Wind and Structures

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Probability density evolution analysis on dynamic response and reliability estimation of wind-excited transmission towers

  • Zhang, Lin-Lin (Department of Building Engineering, School of Civil Engineering, Tongji University) ;
  • Li, Jie (Department of Building Engineering, School of Civil Engineering, Tongji University)
  • Received : 2005.11.15
  • Accepted : 2006.11.03
  • Published : 2007.02.25
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Abstract

Transmission tower is a vital component in electrical system. In order to accurately compute the dynamic response and reliability of transmission tower under the excitation of wind loading, a new method termed as probability density evolution method (PDEM) is introduced in the paper. The PDEM had been proved to be of high accuracy and efficiency in most kinds of stochastic structural analysis. Consequently, it is very hopeful for the above needs to apply the PDEM in dynamic response of wind-excited transmission towers. Meanwhile, this paper explores the wind stochastic field from stochastic Fourier spectrum. Based on this new viewpoint, the basic random parameters of the wind stochastic field, the roughness length $z_0$ and the mean wind velocity at 10 m heigh $U_{10}$, as well as their probability density functions, are investigated. A latticed steel transmission tower subject to wind loading is studied in detail. It is shown that not only the statistic quantities of the dynamic response, but also the instantaneous PDF of the response and the time varying reliability can be worked out by the proposed method. The results demonstrate that the PDEM is feasible and efficient in the dynamic response and reliability analysis of wind-excited transmission towers.

Keywords

References

  1. Alvin, K. F. (1997), "Finite element model update via Bayesian estimation and minimization of dynamic residuals", AIAA J., 35(5), 879-886. https://doi.org/10.2514/2.7462
  2. Chen, J. B. and Li, J. (2005), "Dynamic response and reliability analysis of non-linear stochastic structures", Probab. Eng. Mech., 20, 33-44. https://doi.org/10.1016/j.probengmech.2004.05.006
  3. Clough, R. W. and Penzien, J. (1993), Dynamics of Structures; 2nd edn, McGraw-Hill, New York.
  4. Crandall, S. H. and Mark, M. D. (1958), Random Vibration in Mechanical System, Academic Press, New York.
  5. Crandall, S. H. (1970), "First-crossing probabilities of the linear oscillator", J. Sound Vib., 12, 285-299. https://doi.org/10.1016/0022-460X(70)90073-8
  6. Davenport, A. G. (1961), "The spectrum of horizontal gustiness near the ground in high winds", Q. J. Roy. Meteor. Soc., 87, 194-211. https://doi.org/10.1002/qj.49708737208
  7. Davenport, A. G. (1961), "The dependence of wind load upon meteorological parameters", Proceeding of the International Research Seminar on Wind Effects on Buildings and Structures, University of Toronto Press, Toronto.
  8. Deodatis, G. (1996), "Simulation of ergodic multivariate stochastic process", J. Eng. Mech. ASCE, 122(8), 91-109.
  9. Li, J. and Chen, J. B. (2003), "Probability density evolution method for dynamic response analysis of stochastic structures", Proceeding of the Fifth International Conference on Stochastic Structural Dynamics, Hangzhou, China, August.
  10. Li, J. and Chen, J. B. (2005), "Dynamic response and reliability analysis of structures with uncertain parameters", Int. J. Num. Meth. Eng., 62, 289-315. https://doi.org/10.1002/nme.1204
  11. Li, J. and Chen, J. B. (2006a), "The probability density evolution method for dynamic response analysis of nonlinear stochastic structures", Int. J. Num. Meth. Eng., 65, 882-903. https://doi.org/10.1002/nme.1479
  12. Li, J. and Chen, J. B. (2006b), "The principle of preservation of probability and the generalized density evolution equation", Structural Safety, (available on line).
  13. Li, J. and Zhang, L. L. (2004), "A study on the relationship between turbulence power spectrum and stochastic Fourier amplitude spectrum", J. Disaster Prevention and Mitigation Eng., 24(4), 363-369 [in Chinese].
  14. Lin, J. H., Zhang, W. S., and Li, J. J. (1994), "Structural response to arbitrarily coherent stationary random excitations", Comput. Struct., 50(5), 629-634
  15. Shinozuka, M. (1972), "Monte-Carlo solution of structural dynamics", Comput. Struct., 2, 855-874. https://doi.org/10.1016/0045-7949(72)90043-0
  16. Shen, M. Y., Zhang, Z. B., and Niu, X. L. (2001), "Some advances in study of high order accuracy and high resolution finite difference schemes", In New Advances in Computational Fluid Dynamics, Dubois, F., Wu, H. M. (eds). Higher Education Press: Beijing.
  17. Shinozuka, M. and Deodatis, G. (1991), "Simulation of stochastic processes by spectral representation", Appl. Mech. Rev., 44(4), 191-204. https://doi.org/10.1115/1.3119501
  18. Simiu, E. and Scanlan, R. H. (1978), Wind Effects on Structures: An Introduction to Wind Engineering, Wiley, New York.
  19. Tennekes, H. (1973), "The logarithmic wind profile", J. Atmospheric Sci., 30, 234-238. https://doi.org/10.1175/1520-0469(1973)030<0234:TLWP>2.0.CO;2
  20. Zhang, L. L. and Li, J. (2006), "Research on the cross stochastic Fourier spectrum of turbulence", J. Architecture and Civil Eng., 23(2), 57-61.

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