aerostatic post-buckling and multi-stability of long-span bridges.” Struct. Infrastruct. Eng. (Jan): 1–15. https://doi.org/10.1080/15732479.2022.2164596.
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Published In
Journal of Structural Engineering
Volume 149 • Issue 11 • November 2023
Copyright
© 2023 American Society of Civil Engineers.
History
Received: Apr 5, 2022
Accepted: Jun 23, 2023
Published online: Sep 14, 2023
Published in print: Nov 1, 2023
Discussion open until: Feb 14, 2024
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