Nonlinear Response of Moored Floating Structures in Random Waves and its Stochastic Analysis : Part 1. Theory and Model Experiments

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This paper deals with stochastic analysis of slow drift responses(forces and motions) of floating structures moored in random seas and their statistical predictions. First the study review for slow drift forces causing the slow drift motion is described, and four problems which must be solved in future are discussed. Second it is shown that nonlinear responses (total second order responses) including the slow drift responses can be represented by a two term Volterra functional series. Physical meanings of kernel functions in the functional series are investigated from a viewpoint of transfer functions(or frequency response functions). It is shown that the kernel functions can be estimated not only from bispectral analyses of experimental data but also by numerical calculations based on the potential theory. Furthermore on the basis of the mathematical fact that the second term in the Volterra functional series can be expressed by an equivalent linear process of instantaneous wave power in stochastic sense, new functional model is developed. This is based on the Wiener filter theory. This model is used to solve the problems excluded in the investigations obtained up to now. The problems are as folows: a) Hydrodynarnic forces of slow drift motion in still water are modified in waves; b) Newman- Pinkster's approximation for slowly varying drift forces does not satisfy the condition of physical causality. Comparisons between simulated results and experimental ones have been conducted in both frequency and time domains. Main results are as follows: 1) Viscous drift force exists in addition to the drift force driven from the potential theory and it becomes significant compared with the potential drift force for large wave height. It is shown that the approximate method which takes into account the viscous drift force; 2) The hydrodynamic forces of slow drift motions are modified in waves and this phenomenon is caused not only by the wave drift damping ( speed dependence of added resistance in waves) but also by increase of viscous damping force in waves. The ratio between the damping force in waves and that in still water was not more than 1.6 in the experiments which we carried out during this research project. But the problem why the hydrodynamic forces in still water are modified in waves remains completely unsolved; 3) It has been confirmed that the experimental and simulated results are in good agreement with each other provided we know how much the added mass and the damping forces in still water are modified in waves. Finally a theory of probability density functions (p.d.f.'s) is developed for an instantaneous total second order response and its maxima, in order to predict 1/n th highest mean amplitudes and extreme statistics of total second order responses. New formula for the total second order p.d.f.'s which include not only quadratic but also linear responses are derived. These p.d.f.'s can be represented by the generalized Laguerre polynomials of which the first term is a Gamma p.d.f. consisting of three parameters. Assuming that the response and its time derivative processes are mutually independent, the 1/n th highest mean amplitude can be evaluated numerically from the derivative of the instantaneous response p.d.f.. This method is first applied to the sway motions of moored floating semi-circular and rectangular two dimensional cylinders, and the applicability of the method is studied by comparisons with Naess' exact solution. The variation of the 1/n th highest mean amplitude of the total second order response is then investigated following increases in damping and restoring forces. And comparisons between the experimental results and the estimated ones obtained from the present theory are carried out. The applicability of the present theory has been confirmed. The results are as follows: 1) It is confirmed through comparisons with Naess' exact solution that the present method is an accurate approximation for pure second order responses(slow drift responses); 2) The p.d.f. of the total second order response differs from that of the pure second order response. In fact it becomes a widely-banded distribution with an increase in the damping coefficient. Additionally it significantly deviates from Gaussian p.d.f.; 3) It is confirmed that the usual prediction method based on the Longuet-Higgns' method sigTlificantly underestimates the measured results while the present method estimates them very well. And it is shown that the extreme response of the total second order response is greater than that based on the assumption of the pure second order response.
独立行政法人海上技術安全研究所の論文
1990-07-30

Nonlinear Response of Moored Floating Structures in Random Waves and its Stochastic Analysis : Part 1. Theory and Model Experiments

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