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The objective of the present work was to develop an approximation to the conventional mixed linear-plusquadraticship roll damping model so that analytical obstacles could be overcome in the application of the functional series expansion to nonlinear ship rolling. A mixed linear-plus-cubic approximation was found to be reasonable for this purpose. In the course of analyses, there were indications that this model may be closer to an "equivalent approach" than to an "approximation."

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The methods and results of a digital computer simulation of a nonlinear random process are described. The process was one of the simpler analytical models for ship roll. The main objective of the simulation was to obtain "empirical" data on the distribution of roll maxima, and to test these data against the corresponding theoretical distribution for a random Gaussian (linear) process. Effect was made to confine the variation of parameters within ranges appropriate to ship rolling. Within this range of parameters, the frequency band of response is sufficiently narrow that the theoretical distribution of maxima of the corresponding linear process tends toward the Rayleigh. The results obtained by objective statistical test procedures indicate that the distribution of maxima of the nonlinear process is not Rayleigh in a substantial portion of the parameter range of interest. However, it was possible to conclude from the results that the Rayleigh assumption is reasonable for an important class of engineering predictions; that of the prediction of average, "significant" and "1/10 highest" maxima from a knowledge of the spectrum of roll.

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