Nonlinear and Non-Gaussian Aspects of Morison Equation Induced Fatigue Damage
Authors: Wang Jin , Lutes L.D. 
Published: October 2008

Abstract
Simulation results are presented for the fatigue damage caused by the nonlinear and non-Gaussian structural response induced by the Morison equation wave loading. Four versions of the Morison equation are considered, and various response characteristics are identified as factors affecting fatigue damage. The relative importance of the various factors is investigated and quantified. In comparing the different Morison equation models, the rms value is shown to be the most important factor in predicting fatigue damage and the non-Gaussian effect is second in significance, while the variation in average frequency and the spectral shape are less important. For deepwater compliant offshore structures, the non-Gaussian effect is found to be more significant in an intermediate region than for either the inertia or the drag dominated region.

Introduction
The Morison equation is one of the most widely used models to describe the hydrodynamic wave forces acting on a slender body (Morison et al. 1950, Sarpkaya and Isaacson 1981). Several simplified versions of the Morison equation are often used as well as the full nonlinear fluid-structure interaction model. Fatigue damage is estimated in this study for several of these models in order to investigate the practical consequences of choosing one or another model.
Fatigue damage, in general, can be shown to be affected by at least four factors, each of which may vary from one Morison equation model to another. Such factors are: standard deviation, average frequency, shape of the power spectral density or "narrow-bandness," and probability distribution or "non-Gaussianity." Greater understanding is sought in this study by considering not only how fatigue damage predictions vary from one Morison equation model to another, but also how these four individual factors vary. For example, two different models might be found to both underpredict the fatigue damage but for quite different reasons since one might underpredict the response standard deviation while the other ignored non-Gaussian effects. A clear picture of the problem should result from identification of the ways in which each model is accurate and those in which it is inaccurate. The study particularly focuses on non-Gaussian effects since these have received less prior study than the other significant factors.
The wave loadings on offshore structures are often quite complicated and random. If the wave loading can be idealized as a stationary Gaussian process and the structure behaves linearly, then the structural response and stress time histories will also be Gaussian and, thus, completely described by the first and second moments of the response processes, and complexities in the problem can be greatly reduced. However, there are cases for which the Gaussian randomprocess assumption is no longer valid. Field observations and mathematical analysis of the Morison equation both indicate that the actual structural response and stress time histories may be considerably different from the Gaussian distribution (Heavener, et al. 1985, Hooper and Swannell 1990, Hu 1990). Furthermore, limited studies of fatigue damage accumulation (Lutes et al. 1984, Winterstein 1985) have shown that fatigue life can be significantly affected by the non-Gaussianity of the random processes studied.