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Spectral response of stationary jack-up platforms loaded by sea waves and wind using perturbation method

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The paper addresses non-linear vibrations of offshore jack-up drilling platforms loaded by sea waves and wind in their stationary condition using the perturbation method. Non-linearity of dynamic equations of motion for fixed offshore platforms yields from two factors. The first is load excitation generating non-linear velocity coupling in a dynamic system. This coupling is inherent in the modified Morison equation, involving the excitation function in the form of the sum of the inertial and velocity forces of sea waves, taking into account relative wave–structure kinematics. Moreover, the wind acting on the exciting side causes similar effects. The second source is the subsoil‒structure interaction problem, modelled by a system of springs and dashpots that yields stochastic non-linearity of the dynamic system. The matrix equations of structural motion in FEM terms are set up. The perturbation method is adopted to determine the mechanical response of the system, making it possible to determine response spectra of the first and the second approximations for displacements and internal forces of the platform. The paper is the continuation of research detailed in the paper [1]. It is assumed, that the fluctuation parts of the dynamic loading forces are in line with the direction of sea wave propagation. Sea current and lift forces effects are neglected in this study. A numerical example refers to structural data of the Baltic drilling platform in the stationary configuration, i.e. when three legs support the deck above the seawater level.
Rocznik
Tom
Strony
53--62
Opis fizyczny
Bibliogr. 28 poz., rys., tab.
Twórcy
  • Gdańsk University of Technology, Narutowicza 11/12, 80-233 Gdańsk, Poland
  • Pratt & Whitney, Canada
Bibliografia
  • 1. B. Rozmarynowski, “Spectral dynamic analysis of a stationary jack-up platform,” Polish Marit. Res., vol. 26, no. 101, pp. 40–48, 2019, doi: 10.2478/pomr-2019-0005.
  • 2. S. K. Chakrabarti, Handbook of Offshore Engineering, vol. I. Elsevier Ltd, 2005.
  • 3. Y. Bai, Marine Structural Design. Elsevier Ltd, 2003.
  • 4. S. E. Hirdaris et al., “Loads for use in the design of ships and offshore structures,” Ocean Eng., vol. 78, pp. 131–174, 2014, doi: https://doi.org/10.1016/j.oceaneng.2013.09.012.
  • 5. N. D. Barltrop and A. J. Adams, Dynamics of Fixed Marine Structures, 3rd ed. Butterworth-Heiemann Ltd, 1991.
  • 6. W. Jesien, “Random vibration of the Baltic drilling platform subjected to wind loads and water waves,” Earthq. Eng. Struct. Dyn., vol. 15, pp. 595–617, 1987, doi: 0098-8847/87/050595-23.
  • 7. B. Rozmarynowski, “Averaged damping in random vibrations of the Baltic drilling platform,” J. Sound Vib., vol. 139, no. 3, pp. 437–458, 1990, doi: https://doi.org/10.1016/0022-460X(90)90675-P.
  • 8. G. Clauss, E. Lehmann, and C. Ostergaard, Offshore Structures: Conceptual Design and Hydromechanics, vol. 1. Springer Berlin Heidelberg, 1992.
  • 9. G. Clauss, E. Lehmann, and C. Ostergaard, Offshore Structures Volume II Strength and Safety for Structural Design. Springer Berlin Heidelberg, 1994.
  • 10. J. F. Wilson, Dynamics of offshore structures. John Wiley & Sons, 1988.
  • 11. M. H. Holmes, Introduction to perturbation methods. New York: Springer, 2013.
  • 12. A. Nayfeh, Perturbation methods. New York: John Wiley & Sons, 1973.
  • 13. S. H. Crandall, “Perturbation techniques for random vibration of non-linear systems,” J. Acoust. Soc. Am., vol. 35, pp. 1700–1705, 1963, doi: https://doi.org/10.1121/1.1918792.
  • 14. Y. K. Lin, Probabilistic theory of structural dynamics. New York: McGraw Hill, 1967.
  • 15. M. Kaminski, The stochastic perturbation method for computational mechanics. Chichester: John Wiley & Sons, 2013.
  • 16. K. Sobczyk, Stochastic differential equations for applications. Lyngby: Technical University of Denmark, 1985.
  • 17. R. E. Taylor and A. Rajagopalan, “Dynamics of offshre structures, part I: perturbation analysis,” J. Sound Vib., vol. 83, no. 3, pp. 401–416, 1982.
  • 18. S. Massel, Ocean surface waves: their physics and prediction. Singapore: World Scientific, 1996.
  • 19. G. Adomian, “Vibration in offshore structures: an analysis for the general non-linear stochastic case - part I,” Math. Comput. Simul., vol. 29, no. 2, pp. 119–122, 1987, doi: https://doi.org/10.1016/0378-4754(87)90102-9.
  • 20. G. Adomian, “Vibration in offshore structures — part II,” Math. Comput. Simul., vol. 29, no. 5, pp. 351–356, 1987, doi: https://doi.org/10.1016/0378-4754(87)90070-X.
  • 21. J. Penzien and S. Tseng, “Three-dimensional dynamic analysis of fixed offshore platforms,” in Numerical Methods in Offshore Engineering, O. C. Zienkiewicz, R. W. Lewis, and K. G. Stagg, Eds. New York: John Wiley & Sons, 1979.
  • 22. J. Thomas and B. Abbas, “Finite element model for dynamic analysis of Timoshenko beam,” J. Sound Vib., vol. 41, no. 3, pp. 291–299, 1975, doi: https://doi.org/10.1016/S0022-460X(75)80176-3.
  • 23. R. W. Clough and J. Penzien, Dynamics of structures. McGraw Hill, 1993.
  • 24. K. J. Bathe, Finite element procedures. Prentice Hall, 1996.
  • 25. A. S. Veletsos and B. Verbic, “Basic response functions for elastic foundations,” J. Eng. Mech., vol. 100, no. 2, pp. 1227–1248, 1974, doi: https://doi.org/10.1061/JMCEA3.0001869.
  • 26. N. C. Tsai, “Modal damping for soil - structure interaction,” J. Eng. Mech., vol. 100, no. 2, pp. 323–341, 1974.
  • 27. A. K. Malhotra and J. Penzien, “Nondeterministic analysis 985–1003, 1970.
  • 28. A. G. Davenport, “The spectrum for horizontal gustiness near the ground in high wind,” Q. J. R. Meteorol. Soc., vol. 87, pp. 194–211, 196
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-27f3da91-5b4e-4f04-b2ef-0feb3e0775c9
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