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A study of wind effect on damping and frequency of a long span cable-stayed bridge from rational function approximation of self-excited forces

  • Received : 2006.05.29
  • Accepted : 2007.02.22
  • Published : 2007.06.25

Abstract

This paper presents an aeroelastic analysis procedure to highlight the influence of wind velocity on the structural damping and frequency of a long span cable-stayed bridge. Frequency dependent self-excited forces in terms of flutter derivatives are expressed as continuous functions using rational function approximation technique. The aeroelastically modified structural equation of motion is expressed in terms of frequency independent modal state-space parameters. The modal logarithmic dampings and frequencies corresponding to a particular wind speed are then determined from the eigen solution of the state matrix.

Keywords

References

  1. Arnoldi, W. E. (1951), "The principle of minimised iterations in the solutions of the matrix eigenvalue problem", Quart. Appl. Math., 9, 17-29. https://doi.org/10.1090/qam/42792
  2. Bisplinghoff, R. L., Ashley, H. and Halfman, R. L. (1955), Aeroelasticity, Addison-Wesley Publishing Co. Inc., Cambridge, USA.
  3. Bucher, C. G. and Lin, Y. K. (1988), "Stochastic stability of bridge considering coupled modes", J. Eng. Mech., ASCE, 114(12), 2055-2071. https://doi.org/10.1061/(ASCE)0733-9399(1988)114:12(2055)
  4. Bevington, P. R. (1969), Data Reduction and Error Analysis for the Physical Science, McGraw-Hill Book Company, NY.
  5. Boonyapinyo, V., Miyata, T. and Yamada, H. (1999), "Advanced aerodynamic analysis of suspension bridges by state space approach", J. Struct. Eng., ASCE, 125(12), 1357-1366. https://doi.org/10.1061/(ASCE)0733-9445(1999)125:12(1357)
  6. Caracoglia, L. and Jones, N. P. (2003), "Time domain vs. frequency domain characteristics of aeroelastic forces for bridge deck sections", J. Wind Eng. Ind. Aerodyn., 91, 371-402. https://doi.org/10.1016/S0167-6105(02)00399-9
  7. Chen, X. and Kareem, A. (2002), "Advances in modeling of aerodynamic forces on bridge decks", J. Eng. Mech., ASCE, 128(11), 1193-1205. https://doi.org/10.1061/(ASCE)0733-9399(2002)128:11(1193)
  8. Chen, X., Matsumoto, M. and Kareem, A. (2000a), "Time domain flutter and buffeting response analysis of bridges", J. Eng. Mech., ASCE, 126(1), 7-16. https://doi.org/10.1061/(ASCE)0733-9399(2000)126:1(7)
  9. Chen, X., Matsumoto, M. and Kareem, A. (2000b), "Aerodynamic coupling effects on the flutter and buffeting of bridges", J. Eng. Mech., ASCE, 126(1), 17-26. https://doi.org/10.1061/(ASCE)0733-9399(2000)126:1(17)
  10. Dowell, E. H. (1980), "A simple approach of converting frequency domain aerodynamics to the time domain", NASA TM-81844.
  11. Edwards, J. H. (1979), "Application of Laplace transform methods to airfoil motion and stability calculations", AIAA Paper 70-0772.
  12. Fujino, Y., Wilde, K., Masukawa, J. and Bhartia, B. (1995), "Rational function approximation of aerodynamics forces on bridge deck and its application to active control of flutter", Proc. 9ICWE, New Delhi, India, 994-1005.
  13. Guyan, R. J. (1965), "Reduction of stiffness and mass matrices", J. AIAA, 3(2), 380. https://doi.org/10.2514/3.2874
  14. Hjorth-Hansen, E. (1992), "Section model tests", Proc. of 1st Int. Symp. on Aerodynamics of Large Bridges, A. Larsen (ed.), Balkema, Rotterdam, 95-112.
  15. Jain, A., Jones, N. P. and Scanlan, R. H. (1996a), "Coupled flutter and buffeting analysis of long-span bridges", J. Struct. Eng., ASCE, 122(7), 716-725. https://doi.org/10.1061/(ASCE)0733-9445(1996)122:7(716)
  16. Jain, A., Jones, N. P. and Scanlan, R. H. (1996b), "Coupled aeroelastic and aerodynamic response analysis of long-span bridges", J. Wind Eng. Ind. Aerodyn., 60, 69-80. https://doi.org/10.1016/0167-6105(96)00024-4
  17. Jones, N. P. and Scanlan, R. H. (1991), "Issues in the multimode aeroelastic analysis of cable-stayed bridges", Proceedings of International Workshop on Technology, for Hong Kong's Infrastructure, 281-290.
  18. Jones, N. P. and Scanlan, R. H. (2001), "Theory and full bridge modeling of wind response of cable supported bridges", J. Bridge. Eng., ASCE, 6(6), 365-375. https://doi.org/10.1061/(ASCE)1084-0702(2001)6:6(365)
  19. Jones, R. T. (1941), "The unsteady lift of a wing of finite aspect ratio", NACA Rept., 681.
  20. Karpel, M. (1982), "Design for active flutter suppression and gust alleviation using state-space aeroelastic modeling", J. Aircraft, 19(3), 221-227. https://doi.org/10.2514/3.57379
  21. Katsuchi, H., Jones, N.P., Scanlan, R. H. and Akiyama, H. (1998), "Multimode flutter and buffeting analysis of the Akashi-Kaikyo Bridge", J. Wind Eng. Ind. Aerodyn., 77&78, 431-441.
  22. Lin, Y. K. and Yang, J. N. (1983), "Multimode bridge response to wind excitations", J. Eng. Mech., ASCE, 109(2), 586-603. https://doi.org/10.1061/(ASCE)0733-9399(1983)109:2(586)
  23. Marquardt, D. W. (1963), "An algorithm for least-squares estimation of nonlinear parameters", J. Soc. Ind. Appl. Math., 11(2), 431-441. https://doi.org/10.1137/0111030
  24. MATLAB (1996), Using Matlab version 5, The Mathworks Inc, Nattick, MA, USA, [http://www.mathworks.com].
  25. Mishra, S. S. (2005), "Effect of wind drag on flutter of long span cable-stayed bridges", Ph.D. Thesis, Indian Institute of Technology Roorkee, India.
  26. Mishra, S. S., Kumar, K. and Krishna, P. (2006), "Identification of 18 flutter derivatives by covariance driven stochastic subspace method", Wind Struct., 9(2), 159-178. https://doi.org/10.12989/was.2006.9.2.159
  27. Peterson, L. D. and Crawley, E. F. (1988), "Improved exponential time series approximations of unsteady aerodynamic operators", J. Aircraft, 25(2).
  28. Press, W. H., Teukolsky, S. A., Vellerling, W. T. and Flannery, B. P. (1992), Numerical Recipes in FORTRAN, 2nd ed., Cambridge University Press.
  29. Roger, K. (1977), "Airplane math modeling methods for active control design", Structural Aspects of Active Control, Agard-CP-228.
  30. Sarkar, P. P., Jones, N. P. and Scanlan, R. H. (1994), "Identification of aeroelastic parameters of flexible bridges", J. Eng. Mech., ASCE, 120(8), 1718-1742. https://doi.org/10.1061/(ASCE)0733-9399(1994)120:8(1718)
  31. 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
  32. Scanlan, R. H. (1993), "Problematics in formulation of wind-force models for bridge decks", J. Eng. Mech., ASCE, 119(7), 1353-1375. https://doi.org/10.1061/(ASCE)0733-9399(1993)119:7(1353)
  33. Scanlan, R. H., Beliveau, J. G., and Budlong, K. S. (1974), "Indicial aerodynamic functions for bridge decks", J. Eng. Mech., ASCE, 100(EM 4), 657-672.
  34. Scanlan, R. H. and Jones, N. P. (1990), "Aeroelastic analysis of cable stayed bridges", J. Struct. Eng., ASCE, 116(2), 279-297. https://doi.org/10.1061/(ASCE)0733-9445(1990)116:2(279)
  35. Singh, L., Jones, N. P., Scanlan, R. H. and Lorendeaux, O. (1995), "Simultaneous identification of 3-dof aeroelastic parameters", Proceedings of 9th International Conference on Wind Engineering, New Delhi, India. Wiley Eastern Ltd., 872-881.
  36. Tanaka, H., Yamamura, N. and Tatsumi, M. (1992), "Coupled mode flutter analysis using flutter derivatives", J. Wind Eng. Ind. Aerodyn., 41-44, 1279-1290.
  37. Theodorsen, T. (1935), "General theory of aerodynamic instability and mechanism of flutter", NACA report No: 496, US Advisory Committee for Aeronautics, Langley, VA.
  38. Tiffany, S. H. and Adams Jr., W. M. (1987), "Nonlinear programming extensions to rational function approximation of unsteady aerodynamics", Proceedings of AIAA Symp. on Structural Dynamics and Aeroelasticity, AIAA, Washington, D.C.
  39. Xie, J. and Xiang, H. (1985), "State space method for 3D flutter analysis of bridge structures", Proc. Asia Pacific Symp on Wind Engineering, New Delhi, India, 269-276.

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