Stochastic Response of Offshore Platforms by Statistical Cubicization
Publication: Journal of Engineering Mechanics
Volume 121, Issue 10
Abstract
In this study, a method of statistical cubicization is proposed to predict stochastic response of offshore platform to a Morison-type nonlinear random wave loading. The nonlinearity is replaced by an equivalent polynomial expansion up to cubic order. The Volterra series method is used to solve the resulting nonlinear equivalent system in the frequency domain. Complete expressions to evaluate response central moments up to the fourth order are obtained for a three-term Volterra system driven by a stationary Gaussian input. To make the developed method efficient and practical, an efficient solution scheme is proposed to implement the Volterra series method. Results (i.e., response mean, variance, skewness, and kurtosis) are presented for the cases of fixed offshore structures and compared with those obtained by simulation, equivalent linearization, and quadratization methods. The statistical cubicization method is superior to both the statistical linearization and quadratization method.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Bedrosian, E., and Rice, S. O.(1971). “The output properties of Volterra systems (nonlinear systems with memory) driven by harmonic and Gaussian inputs.”Proc., Institute of Electrical and Electronics Engineers, New York, N.Y., 59, 1688–1707.
2.
Donley, M. G., and Spanos, P. D. (1990). Dynamic analysis of non-linear structures by the method of statistical quadratization . Springer-Verlag, New York, N.Y.
3.
Grigoriu, M.(1984a). “Crossing of non-gaussian translation process.”J. Engrg. Mech., ASCE, 110(4), 610–620.
4.
Grigoriu, M. (1984b). “Dynamic response of offshore platforms to environmental loads.”Proc. 4th ASCE Specialty Conf. on Probabilistic Mech. and Struct. Reliability, ASCE, New York, N.Y., 115–118.
5.
Hu, S. L. J.(1990). “Stochastic dynamic response to nonlinear wave loading: Fourth-moment analysis.”J. Engrg. Mech., ASCE, 116(1), 107–124.
6.
Johnson, N. L., and Kotz, S. (1972). Distribution in statistics: Continuous multivariate distribution . John Wiley, New York, N.Y.
7.
Kareem, A., and Zhao, J. (1994). “Stochastic response analysis of tension leg platform: A statistical quadratization and cubicization approach.”Proc., 13th Conf. on Offshore Mech. and Arctic Engrg., American Society of Mechanical Engineers, New York, N.Y., 281–292.
8.
Koliopulos, P. K.(1988). “Quasi-static and dynamic response statistics of linear SDOF system under Morison-type wave forces.”Engrg. Struct., 10(1), 24–36.
9.
Li, X. M. (1994). “Stochastic response of offshore platforms by methods of statistical linearization, quadradization and cubicization,” PhD thesis, National University of Singapore, at Singapore.
10.
Lutes, L. D., Corazao, M., Hu, S. L., and Zimmerman, J.(1984). “Stochastic fatigue damage accumulation.”J. Struct. Engrg., ASCE, 110(11), 2585–2601.
11.
Malhotra, A. K., and Penzien, J.(1970). “Non-deterministic analysis of offshore structures.”J. Engrg. Mech. Div., ASCE, 96(6), 985–998.
12.
Naess, A.(1986). “The statistical distribution of second-order slowly-varying forces and motions.”Appl. Oc. Res., 8(2), 110–118.
13.
Naess, A., and Ness, G. M.(1992). “Second-order, sum-frequency response statistics of tethered platforms in random waves.”Appl. Oc. Res., 14(2), 23–32.
14.
Roberts, J. B., and Spanos, P. D. (1989). Random vibrations and statistical linearization . John Wiley, New York, N.Y.
15.
Rugh, W. J. (1981). Nonlinear system theory—The Volterra/Wiener approach. Johns Hopkins Univ. Press, Baltimore, Md.
16.
Schetzen, M. (1980). The Volterra and Wiener theories of nonlinear systems . John Wiley, New York, N.Y.
17.
Wang, J., and Lutes, L. D. (1992). “Effects of Morison equation nonlinearity on stochastic dynamics and fatigue of offshore structures.”Technical Report, Offshore Tech. Res. Ctr., Texas A & M Univ., College Station, Tex.
18.
Wilson, J. F. (1984). Dynamics of offshore structures . John Wiley & Sons, New York, N.Y.
19.
Winterstein, S. R.(1985). “Non-normal responses and fatigue damage.”J. Engrg. Mech., ASCE, 111(10), 1291–1295.
20.
Winterstein, S. R., and Loseth, R. (1990). “Jackup structures nonlinear forces and dynamic response.”Proc. 3rd IFIP Conf., Reliability and Optimization of Struct. Systems '90, Berkeley, Calif., 349–358.
21.
Winterstein, S. R., Ude, T. C., and Marthinsen, T.(1994). “Volterra models of ocean structures: Extreme and fatigue reliability.”J. Engrg. Mech., ASCE, 120(6), 1396–1385.
22.
Wu, S. C. (1976). “The effects of current on dynamic response of offshore platforms.”Proc. 8th Offshore Tech. Conf., Dallas, Tex., 185–196.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 121 • Issue 10 • October 1995
Pages: 1056 - 1068
Copyright
Copyright © 1995 American Society of Civil Engineers.
History
Published online: Oct 1, 1995
Published in print: Oct 1995
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.