Estimation of Nonlinear Ship Roll Damping from Free-Decay Data

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Abstract
A common method of assessing the damping present in ship rolling motion is to perform a free-decay experiment, in which, in the absence of waves, the ship is given an initial roll amplitude and then released. By processing the resulting decaying, oscillatory trace it is possible to estimate quantitatively the degree of damping, even when this is nonlinear. In this paper an approach to the estimation of nonlinear damping is proposed which involves the use of a cubic spline interpolation of the peak amplitudes, followed by a parametric identification procedure. This method is first applied to some simulation data and then to some real free-decay data, obtained from a scale model of a ship, with various initial conditions. The experimental data are analyzed using two alternative parametric forms, that is, linear-plus-quadratic and linear-plus-cubic damping. A principal advantage of the proposed technique is that, because nonlinearities in the restoring moment are properly accounted for, it is not limited to small angles of roll. Thus it can be applied to free-decay data relating to very large initial roll amplitudes.

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