Experimental Investigations on the Nonlinear Torsional Flutter of a Bridge Deck
Publication: Journal of Bridge Engineering
Volume 22, Issue 8
Abstract
The nonlinear flutter featured by the limit cycle oscillation (LCO) is a typical aeroelastic phenomenon for bluff decks and/or streamlined decks at large incidence angles. In this study, the flutter characteristics of a streamlined deck were investigated by using comprehensive wind-tunnel tests, and a nonlinear mathematical model was introduced to model the aeroelastic behavior of the nonlinear torsional flutter oscillation. The nonlinear aerodynamic force is the major source of the nonlinear flutter. The nonlinear flutter LCO corresponds to a state in which the energy absorbed by the linear damping and the energy dissipated by the nonlinear damping are balanced within an oscillation period. On the basis of the instantaneous amplitude and instantaneous frequency calculated by using the normalized Hilbert transform, a system identification method was developed to simultaneously extract the linear and nonlinear aerodynamic parameters. The efficacy of the nonlinear mathematical model and the identification accuracy of aerodynamic parameters were validated by two examples. The sensitivities of aerodynamic parameters to the signal length were studied, and the corresponding causes were revealed. The linear aerodynamic damping parameter and structural damping ratio are the dominant parameters for determining the critical flutter wind speed. For the nonlinear torsional flutter, a practical approach was proposed to predict the critical reduced wind speeds and the LCO amplitudes with different structural damping ratios, and its accuracy was verified by comparing the experimental results.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This research is jointly supported by the National Science Foundation of China (Grants 51178086 and 51478087), which is gratefully acknowledged.
References
Barrero, G. A., Sanz, A. A., and Alonso, G. (2009). “Hysteresis in transverse galloping: The role of the inflection points.” J. Fluids Struct., 25(6), 1007–1020.
Bartoli, G., Contri, S., Mannini, C., and Righi, M. (2009). “Toward an improvement in the identification of bridge deck flutter derivatives.” J. Eng. Mech., 771–785.
Bedrosian, E. (1963). “A product theorem for Hilbert transforms.” Proc. IEEE, 51(5), 868–869.
Bogoliubov, N. N., and Mitroposki, I. A. (1961). Asymptotic methods in the theory of non-linear oscillations, CRC, Boca Raton, FL.
Caracoglia, L., Sarkar, P. P., Haan, F. L., Sato, H., and Murakoshi, J. (2009). “Comparative and sensitivity study of flutter derivatives of selected bridge deck sections, Part 2: Implications on the aerodynamic stability of long-span bridges.” Eng. Struct., 31(9), 2194–2202.
Carassale, L., Wu, T., and Kareem, A. (2014). “Nonlinear aerodynamic and aeroelastic analysis of bridges: Frequency domain approach.” J. Eng. Mech., 04014051.
Casalotti, A., Arena, A., and Lacarbonara, W. (2014). “Mitigation of post-flutter oscillations in suspension bridges by hysteretic tuned mass dampers.” Eng. Struct., 69, 62–71.
Diana, G., Resta, F., and Rocchi, D. (2008). “A new numerical approach to reproduce bridge aerodynamic non-linearities in time domain.” J. Wind Eng. Ind. Aerodyn., 96(10–11), 1871–1884.
Diana, G., Rocchi, D., Argentini, T., and Muggiasca, S. (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.
Dimitriadis, G., and Li, J. (2009). “Bifurcation behavior of airfoil undergoing stall flutter oscillations in low-speed wind tunnel.” AIAA J., 47(11), 2577–2596.
Dowell, E. H. (2015). A modern course in aeroelasticity, Springer, Cham, Switzerland.
Feldman, M. (2011). “Hilbert transform in vibration analysis.” Mech. Syst. Sig. Process., 25(3), 735–802.
Gao, G. Z., and Zhu, L. D. (2015). “A novel nonlinear mathematical model of the unsteady galloping force on 2:1 rectangular section.” 14th Int. Conf. on Wind Engineering.
Huang, N. E., Wu, Z. H., Long, S. R., Arnold, K. C., Chen, X. Y., and Blank, K. (2009). “On instantaneous frequency.” Adv. Adapt. Data Anal., 1(2), 177–229.
Katsuchi, H., Yamada, H., Nishio, M., and Okazaki, Y. (2016). “Improvement of aerodynamic stability of suspension bridges with H-shaped simplified stiffening girder.” Front. Struct. Civ. Eng., 10(1), 93–102.
Král, R., Pospisil, S., and Naprstek, J. (2014). “Wind tunnel experiments on unstable self-excited vibration of sectional girders.” J. Fluids Struct., 44(2014), 235–250.
Matsumoto, M., Matsumiya, H., Fujiwara, S., and Ito, Y. (2010). “New consideration on flutter properties based on step-by-step analysis.” J. Wind Eng. Ind. Aerodyn., 98(8), 429–437.
Mishra, S. S., Kumar, K., and Krishna, P. (2008). “Multimode flutter of long-span cable-stayed bridge based on 18 experimental aeroelastic derivatives.” J. Wind Eng. Ind. Aerodyn., 96(1), 83–102.
Náprstek, J., and Pospıšil, S. (2012). “Response types and general stability conditions of linear aero-elastic system with two degrees-of-freedom.” J. Wind Eng. Ind. Aerodyn., 111 1–13.
Náprstek, J., Pospıšil, S., Höffer, R., and Sahlmen, J. (2008). “Self-excited nonlinear response of a bridge-type cross section in post-critical state.” Proc., BBAA VI Int. Colloquium on Bluff Bodies Aerodynamics and Applications, AnsaldoBreda, Milan, Italy, 20–24.
Náprstek, J., Pospís˘il, S., and Hrac˘ov, S., (2007). “Analytical and experimental modelling of non-linear aeroelastic effects on prismatic bodies.” J. Wind Eng. Ind. Aerodyn., 95(9–11), 1315–1328.
Nuttall, A. H. (1966). “On the quadrature approximation to the Hilbert transform of modulated signals.” Proc. IEEE, 54(10), 1458–1459.
Razak, N. A., Andrianne, T., and Dimitriadis, G. (2011). “Flutter and stall flutter of a rectangular wing in a wind tunnel.” AIAA J., 49(10), 2258–2271.
Scanlan, R. H. (1981). “On the state-of-the-art methods for calculations of flutter, vortex-induced and buffeting response of bridge structures.” Technical Rep. FHWA/RD-80/050, National Technical Information Service, Springfield, VA.
Scanlan, R. H., and Tomko, J. J. (1971). “Airfoil and bridge deck aerodynamic parameters.” J. Eng. Mech., 97(6), 1171–1737.
Schmidt, G., and Tondl, A. (1986). Non-linear vibrations, Cambridge University Press, Cambridge, U.K.
Spanos, P. D., Giaralis, A., and Politis, N. P. (2007). “Time–frequency representation of earthquake accelerograms and inelastic structural response records using the adaptive chirplet decomposition and empirical mode decomposition.” Soil. Dyn. Earthquake Eng., 27(7), 675–689.
Wu, T., and Kareem, A. (2013). “Aerodynamics and aeroelasticity of cable-supported bridges: Identification of nonlinear features.” J. Eng. Mech., 1886–1893.
Xu, F. Y., and Chen, A. R. (2009). “Flutter test and analysis for the Suramadu Bridge in Indonesia.” China Civ. Eng. J., 42(1), 35–40 (in Chinese).
Xu, F. Y., Chen, X. Z., Cai, C. S., and Chen, A. R. (2012). “Determination of 18 flutter derivatives of bridge decks by an improved stochastic search algorithm.” J. Bridge Eng., 576–588.
Zhang, C. G. (2007). “Soft flutter and parameters identification of nonlinear self-excited aerodynamic forces of bridge girders.” Master thesis, Tongji Univ., Shanghai, China (in Chinese).
Zhu, L. D., and Gao, G. Z. (2015). “Influential factors of soft flutter phenomenon for typical bridge deck sections.” J. Tongji Univ. (Natural Science), 43(9), 1289–1294 (in Chinese).
Information & Authors
Information
Published In
Journal of Bridge Engineering
Volume 22 • Issue 8 • August 2017
Copyright
© 2017 American Society of Civil Engineers.
History
Received: Aug 2, 2016
Accepted: Mar 8, 2017
Published online: Jun 9, 2017
Published in print: Aug 1, 2017
Discussion open until: Nov 9, 2017
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.