Non‐Normal Descriptions of Morison‐Type Wave Forces
Publication: Journal of Engineering Mechanics
Volume 113, Issue 2
Abstract
The usual description of the force exerted by a stochastic wave is extended to include the non‐normality of that force. In particular, the Morison equation is used to describe the force resulting from a sea state with stationary, normally distributed water velocities. Thus, the force non‐normality which is considered results only from the nonlinearity of the Morison equation. The fourth order cumulant function is used to describe the non‐normality of the force. The same information is also represented as a three‐dimensional spectral density, which results from a three‐fold Fourier transform of the cumulant function. Closed form solutions are not found, but the results of a power series expansion method appear to give good approximations. Potential applications of the results involve determinations of the non‐normality of the response of a structure subjected to a Morison‐type wave force. Such response non‐normality can then be used to substantially Improve estimates of structural failure, due to either first passage or accumulation of fatigue damage.
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References
1.
Borgman, L. E. (1967). “Random hydrodynamic forces on objects.” Ann. Math. Statist., 38, 37–51.
2.
Deutsch, R. (1962). Nonlinear transformation random processes, Prentice‐Hall, Inc., Englewood Cliffs, N.J.
3.
Grigoriu, M. (1984). “Crossings of non‐Gaussian translation process.” J. Engrg. Mech., ASCE, 110(4), 610–620.
4.
Hu, S.‐L. J. (1984). Effects of nonnormality on stochastic structural dynamics and fatigue, thesis submitted to Rice University, at Houston, Tex., in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
5.
Kotulski, Z., and Sobczyk, K. (1981). “Linear systems and normality.” J. Statistical Physics, 24(2), 359–373.
6.
Lin, Y. K. (1976). Probabilistic theory of structural dynamics, McGraw‐Hill Book Company, New York, N.Y.
7.
Lutes, L. D., et al. (1984). Stochastic fatigue damage accumulation.” J. Struct. Engrg., ASCE, 110(11), 2585–2601.
8.
Lutes, L. D., and Hu, S.‐L. J. (1986). “Nonnormal stochastic response of linear systems.” J. Engrg. Mech., ASCE, 112(2), 127–141.
9.
Morison, J. R., et al. (1950). “The force exerted by surface waves on piles.” Petrol. Trans., AIME, 189, 149–154.
10.
Pierson, W. J., and Holmes, P. (1965). “Irregular wave forces on a pile.” J. Waterways and Harbors Div., ASCE, 91(4), 1–10.
11.
Price, R. (1958). “A useful theorem for nonlinear devices having Gaussian inputs.” IRE Trans. of Info. Theory, 69–72.
12.
Sarpkaya, T., and Isaacson, M. (1981). Mechanics of wave forces on offshore structures, Litton Educational Publishing, Inc.
13.
Stratonovich, R. L. (1963). Topics in the theory of random noise, Gordon and Breach Science Publishers, Inc.
14.
Taylor, R. E., and Rajagopolan, A. (1982). “Dynamics of offshore structures.” J. Sound and Vib., 83, 401–416.
15.
Tickell, R. G. (1977). “Continuous random wave loading on structural members.” The Struct. Engr., 55(5), 209–222.
16.
Winterstein, S. R. (1985). “Non‐normal responses and fatigue damage.” J. Engrg. Mech., ASCE, 111(10), 1291–1295.
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Copyright © 1987 ASCE.
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Published online: Feb 1, 1987
Published in print: Feb 1987
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