Effects of Vertical Motion on Nonlinear Flutter of a Bridge Girder
Publication: Journal of Bridge Engineering
Volume 25, Issue 11
Abstract
This study addresses the effects of vertical motion on the nonlinear flutter response of a double-deck truss girder based on section model wind tunnel tests. Six dynamic systems with the same bridge deck section were tested under various wind angles of attack. The nonlinear flutter characteristics under different cases were fully captured. The potential effect of vertical motion on coupled nonlinear flutter was investigated by conducting an additional single-degree-of-freedom wind tunnel test. The aeroelastic mechanism concerning the vertical motion that affects the nonlinear flutter performance is revealed by qualitatively estimating the contribution of coupled aerodynamic damping to the total damping. Results showed that vertical motion introduces noticeable negative damping to the system thus increases vibration amplitude and reduced onset wind speed at lower wind angles of attack, while the vertical motion will be less important at large wind angles of attack since its contribution to the total damping is relatively small. Finally, a preliminary method is proposed to identify nonlinear aerodynamic damping, which helps to understand the participation of vertical motion on coupled nonlinear flutter and to interpret the amplitude dependence of nonlinear flutter.
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Acknowledgments
The supports for this work provided in part by the National Natural Science Foundation of China (Grant Nos. 51778547, 51678508, 51378442, and 51308478) are greatly acknowledged. The author would like to thank Prof. Xinzhong Chen from Texas Tech University for his supervising during the research on nonlinear flutter of bridges.
References
Amandolese, X., S. Michelin, and M. Choquel. 2013. “Low speed flutter and limit cycle oscillations of a two degree of freedom flat plate in a wind tunnel.” J. Fluids Struct. 43: 244–255. https://doi.org/10.1016/j.jfluidstructs.2013.09.002.
Casalotti, A., A. Arena, and W. Lacarbonara. 2014. “Mitigation of post flutter oscillations in suspension bridge by hysteretic tuned mass dampers.” Eng. Struct. 69: 62–71. https://doi.org/10.1016/j.engstruct.2014.03.001.
Chen, X. Z. 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).
Chen, X. Z., and A. Kareem. 2003. “Efficacy of tuned mass dampers for bridge flutter control.” J. Struct. Eng. 129 (10): 1291–1300. https://doi.org/10.1061/(ASCE)0733-9445(2003)129:10(1291).
Chen, X. Z., and A. Kareem. 2006. “Revisiting multimode coupled bridge flutter: Some new insights.” J. Eng. Mech. 132 (10): 1115–1123. https://doi.org/10.1061/(ASCE)0733-9399(2006)132:10(1115).
Chen, X. Z., and A. Kareem. 2008. “Identification of critical structural modes and flutter derivatives for predicting coupled bridge flutter.” J. Wind Eng. Ind. Aerodyn. 96 (10–11): 1856–1870. https://doi.org/10.1016/j.jweia.2008.02.025.
Chen, X. Z., 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).
Cunningham, A. M. 2003. “Buzz, buffet and LCO on military aircraft–the aeroelastician’s nightmares.” In Proc. Int. Forum on Aeroelasticity and Structural Dynamics (IFASD). The Netherlands: National Aerospace Laboratory (NLR).
Gao, G. Z., and L. D. Zhu. 2017. “Nonlinear mathematical model of unsteady galloping force on a rectangular 2:1 cylinder.” J. Fluids Struct. 70: 47–71. https://doi.org/10.1016/j.jfluidstructs.2017.01.013.
Jing, H., H. Liao, C. Ma, Q. Tao, and J. Jiang. 2020. “Field measurement study of wind characteristics at different measuring positions in a mountainous valley.” Exp. Thermal Fluid Sci. 112: 109991.
Jones, N. P., J. D. Raggett, and E. Ozkan. 2003. “Prediction of cable-supported bridge response to wind: Coupled flutter assessment during retrofit.” J. Wind Eng. Ind. Aerodyn. 91 (12–15): 1445–1464. https://doi.org/10.1016/j.jweia.2003.09.030.
Karpel, M. 1982. “Design for active flutter suppression and gust alleviation using state space aeroelastic modeling.” J. Aircr. 19 (3): 221–227. https://doi.org/10.2514/3.57379.
Katsuchi, H., N. P. Jones, and R. H. Scanlan. 1999. “Multimode coupled flutter and buffeting analysis of the Akashi-Kaikyo Bridge.” J. Struct. Eng. 125 (1): 60–70. https://doi.org/10.1061/(ASCE)0733-9445(1999)125:1(60).
Liao, H., H. Jing, C. Ma, Q. Tao, and Z. Li. 2020. “Field measurement study on turbulence field by wind tower and Windcube Lidar in mountain valley.” J. Wind. Eng. Ind. Aerod. 197: 104090.
Matsumoto, M. 1996. “Aerodynamic damping of prisms.” J. Wind Eng. Ind. Aerodyn. 59 (2–3): 159–175. https://doi.org/10.1016/0167-6105(96)00005-0.
Matsumoto, M., H. Shirato, T. Yagi, R. Shijo, A. Eguchi, and H. Tazamaki. 2003. “Effects of aerodynamic interferences between heaving and torsional vibration of bridge decks: The case of Tacoma Narrows Bridges.” J. Wind Eng. Ind. Aerodyn. 91 (12–15): 1547–1557. https://doi.org/10.1016/j.jweia.2003.09.010.
Matsumoto, M., F. Yoshizumi, T. Yabutani, K. Abe, and N. Nakajima. 1999. “Flutter stabilization and heaving-branch flutter.” J. Wind Eng. Ind. Aerodyn. 83 (1–3): 289–299. https://doi.org/10.1016/S0167-6105(99)00079-3.
Náprstek, J., and C. Fischer. 2009. “Auto-parametric semi-trivial and post critical response of a spherical pendulum damper.” Comput. Struct. 87 (19–20): 1204–1215. https://doi.org/10.1016/j.compstruc.2008.11.015.
Náprstek, J., and S. Pospisil. 2011. “Post-critical behavior of a simple non-linear system in a cross wind.” Eng. Mech. 18 (3–4): 193–201.
Náprstek, J., S. Pospisil, and S. Hracov. 2007. “Analytical and experimental modeling 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.
Nobuto, J., Y. Fujino, and M. Ito. 1988. “A study on the effectiveness of TMD to suppress a coupled flutter of bridge deck.” Proc. JSCE 1988 (398): 413–416. https://doi.org/10.2208/jscej.1988.398_413.
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.
Scanlan, R. H. 1978. “The action of flexible bridges under wind, I:. Flutter theory.” J. Sound Vib. 60 (2): 187–199. https://doi.org/10.1016/S0022-460X(78)80028-5.
Scanlan, R. H. 1997. “Amplitude and turbulence effects on bridge flutter derivatives.” J. Struct. Eng. 123 (2): 232–236. https://doi.org/10.1061/(ASCE)0733-9445(1997)123:2(232).
Scanlan, R. H., and J. Tomko. 1971. “Airfoil and bridge deck flutter derivatives.” J. Soil Mech. Found. Div. 97 (6): 1717–1737.
Tang, Y., X. Hua, Z. Chen, Y. Zhou. 2019. “Experimental investigation of flutter characteristics of shallow Π section at post-critical region.” J. Fluids Struct. 88: 275–291. https://doi.org/10.1016/j.jfluidstructs.2019.05.010.
Wu, B., X. Chen, Q. Wang, H. Liao, and J. Dong. 2020a. “Characterization of vibration amplitude of nonlinear bridge flutter from section model test to full bridge estimation.” J. Wind. Eng. Ind. Aerod. 197: 104048.
Wu, B., Q. Wang, H. Liao, and H. Mei. 2020b. “Hysteresis response of nonlinear flutter of a truss girder: experimental investigation and theoretical predictions.” Comput. Struct. 238: 106267.
Xu, F. Y. 2014. “Practical diagrammatical technique for 3-DOF bridge flutter analysis.” J. Bridge Eng. 19 (12): 04014050. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000626.
Xu, F. Y. 2015. “System decoupling approach for 3-DOF bridge flutter analysis.” J. Struct. Eng. 141 (7): 04014168. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001129.
Xu, F. Y., X. Y. Ying, and Z. Zhang. 2016. “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.
Ying, X. Y., F. Y. 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. J., F. Y. Xu, and X. Y. 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. J., F. Xu, Z. Zhang, and X. Y. 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.
Zheng, S. X., J. F. Guo, J. B. Zhu, and Y. Tang. 2017. “Characteristics and suppression measures for nonlinear flutter of main girder with Π-shaped cross section.” [In Chinese.] J. Southwest Jiaotong Univ. 52 (3): 458–465. https://doi.org/10.3969/j.issn.0258-2724.2017.03.004.
Zhu, L. D., and G. Z. Gao. 2015. “Influential factors of nonlinear flutter phenomenon for typical bridge deck sections.” [In Chinese.] J. Tongji Univ. Nat. Sci. 43 (9): 1289–1294.
Zhu, L. D., and G. Z. Gao. 2016. “A nonlinear self-excited force model for nonlinear flutter phenomenon of a twin-side-girder bridge section.” [In Chinese.] J. Vib. Shock 35 (21): 29–35.
Zhu, L. D., X. L. Meng, and Z. S. Guo. 2013. “Nonlinear mathematical model of vortex induced vertical force on a flat closed box bridge deck.” J. Wind Eng. Ind. Aerodyn. 122: 69–82. https://doi.org/10.1016/j.jweia.2013.07.008.
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Published In
Journal of Bridge Engineering
Volume 25 • Issue 11 • November 2020
Copyright
© 2020 American Society of Civil Engineers.
History
Received: Dec 12, 2019
Accepted: Jun 15, 2020
Published online: Aug 31, 2020
Published in print: Nov 1, 2020
Discussion open until: Jan 31, 2021
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