Postflutter Analysis of Bridge Decks Using Aerodynamic-Describing Functions
Publication: Journal of Bridge Engineering
Volume 25, Issue 8
Abstract
An aerodynamic describing function (ADF)-based model for simulating the nonlinear self-excited forces on bridge decks is developed, where the ADFs can be conveniently identified using the experimentally or numerically obtained free or forced vibration data. An efficient calculation procedure based on the ADFs is accordingly established to predict the nonlinear flutter state and/or postflutter limit cycle oscillations (LCOs). Two numerical examples are utilized to demonstrate the simulation accuracy and efficiency of nonlinear bridge flutter with the proposed ADF-based model. The capabilities of the ADF-based model in capturing typical features of nonlinear postflutter vibration such as LCO and a hysteresis phenomenon are demonstrated. A nondimensional postflutter index is designed to quantitatively assess the postflutter performance of bridge decks. Finally, the effects of structural dynamics and aerodynamic properties (e.g., structural damping ratios, natural frequencies, and aerodynamic derivatives) on the postflutter behavior of a bridge deck are examined in terms of the wind speed extension after the critical state with acceptable postcritical vibrations and the proposed postflutter index.
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Acknowledgments
The research is jointly supported by the National Science Foundation of China (51678115 and 51978130), which are gratefully acknowledged.
References
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.
Barrero-Gil, A., A. Sanz-Andrés, and G. Alonso. 2009. “Hysteresis in transverse galloping: The role of the inflection points.” J. Fluids Struct. 25 (6): 1007–1020. https://doi.org/10.1016/j.jfluidstructs.2009.04.008.
Carassale, L., T. Wu, and A. Kareem. 2014. “Nonlinear aerodynamic and aeroelastic analysis of bridges: Frequency domain approach.” J. Eng. Mech. 140 (8): 04014051. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000737.
Casalotti, A., A. Arena, and W. Lacarbonara. 2014. “Mitigation of postflutter oscillations in suspension bridges by hysteretic tuned mass dampers.” Eng. Struct. 69: 62–71. https://doi.org/10.1016/j.engstruct.2014.03.001.
Chen, X. 2007. “Improved understanding of bimodal coupled bridge flutter based on closed-form solutions.” J. Struct. Eng. 133 (1): 22–31. https://doi.org/10.1061/(ASCE)0733-9445(2007)133:1(22).
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: 227–241. https://doi.org/10.1016/j.jweia.2017.12.007.
Gelb, A., and W. E. Vander Velde. 1968. Multiple-input describing functions and nonlinear system design. New York: McGraw-Hill.
He, S., Z. Yang, and Y. Gu. 2014. “Transonic limit cycle oscillation analysis using aerodynamic describing functions and superposition principle.” AIAA J. 52 (7): 1393–1403. https://doi.org/10.2514/1.J052559.
Huang, N. E., Z. Wu, S. R. Long, K. C. Arnold, X. Chen, and K. Blank. 2009. “On instantaneous frequency.” Adv. Adapt. Data Anal. 1 (2): 177–229. https://doi.org/10.1142/S1793536909000096.
Katsuchi, H., H. Yamada, M. Nishio, and Y. Okazaki. 2016. “Improvement of aerodynamic stability of suspension bridges with H-shaped simplified stiffening girder.” Front. Struct. Civ. Eng. 10 (1): 93–102. https://doi.org/10.1007/s11709-015-0311-0.
Král, R., S. Pospíšil, and J. Náprstek. 2014. “Wind tunnel experiments on unstable self-excited vibration of sectional girders.” J. Fluids Struct. 44: 235–250. https://doi.org/10.1016/j.jfluidstructs.2013.11.002.
Kryloff, N., and N. Bogoliuboff. 1947. Introduction to nonlinear mechanics Translated by S. Lefschetz. Annals of Mathematics Study. Princeton, NJ: Princeton University Press.
Ma, C. M., Y. Z. Liu, Q. S. Li, and H. L. Liao. 2018. “Prediction and explanation of the aeroelastic behavior of a square-section cylinder via forced vibration.” J. Wind Eng. Ind. Aerodyn. 176: 78–86. https://doi.org/10.1016/j.jweia.2018.03.007.
Marra, A. M., C. Mannini, and G. Bartoli. 2015. “Measurements and improved model of vortex-induced vibration for an elongated rectangular cylinder.” J. Wind Eng. Ind. Aerodyn. 147: 358–367. https://doi.org/10.1016/j.jweia.2015.08.007.
Matsumoto, M., K. Okubo, Y. Ito, H. Matsumiya, and G. Kim. 2008. “The complex branch characteristics of coupled flutter.” J. Wind Eng. Ind. Aerodyn. 96 (10–11): 1843–1855. https://doi.org/10.1016/j.jweia.2008.02.011.
Menter, F. R. 1994. “Two-equation eddy-viscosity turbulence models for engineering applications.” AIAA J. 32 (8): 1598–1605. https://doi.org/10.2514/3.12149.
Náprstek, J., S. Pospís˘il, and S. Hrac˘ov. 2007. “Analytical and experimental modelling of non-linear aeroelastic effects on prismatic bodies.” J. Wind Eng. Ind. Aerodyn. 95 (9−11): 1315–1328. https://doi.org/10.1016/j.jweia.2007.02.022.
Noda, M., H. Utsunomiya, F. Nagao, M. Kanda, and N. Shiraishi. 2003. “Effects of oscillation amplitude on aerodynamic derivatives.” J. Wind Eng. Ind. Aerodyn. 91 (1−2): 101–111. https://doi.org/10.1016/S0167-6105(02)00338-0.
Peyton Jones, J. C., and S. A. Billings. 1991. “Describing functions, Volterra series, and the analysis of non-linear systems in the frequency domain.” Int. J. Control 53 (4): 871–887. https://doi.org/10.1080/00207179108953654.
Price, S. J., H. Alighanbari, and B. H. K. Lee. 1995. “The aeroelastic response of a two-dimensional airfoil with bilinear and cubic structural nonlinearities.” J. Fluid. Struct. 9 (2): 175–193. https://doi.org/10.1006/jfls.1995.1009.
Scanlan, R. H., and J. J. Tomko. 1971. “Airfoil and bridge deck flutter derivatives.” J. Eng. Mech. 97 (6): 1717–1737.
Selberg, A. 1957. Aerodynamic effects on suspension bridges. Zurich, Switzerland: IABSE.
Ueda, T., and E. H. Dowell. 1984. “Flutter analysis using nonlinear aerodynamic forces.” J. Aircr. 21 (2): 101–109. https://doi.org/10.2514/3.48232.
van Rooij, A. C. L. M., J. Nitzsche, and R. P. Dwight. 2017. “Prediction of aeroelastic limit cycle oscillations based on harmonic forced-motion oscillations.” AIAA J. 55 (10): 1–13. https://doi.org/10.2514/1.J055852.
Wu, T., and A. Kareem. 2013a. “A nonlinear convolution scheme to simulate bridge aerodynamics.” Comput. Struct. 128: 59–271. https://doi.org/10.1016/j.compstruc.2013.06.004.
Wu, T., and A. Kareem. 2013b. “Aerodynamics and aeroelasticity of cable-supported bridges: Identification of nonlinear features.” J. Eng. Mech. 139 (12): 1886–1893. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000615.
Wu, T., and A. Kareem. 2014. “Simulation of nonlinear bridge aerodynamics: A sparse third-order Volterra model.” J. Sound Vib. 333 (1): 178–188. https://doi.org/10.1016/j.jsv.2013.09.003.
Wu, T., A. Kareem, and Y. Ge. 2013. “Linear and nonlinear aeroelastic analysis frameworks for cable-supported bridges.” Nonlinear Dyn. 74 (3): 487–516. https://doi.org/10.1007/s11071-013-0984-7.
Xu, F., T. Wu, X. Ying, and A. Kareem. 2016a. “Higher-order self-excited drag forces on bridge decks.” J. Eng. Mech. 142 (3): 06015007. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001036.
Xu, F., X. Ying, and Z. Zhang. 2016b. “Effects of exponentially modified sinusoidal oscillation and amplitude on bridge deck flutter derivatives.” J. Bridge Eng. 21 (5): 06016001. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000884.
Xu, F., and Z. Zhang. 2017. “Free vibration numerical simulation technique for extracting flutter derivatives of bridge decks.” J. Wind Eng. Ind. Aerodyn. 170: 226–237. https://doi.org/10.1016/j.jweia.2017.08.018.
Xu, F. Y., X. Y. Ying, and Z. Zhang. 2014. “Three-degree-of-freedom coupled numerical technique for extracting 18 aerodynamic derivatives of bridge decks.” J. Struct. Eng. 140 (11): 04014085. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001009.
Yang, Y., T. Wu, Y. Ge, and A. Kareem. 2015. “Aerodynamic stabilization mechanism of a twin box girder with various slot widths.” J. Bridge Eng. 20 (3): 04014067. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000645.
Ying, X., F. Xu, M. Zhang, and Z. Zhang. 2017. “Numerical explorations of the limit cycle flutter characteristics of a bridge deck.” J. Wind Eng. Ind. Aerodyn. 169: 30–38. https://doi.org/10.1016/j.jweia.2017.06.020.
Zhang, M., and F. Xu. 2018. “Nonlinear vibration characteristics of bridge deck section models in still air.” J. Bridge Eng. 23 (9): 04018059. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001263.
Zhang, M., F. Xu, and X. Ying. 2017. “Experimental investigations on the nonlinear torsional flutter of a bridge deck.” J. Bridge Eng. 22 (8): 04017048. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001082.
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: 410–420. https://doi.org/10.1016/j.jweia.2019.03.010.
Zhang, W., Y. Jiang, and Z. Ye. 2007. “Two better loosely coupled solution algorithms of CFD based aeroelastic simulation.” Eng. Appl. Comput. Fluid Mech. 1 (4): 253–262. https://doi.org/10.1080/19942060.2007.11015197.
Zhang, Z. 2018. “Multistage indicial functions and postflutter simulation of long-span bridges.” J. Bridge Eng. 23 (4): 04018010. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001218.
Zhou, R., Y. Ge, Y. Yang, Y. Du, S. Liu, and L. Zhang. 2019. “Nonlinear behaviors of the flutter occurrences for a twin-box girder bridge with passive countermeasures.” J. Sound Vib. 447: 221–235. https://doi.org/10.1016/j.jsv.2019.02.002.
Zhu, J., S. Zheng, Y. Tang, and J. Guo. 2018. “A study on the nonlinear flutter amplitude characteristics of a streamlined box girder section.” J. Vib. Shock 37 (24): 158–165. https://doi.org/10.13465/j.cnki.jvs.2018.24.024.
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© 2020 American Society of Civil Engineers.
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Received: Jun 4, 2019
Accepted: Mar 13, 2020
Published online: May 27, 2020
Published in print: Aug 1, 2020
Discussion open until: Oct 27, 2020
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