A Statistical Study on the Rolling Motion with Non-Linear Roll Damping

Abstract

In this paper, we deal with the statistical estimation of the rolling motion with non-linear roll damping in irregular waves. The term which is proportional to the square of the roll angular velocity, namely B_2 φ^^・∣φ^^・∣ is considered as non-linear roll damping. We take some approximate methods to obtain the statistical data of non-linear roll motions. In some methods, we use two kinds of equivalent linearlized roll damping instead of non-linear roll damping, and the calculations are carried out linearly. In other method, the time histories of rolling motion are obtained by numerically solving the equations with non-linear roll damping term, and we can get the statistical data to analyze the time histories. Using these methods, we calculated some examples in the case of a container ship, and discuss the effects of the difference among roll damping terms from the statistical point of view.