Multivariate Hermite Expansion of Hydrodynamic Drag Loads on Tension Leg Platforms
Publication: Journal of Engineering Mechanics
Volume 119, Issue 1
Abstract
In this paper, a new method is proposed for the expansion of nonlinear drag forces in terms of multivariate Hermite polynomials correct up to the second order. The drag‐force formulation includes the effect of instantaneous wave surface profile and it caters for the waves and currents approaching from any arbitrary direction with respect to the platform orientation. These attributes are critical for a reliable treatment of the wave‐induced viscous effects on tension leg platforms (TLP). The viscous nonlinear drag force expressed in terms of Hermite polynomials is decomposed into the mean (zeroth‐order), viscous exciting and viscous damping terms (first‐order) and the slowly varying drift‐force term (second‐order). This decomposition permits spectral representation of the first‐order viscous forces in terms of the spectral density function of the water particle velocities. Accordingly, the second‐order viscous force can be described within the spectral framework by the spectral convolution or other related techniques involving the spectral density functions of the relative fluid‐structure velocities and the wave surface elevation. The response statistics derived from the frequency domain provides a very good agreement with the time‐domain simulation. The present approach based on an equivalent quadratization concept not only retains the important features of the nonlinear interactions in the frequency domain analysis, e.g., the spectral contents at the sum and difference frequencies, but also clearly offers accuracy comparable to the time‐domain approach at a fraction of the computational effort. Immediate applications of the present analysis approach are possible in the analysis of marine risers and suspended pipelines to ocean waves and currents.
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References
1.
Abramowitz, M., and Stegun, I. A. (1965). Handbook of mathematical functions. Dover Publications, Inc., New York, N.Y.
2.
Berge, B., and Penzien, J. (1974). “Three‐dimensional stochastic response of offshore towers to wave forces.” OTC 2050, Offshore Technology Conference, Houston, Tex.
3.
Borgman, L. F. (1982). “Specification of the wave environment.” Proc. Ocean Structural Dyn. Symp. '82.
4.
Crandall, S. H. (1963). “Perturbation techniques for random vibrations of nonlinear systems.” J. Acoustical Society of America, 35(11), 1700–1705.
5.
Eatock Taylor, R., and Rajagopalan, A. (1982). “Dynamics of offshore structures, part I: Perturbation analysis.” J. Sound Vib., 83(3), 401–416.
6.
Eatock Taylor, R., and Rajagopalan, A. (1983). “Load spectra for slender offshore structures in waves and currents.” Earthquake Eng. Struct. Dyn., 11(6), 831–842.
7.
Foster, E. T. (1990). “Model for nonlinear dynamics of offshore towers.” J. Engr. Mech., ASCE, 41–67.
8.
Hamilton, J. (1982). “Three‐dimensional Fourier analysis of drag force for compliant offshore structures.” Dynamic analysis of offshore structures: Recent developments, C. L. Kirk, ed., Gulf Publications, Houston, Tex.
9.
Kareem, A., and Li, Y. (1988). “Stochastic response of tension leg platforms to wind and wave fields.” Report No. UHCE 88‐18, Dept. of Civ. Engrg., University of Houston, Houston, Tex.
10.
Kareem, A., and Li, Y. (1992). “Equivalent statistical quadratization of nonlinear hydrodynamic loads on TLPs.” Proc. ASCE Specialty Conf., Civ. Engrg. in the Oceans V, ASCE.
11.
Leira, B. J., and Olufsen, A. (1986). “Biplanar linearization of drag forces with application to riser analysis.” OTC 5100, Offsore Technology Conference, Houston, Tex.
12.
Li, Y., and Kareem, A. (1990). “A description of hydrodynamic forces on tension leg platforms using a multivariate hermite expansion.” Proc. Ninth Int. Conf. on Offshore Mech. and Arctic Engrg., American Society of Mechanical Engineers, ASME, II.
13.
Lin, Y. K. (1976). Probabilistic theory of structural dynamics. R. E. Krieger Publishing Co., New York, N.Y.
14.
Lipsett, A. W. (1986). “Nonlinear structural response in random waves.” J. Struct. Engrg., ASCE, 112(11), 2416–2429.
15.
Mo, O., and Moan, T. (1985). “Environmental load effect analysis of guyed towers.” J. Energy Resour. Technol. Trans ASME, 24, 107, 24–33.
16.
Nayfeh, A. H. (1974). Perturbation methods. John Wiley and Sons, New York, N.Y.
17.
Roberts, J. B., and Spanos, P. D. (1990). Random vibration and statistical linearization. John Wiley and Sons, New York, N.Y.
18.
Rodenbusch, G., and Forristall, G. Z. (1986). “An empirical model for random directional wave kinematics near the free surface.” OTC 5097, Offsore Technology Conference, Houston, Tex.
19.
Rodenbusch, G., Garrett, D. L., and Anderson, S. L. (1986). “Statistical linearization of velocity‐squared drag forces.” Proc., Offshore Mechanics and Arctic Engineering, American Society of Mechanical Engineers.
20.
Sigbjornsson, R., and Smith, E. (1980). “Wave induced vibrations of gravity platforms.” Appl. Mathematical Modelling, Vol. 4, Butterworths, England.
21.
Spanos, P. T. D., and Chen, T. W. (1981). “Random response to flow‐induced forces.” J. Engrg. Mech. Div., ASCE, 107(6), 1173–1190.
22.
Spanos, P. D., and Donley, M. G. (1990). “Stochastic response of a tension leg platform to viscous drift forces.” Proc. Ninth Int. Conf. on Offshore Mech. and Arctic Engrg., American Society of Mechanical Engineers, I.
23.
Spanos, P. D., and Donley, M. G. (1991). “Equivalent statistical quadratization for nonlinear systems.” J. Engrg. Mech., ASCE, 117(6), 1289–1310.
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Copyright © 1993 American Society of Civil Engineers.
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Received: Jan 2, 1991
Published online: Jan 1, 1993
Published in print: Jan 1993
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