Quasi-Static Response of Fixed Offshore Platforms to Morison-Type Wave Loadings
Publication: Journal of Engineering Mechanics
Volume 135, Issue 10
Abstract
The stochastic response of a rigid platform is quasi-static and can be represented as a linear combination of nonlinear random wave loadings. In this study two efficient probabilistic approaches are respectively presented to estimate the higher-order statistics of mildly and highly non-Gaussian structural responses. The eigenvalue analysis of structural quasi-static response in the first approach is based on the expansion of the response in terms of independent Gaussian random variables. The second approach extends the earlier quasi-static analysis procedures to obtain the higher moments of response by including current effects and inundation effects. The interested prediction of extreme responses during a short-term storm, by mean upcrossing rates and mean extremes, can then be achieved by applying Winterstein’s functional transformation. These quantities are found in good agreement with not only Monte Carlo simulation results but also the extreme values obtained using a recently proposed method by Naess et al. in 2007.
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Acknowledgments
The writers thank Dr. Oleg Gaidai [Centre for Ships and Ocean Structures (CeSOS), Norwegian University of Science and Technology] for conducting a discussion on the double logarithm fit of mean upcrossing rates. Acknowledgment also goes to the financial support from the National Research Council of Norway through CeSOS.
References
Boccotti, P. (1989). “On mechanics of irregular gravity waves.” Atti Accad. Naz. Lincei, Mem., Cl. Sci. Fis., Mat. Nat., Sez. 1a, 19, 11–170.
Boccotti, P. (2000). Wave mechanics for ocean engineering, Elsevier Science, New York.
Borgman, L. E. (1967). “Random hydrodynamic forces on objects.” Ann. Math. Stat., 38(1), 37–51.
Borgman, L. E. (1969). “Ocean wave simulation for engineering design.” J. Wtrwy. and Harb. Div., 95(4), 557–583.
Bruce, R. L. (1985). “Quasi-static response of jacket platforms subjected to non-linear wave loading.” Proc., Behaviour of Offshore Structures, Elsevier science Publishers B. V., Amsterdam, 899–905.
Burrows, R. (1983). “Expected value analysis for the quasi-static response of offshore structures.” Appl. Math. Model., 7, 317–328.
Cassidy, M. J., Eatock Taylor, R., and Houlsby, G. T. (2001). “Analysis of jack-up units using constrained NewWave methodology.” Appl. Ocean Res., 23, 221–234.
Der Kiureghian, A. (2000). “The geometry of random vibrations and solutions by FORM and SORM.” Probab. Eng. Mech, 15, 81–90.
Gudmestad, O. T., and Connor, J. J. (1983). “Linearization methods and the influence of current on the nonlinear hydrodynamic drag force.” Appl. Ocean Res., 5(4), 184–194.
Hu, J. S., Gupta, M., and Zhao, D. (1995). “Effects of wave intermittency/nonlinearity on forces and responses.” J. Eng. Mech., 121(7), 819–827.
Isaacson, M. (1991). “Some recent research on random wave forces.” Int. J. Offshore Polar Eng., 1(1), 64–70.
Jensen, J. J., and Capul, J. (2006). “Extreme response predictions for jack-up units in second order stochastic waves by FORM.” Probab. Eng. Mech., 21(4), 330–337.
Jha, A. K., and Winterstein, S. R. (2000). “Nonlinear random ocean waves: Prediction and comparison with data.” Proc. ETCE/OMAE2000 Joint Conf. Energy for the New Millennium (CD-ROM), ASME, New York.
Kareem, A., Hsieh, C. C., and Tognarelli, M. A. (1998). “Frequency-domain analysis of offshore platform in non-gaussian seas.” J. Eng. Mech., 124(6), 668–683.
Karunakaran, D., Haver, S., Baerheim, M., and Spidsoe, N. (2001). “Dynamic behavior of Kvitebjørn Jacket in the North Sea.” Proc., Offshore Mechanics and Arctic Engineering Conf. (CD-ROM), ASME, New York.
Langley, R. S. (1987). “A statistical analysis of non-linear random waves.” Ocean Eng., 14(5), 389–407.
Liaw, C. Y., and Zheng, X. Y. (2004). “Least squares, moment-based and hybrid polynomializations of drag forces.” J. Eng. Mech., 130(3), 294–302.
Lighthill, J. (1979). “Waves and hydrodynamic loading.” Proc., Behaviour of Offshore Structures, CSA, London, 1, 1–40.
Lin, Y. K. (1967). Probabilistic theory of structural dynamics, McGraw-Hill, New York.
Lindgren, G. (1970). “Some properties of a normal process near a local maximum.” Ann. Math. Stat., 41(6), 1870–1883.
Lindgren, G. (1972). “Local maxima of Gaussian fields.” Ark. Mat., 10, 195–218.
Madsen, H. O., Krenk, S., and Lind, N. C. (1986). Methods of structural safety, Prentice-Hall, Englewood Cliffs, N.J.
Manuel, L., and Cornell, C. A. (1996). “The influence of alternative wave loading and support modeling assumptions on jack-up rig response extremes.” J. Offshore Mech. Arctic Eng., 118(2), 109–114.
Moan, T., Zheng, X. Y., and Quek, S. T. (2007). “Frequency-domain analysis of non-linear wave effects on offshore platform responses.” Int. J. Non-linear Mech., 42, 555–565.
Moe, G. and Niedzweicki, J. M. (2005). “Frequency of maxima of non-narrow banded stochastic processes.” Appl. Ocean Res., 27(1–2), 265–272.
Morison, J. W., O'Brien, M. P., John son, J. R., and Schaaf, J. M. (1950). “The force exerted by surface waves on piles.” Petrol. Trans., AIME, 189, 149–157.
Naess, A., Gaidai, O., and Haver, S. (2007). “Efficient estimation of extreme response of drag-dominated offshore structures by Monte Carlo simulation.” Ocean Eng., 34(16), 2188–2197.
Najafian, G. (2007a). “Application of system identification techniques in efficient modeling of offshore structural response. Part I: Model development.” Appl. Ocean Res., 29(1–2), 1–16.
Najafian, G. (2007b). “Application of System identification techniques in efficient modeling of offshore structural response. Part II: Model validation.” Appl. Ocean Res., 29(1–2), 17–36.
Najafian, G. (2007c). “Derivation of statistical properties of wave-induced offshore structural response by principal component technique.” Ocean Eng., 34(7), 987–999.
Najafian, G. (2007d). “Probability models for offshore structural response due to morison wave loading. Part I: Drag-only response.” Ocean Eng., 34(17–18), 2277–2288.
Najafian, G. (2007e). “Probability models for offshore structural response due to morison wave loading. Part II: Inertia-only and total responses.” Ocean Eng., 34(17–18), 2289–2299.
Najafian, G., and Burrows, R. (1994). “Probabilistic modeling of quasi-static response of offshore structures subject to nonlinear wave loading: Two approximate approaches.” Appl. Ocean Res., 16, 205–221.
Papoulis, A. (1991). Probability, random variables, and stochastic processes, 3rd Ed., McGraw-Hill, New York.
Pierson, W. J., and Holmes, P. (1965). “Irregular wave forces on a pile.” J. Wtrwy. and Harb. Div., 91(4), 1–10.
Price, R. (1958). “A useful theorem for non-linear devices having Gaussian inputs.” IRE Trans. Inf. Theory, IT-4, 69–72.
Rice, S. O. (1945). “Mathematical analysis of random noise.” Bell Syst. Tech. J., 24, 45–156.
Rozario, J. B., Tromans, P. S., Taylor, P. H., and Efthymiou, M. (1993). “Comparison of loads predicted using NewWave and other wave models with measurements on the tern structure.” Int. J. Society Underwat. Technol., 19(2), 24–30.
Society of Naval Architects and Marine Engineers (SNAME). (1994). Recommended practice for site specific assessment of mobile jack-up units, 1st Ed., HSE, London, 81–96.
Tickell, R. G. (1977). “Continuous random wave loading on structural members.” Struct. Eng., 55(5), 209–222.
Tromans, P. S., Anaturk, A. R., and Hagemeijer, P. (1991). “A new model for the kinematics of large ocean waves—Application as a design wave.” Proc., 1st Offshore and Polar Engineering Conf., 3, 64–71.
Tung, C. C. (1995). “Effects of free surface fluctuation on total wave forces on cylinder.” J. Eng. Mech., 121(2), 274–280.
Winterstein, S. R. (1988). “Nonlinear vibration models for extremes and fatigue.” J. Eng. Mech., 114(10), 1772–1790.
Winterstein, S. R., and Torhaug, R. (1996). “Extreme jack-up response: Simulation and nonlinear analysis methods.” J. Offshore Mech. Arct. Eng., 118(2), 103–108.
Yang, J., and Zhang, J. (2000), “Effects of wave intermittency and nonlinearity on wave loads.” Proc. ETCE/OMAE2000 Joint Conf. Energy for the New Millennium (CD-ROM), ASME, New York.
Zheng, X. Y., and Liaw, C. Y. (2004). “Nonlinear frequency-domain analysis of jack-up platforms.” Int. J. Non-linear Mech., 39(9), 1519–1534.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 135 • Issue 10 • October 2009
Pages: 1057 - 1068
Copyright
© 2009 ASCE.
History
Received: Oct 25, 2007
Accepted: May 11, 2009
Published online: Sep 15, 2009
Published in print: Oct 2009
Notes
Note. Associate Editor: Arvid Naess
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