Hineno®® also calculated the relative motion of a semi—submersible in this kind of 
nonlinear wave, assuming a linear response to the excitation by the waves. 
Hy = 11.6m 
To = 16.1 sec 
— MAXIMA 
—-— MINIMA 
——- LINEAR 
Fig. 12.14. Cumulative probability distribution function of wave amplitude. 
(From Hineno.®’) 
Hig = 11.6m 
To = 16.1 sec 
— MAXIMA 
—— MINIMA 
—— LINEAR 
2 
Zines 
Fig. 12.15. Probability density distribution function of wave amplitude. 
(From Hineno.®) 
12.7.2 Wide-—Banded Case 
J. F. Dalzell** (1984) extended this technique further. He did not assume narrow 
bandedness of the response and did not truncate the functional polynomials at n=2 but 
continued to n=3. He thus formulated the technique for calculating the probability distri- 
bution function of extremes of the nonlinear responses to Gaussian inputs. Here the 
characters of the nonlinear frequency response functions up to degree 3 are assumed to be 
known from the analysis as discussed in Section 11.5. The nonlinear response Y(t) to 
Gaussian input X(r) is expressed by 
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