Multistage Indicial Functions and Postflutter Simulation of Long-Span Bridges
Publication: Journal of Bridge Engineering
Volume 23, Issue 4
Abstract
This article addresses a time-domain method for the postflutter analysis of long-span suspension bridges. The energy input properties of indicial functions (IFs) were first analyzed, and based on the findings, the concept of multistage IFs was brought forward to describe the nonlinear aeroelastic properties of bridge decks. The application of the multistage IFs to the nonlinear postflutter analysis entails resolution of two basic issues: smooth switching between groups of IFs and the integration of the mean wind loads. To avoid nonphysical transient responses that result from the abrupt involvement of a group of IFs, a strategy was developed that shows that groups of IFs participate in the aeroelasticity simulation simultaneously and independently; however, in this strategy, only two appropriate groups of IFs were engaged in denoting the aeroelasticity. To avoid double counting of the mean wind loads and to reflect the nonlinear properties of the loads correctly, separation of the pseudosteady effects from the aerodynamic loads denoted by IFs is suggested. The numerical example presented in this paper indicates that multistage IFs can be applied successfully to describe amplitude-dependent nonlinear aeroelastic effects and to conduct a time-domain postflutter analysis.
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Acknowledgments
For the work described in this paper, the authors express their gratitude to the financial support from the National Natural Science Foundation of China (Grants 51178182 and 51578233) and also for the support from the open project of the State Key Laboratory of Disaster Reduction in Civil Engineering (Project SLDRCE10-MB-03).
References
Bendiksen, O., and Davis, G. (1995). “Nonlinear traveling wave flutter of panels in transonic flow.” Proc., 36th Structures, Structural Dynamics and Materials Conf., American Institute of Aeronautics and Astronautics, Reston, VA, Paper 95-1486.
Borri, C., Costa, C., and Zahlten, W. (2002). “Non-stationary flow forces for the numerical simulation of aeroelastic instability of bridge decks.” Comput. Struct., 80(12), 1071–1079.
Caracoglia, L., and Jones, N. P. (2003). “Time domain vs. frequency domain characterization of aeroelastic forces for bridge deck sections.” J. Wind Eng. Ind. Aerodyn., 91(3), 371–402.
Costa, C., and Borri, C. (2006). “Application of indicial functions in bridge deck aeroelasticity.” J. Wind Eng. Ind. Aerodyn., 94(11), 859–881.
de Miranda, S., Patruno, L., Ubertini, F., and Vairo, G. (2013). “Indicial functions and flutter derivatives: A generalized approach to the motion-related wind loads.” J. Fluids Struct., 42(Oct), 466–487.
Diana, G., Resta, F., Rocchi, D., and Argentini, T. (2008). “Aerodynamic hysteresis: Wind tunnel tests and numerical implementation of a fully non linear model for the bridge aeroelastic forces.” Proc., 4th Int. Conf., Advances in Wind and Structures (AWAS08), Vol. 8, Techno, Daejeon, Korea, 944–960.
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, 363–374.
Farquharson, F. B. (1952). “Aerodynamic stability of suspension bridges, part III: The investigation of models of the original Tacoma Narrows Bridge under the action of wind.” Aerodynamic Stability of Suspension Bridges with Special Reference to the Tacoma Narrows Bridge, Bulletin 116, University Washington Press, Seattle.
Farsani, H. Y., Valentine, D. T., Arena, A., Lacarbonara, W., and Marzocca, P. (2014). “Indicial functions in the aeroelasticity of bridge deck.” J. Fluids Struct., 48(Jul), 203–215.
Feistauer, M., Horáček, J., Růžička, M., and Sváček, P. (2011). “Numerical analysis of flow-induced nonlinear vibrations of an airfoil with three degrees of freedom.” Comput. Fluids, 49(1), 110–127.
Galvanetto, U., Peiró, J., and Chantharasenawong, C. (2008). “An assessment of some effects of the nonsmoothness of the Leishman-Beddoes dynamic stall model on the nonlinear dynamics of a typical aerofoil section.” J. Fluids Struct., 24(1), 151–163.
Gao, G. Z., and Zhu, L. D. (2015). “A novel nonlinear mathematical model of the unsteady galloping force on 2:1 rectangular section.” Proc., 14th Int. Conf., Wind Engineering, International Association for Wind Engineering, Kanagawa, Japan.
Gharali, K., and Johnson, D. A. (2013). “Dynamic stall simulation of a pitching airfoil under unsteady free stream velocity.” J. Fluids Struct., 42(Oct), 228–244.
Gordnier, R. E., and Visbal, M. R. (2002). “Development of a three-dimensional viscous aeroelastic solver for nonlinear panel flutter.” J. Fluids Struct., 16(4), 497–527.
Gordnier, R. E., and Visbal, M. R. (2003). “Computation of three-dimensional nonlinear panel flutter.” J. Aerosp. Eng., 155–166.
Jones, R. T. (1940). “The unsteady lift on a wing of finite aspect ratio.” NACA Rep. 681, National Advisory Committee for Aeronautics, Langley Memorial Aeronautical Laboratory, Langley, VA.
Katsuchi, H., Jones, N. P., and Scanlan, R. H. (1999). “Multimode coupled flutter and buffeting analysis of the Akashi-Kaikyo Bridge.” J. Struct. Eng., 60–70.
Larsen, J. W., Nielsen, S. R. K., and Krenk, S. (2007). “Dynamic stall model for wind turbine airfoils.” J. Fluids Struct., 23(7), 959–982.
Leishman, J. G. (1988). “Validation of approximate indicial aerodynamic functions for two-dimensional subsonic flow.” J. Aircr., 25(10), 914–922.
Leishman, J. G., and Beddoes, T. S. (1989). “A semi-empirical model for dynamic stall.” J. Am. Helicopter Soc., 34(3), 3–17.
Noda, M., Utsunomiya, H., Nagao, F., Kanda, M., and Shiraishi, N. (2003). “Effects of oscillation amplitude on aerodynamic derivatives.” J. Wind Eng. Ind. Aerodyn., 91(Jan), 101–111.
Oye, S. (1991). “Dynamic stall simulated as time lag of separation.” Technical Report, Dept. of Fluid Mechanics, Technical Univ. of Denmark, Copehagen, Denmark.
Salvatori, L., and Borri, C. (2007). “Frequency- and time-domain methods for the numerical modeling of full-bridge aeroelasticity.” Comput. Struct., 85, 675–687.
Sarkar, S., and Bijl, H. (2008). “Nonlinear aeroelastic behavior of an oscillating airfoil during stall-induced vibration.” J. Fluids Struct., 24(6), 757–777.
Scanlan, R. H. (1993). “Problematics in formulation of wind-force models for bridge decks.” J. Eng. Mech., 1353–1375.
Scanlan, R. H. (2000). “Motion-related body-force functions in two-dimensional low-speed flow.” J. Fluids Struct., 14(1), 49–63.
Stanford, B., and Beran, P. (2013). “Direct flutter and limit cycle computations of highly flexible wings for efficient analysis and optimization.” J. Fluids Struct., 36(Jan), 111–123.
Tang, D. M., and Dowell, E. H. (1993). “Nonlinear aeroelasticity in rotorcraft.” Math. Comput. Modell., 18(Aug), 157–184.
Tang, D. M., Dowell, E. H., and Hall, K. C. (1999). “Limit cycle oscillations of a cantilevered wing in low subsonic flow.” AIAA J., 37, 364–371.
Tang, D. M., and Dowell, E. H. (2004). “Effects of geometric structural nonlinearity on flutter and limit cycle oscillations of high-aspect-ratio wings.” J. Fluids Struct., 19(3), 291–306.
Theodorsen, T. (1949). “General theory of aerodynamic instability and the mechanism of flutter.” NACA Rep. 496, National Advisory Committee for Aeronautics, Langley Memorial Aeronautical Laboratory, Langley, VA.
Tran, C. T., and Petot, D. (1981). “Semi-empirical model for the dynamic stall of airfoils in view of the application to the calculation of responses of a helicopter blade in forward flight.” Vertica, 5(1), 35–53.
Wang, S., Ingham, D. B., Ma, L., Pourkashanian, M., and Tao, Z. (2012). “Turbulence modeling of deep dynamic stall at relatively low Reynolds number.” J. Fluids Struct., 33(Aug), 191–209.
Weber, S., and Platzer, M. F. (2000). “Computational simulation of dynamic stall on the NLR 7301 airfoil.” J. Fluids Struct., 14(6), 779–798.
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. (2015). “A nonlinear analysis framework for bluff-body aerodynamics: A Volterra representation of the solution of Navier-Stokes equations.” J. Fluids Struct., 54(Apr), 479–502.
Ying, X., Xu, F., and Zhang, Z. (2016). “Study on numerical simulation and mechanism of soft flutter of a bridge deck.” Proc., 2016 World Congress, Advances in Civil, Environmental, and Materials Research (ACEM16), the Structures Congress (Structures16), Techno Press, Daejeon, Korea.
Yoo, J.-H., Kim, D.-H., Kwon, H.-J., and Lee, I. (2005). “Nonlinear aeroelastic simulation of a full-span aircraft with oscillating control surfaces.” J. Aerosp. Eng., 156–167.
Zhang, Z., Chen, Z., Cai, Y., and Ge, Y. (2011). “Indicial functions for bridge aeroelastic forces and time-domain flutter analysis.” J. Bridge Eng., 546–557.
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Published In
Journal of Bridge Engineering
Volume 23 • Issue 4 • April 2018
Copyright
© 2018 American Society of Civil Engineers.
History
Received: Apr 14, 2016
Accepted: Oct 23, 2017
Published online: Jan 31, 2018
Published in print: Apr 1, 2018
Discussion open until: Jul 1, 2018
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