Wind and Structures

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Monte Carlo simulation for the response analysis of long-span suspended cables under wind loads

  • Di Paola, M. (Dipartimento di Ingegneria Strutturale e Geotecnica, Universita di Palermo) ;
  • Muscolino, G. (Dipartimento di Costruzioni e Tecnologie Avanzate, Universita di Messina) ;
  • Sofi, A. (Dipartimento di Costruzioni e Tecnologie Avanzate, Universita di Messina)
  • Received : 2003.03.01
  • Accepted : 2003.12.10
  • Published : 2004.04.25
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Abstract

This paper presents a time-domain approach for analyzing nonlinear random vibrations of long-span suspended cables under transversal wind. A consistent continuous model of the cable, fully accounting for geometrical nonlinearities inherent in cable behavior, is adopted. The effects of spatial correlation are properly included by modeling wind velocity fluctuation as a random function of time and of a single spatial variable ranging over cable span, namely as a one-variate bi-dimensional (1V-2D) random field. Within the context of a Galerkin's discretization of the equations governing cable motion, a very efficient Monte Carlo-based technique for second-order analysis of the response is proposed. This procedure starts by generating sample functions of the generalized aerodynamic loads by using the spectral decomposition of the cross-power spectral density function of wind turbulence field. Relying on the physical meaning of both the spectral properties of wind velocity fluctuation and the mode shapes of the vibrating cable, the computational efficiency is greatly enhanced by applying a truncation procedure according to which just the first few significant loading and structural modal contributions are retained.

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References

  1. Carassale, L., Piccardo, G. and Solari, G. (2001), "Double modal transformation and wind engineering applications", J. Eng. Mech. ASCE, 127(5), 432-439. https://doi.org/10.1061/(ASCE)0733-9399(2001)127:5(432)
  2. Carassale, L. and Solari, G. (2002), "Wind modes for structural dynamics: a continuous approach", Probab. Eng. Mech., 17, 157-166. https://doi.org/10.1016/S0266-8920(01)00036-4
  3. Carassale, L. and Piccardo, G. (2003), "Wind-induced nonlinear oscillations of cables by Volterra approach", Proceedings of Fifth International Symposium on Cable Dynamics, Santa Margherita Ligure (Italy), 15-18 September, 149-156.
  4. Davenport, A.G. (1968), "The dependence of wind load upon meteorological parameters", Proceedings of the International Research Seminar on Wind Effects on Buildings and Structures, University of Toronto Press, Toronto, (Canada) 19-82.
  5. Deodatis, G. and Shinozuka, M. (1988), "Autoregressive model for non-stationary stochastic processes", J. Eng. Mech. ASCE, 114(11), 1995-2012. https://doi.org/10.1061/(ASCE)0733-9399(1988)114:11(1995)
  6. Deodatis, G. (1996), "Simulation of ergodic multivariate stochastic processes", J. Eng. Mech. ASCE, 122(8), 778-787. https://doi.org/10.1061/(ASCE)0733-9399(1996)122:8(778)
  7. Desai, Y.M., Popplewell, N. and Shah, A.H. (1995), "Finite element modelling of transmission lines", Comput. Struct., 57(3), 407-420. https://doi.org/10.1016/0045-7949(94)00630-L
  8. Di Paola, M. (1998), "Digital simulation of wind field velocity", J. Wind Eng. Ind. Aerodyn., 74-76, 91-109. https://doi.org/10.1016/S0167-6105(98)00008-7
  9. Di Paola, M. and Gullo, I. (2001), "Digital generation of multivariate wind field processes", Probab. Eng. Mech., 16, 1-10. https://doi.org/10.1016/S0266-8920(99)00032-6
  10. Di Paola, M., Muscolino, G. and Sofi, A. (2002), "Nonlinear random vibrations of a suspended cable under wind loading", Fourth International Conference on Computational Stochastic Mechanics, Kerkyra (Corfu), Greece 9-12 June, 159-168.
  11. Gattulli, V., Martinelli, L., Perotti, F. and Vestroni, F. (2001), "Nonlinear interactions in cables investigated using analytical and finite element models", Proceedings of Fourth International Symposium on Cable Dynamics, Montreal (Canada), 28-30 May, 339-346.
  12. Grigoriu, M. (1993), "Simulation of non-stationary Gaussian processes by random trigonometric polynomials", J. Eng. Mech. ASCE, 119(2), 328-343. https://doi.org/10.1061/(ASCE)0733-9399(1993)119:2(328)
  13. Irvine, H.M. (1981), Cable Structures, The MIT Press, Cambridge.
  14. Kaimal, J.C., et al. (1972), "Spectral characteristics of surface-layer turbulence", J. Royal Meteorological Soc., London, England, 98, 563-589. https://doi.org/10.1002/qj.49709841707
  15. Li, Y. and Kareem, A. (1990), "ARMA system in wind engineering", Probab. Eng. Mech., 5(2), 50-59. https://doi.org/10.1016/0266-8920(90)90007-7
  16. Li, Y. and Kareem, A. (1993), "Simulation of multivariate random processes: a hybrid DFT and digital filtering approach", J. Eng. Mech. ASCE, 119(5), 1078-1098. https://doi.org/10.1061/(ASCE)0733-9399(1993)119:5(1078)
  17. Li, Y. and Kareem, A. (1995), "Stochastic decomposition and its application to probabilistic dynamics", J. Eng. Mech. ASCE, 121(1), 162-174. https://doi.org/10.1061/(ASCE)0733-9399(1995)121:1(162)
  18. Loeve, M. (1955), Probability theory, Van Nostrand, New York.
  19. Luongo, A., Paolone, A. and Piccardo, G. (1998), "Postcritical behavior of cables undergoing two simultaneous galloping modes", Meccanica, 33, 229-242. https://doi.org/10.1023/A:1004343029604
  20. Luongo, A., Rega, G. and Vestroni, F. (1984), "Planar non-linear free vibrations of an elastic cable", Int. J. Nonlinear Mech., 9(1), 39-52.
  21. Martinelli, L., Gattulli, V. and Vestroni, F. (2002), "Nonlinear behaviour of a suspended cable under stationary and non-stationary loading", Proceedings of Fifth International Conference on Structural Dynamics, Munich (Germany), 2-5 September, 893-898.
  22. Naganuma, T., Deodatis, G. and Shinozuka, M. (1987), "ARMA model for two dimensional processes", J. Eng. Mech. ASCE, 113(2), 234-251. https://doi.org/10.1061/(ASCE)0733-9399(1987)113:2(234)
  23. Papoulis, A. (1965), Probability, Random Variables and Stochastic Processes, MacGraw-Hill, New York.
  24. Pasca, M., Vestroni, F. and Gattulli, V. (1998), "Active longitudinal control of wind-induced oscillations of a suspended cable", Meccanica, 33, 255-266. https://doi.org/10.1023/A:1004347130512
  25. Piccardo, G. (1993), "A methodology for the study of coupled aeroelastic phenomena", J. Wind Eng. Ind. Aerodyn., 48(2-3), 241-252. https://doi.org/10.1016/0167-6105(93)90139-F
  26. Priestley, M.B. (1999), Spectral analysis and time series, Academic Press, London.
  27. Shinozuka, M. (1971), "Simulation of multivariate and multidimensional random processes", J. Acoust. Soc. Am., 49(1), 357-367. https://doi.org/10.1121/1.1912338
  28. Shinozuka, M. and Jan, C. M. (1972), "Digital simulation of random processes and its applications", J. Sound Vib., 25(1), 111-128. https://doi.org/10.1016/0022-460X(72)90600-1
  29. Shinozuka, M. and Deodatis, G. (1996), "Simulation of multi-dimensional Gaussian stochastic fields by spectral representation", Appl. Mech. Rev. ASME, 49(1), 29-53. https://doi.org/10.1115/1.3101883
  30. Simiu, E. and Scanlan, R.H. (1996), Wind Effects on Structures. Fundamentals and Applications to Design, John Wiley & Sons, Inc New York.
  31. Spanos, P.D. and Mignolet, M.P. (1986), "Z-transform modeling of P-M wave spectrum", J. Eng. Mech. ASCE, 192(8), 745-759.
  32. Spanos, P.D. and Ghanem, R. (1989), "Stochastic finite element expansion for random media", J. Eng. Mech., 115(5), 1035-1053. https://doi.org/10.1061/(ASCE)0733-9399(1989)115:5(1035)
  33. Van Trees, H.I. (1968), Detection, Estimation and Modulation Theory, Part 1, vol. 1., Wiley, New York.

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