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Susceptibility of the roll equation to the bifurcation phenomenon depending on the damping coefficient value and form of the roll damping formula

Wawrzyński W.

Zeszyty Naukowe Akademii Morskiej w Szczecinie

2017

nr 52 (124)

161--169

This paper deals with the susceptibility of the roll equation to the bifurcation phenomenon depending on the damping coefficient value and form of the roll damping formula. Generally, the bifurcation phenomenon depends mainly on the shape of the righting arm curve (GZ curve), but roll damping also has a significant impact. The commonly used formulas for roll damping are presented, as well as values of the linear equivalent roll damping coefficient, calculated according to the simple Ikeda method. Values of the linear equivalent roll damping coefficient were calculated for a wide spectrum of roll amplitudes and roll frequencies for two ships. The loading conditions for these ships were selected to show different GZ curve characteristics. One ship has a softening spring characteristic and the second has a hardening spring characteristic. For these two ships, a number of calculations of roll spectra are presented where the bifurcation phenomenon occurs. Calculations were made for different damping coefficient values and forms of the roll damping formula.

Prediction of the natural frequency of ship’s roll with regard to various models of roll damping

Krata P., Wawrzyński W.

Journal of KONES

2016

Vol. 23, No. 3

289--296

One of the most important dynamic phenomenon recognized as dangerous to seagoing ships is the resonance gain of rolling. This may occur due to nonlinearity of ship response in resonance conditions, i.e. when the encounter wave frequency is similar to the natural frequency of ship roll motion. Such coincidence should be avoided therefore shipmaster steers clear of some configurations of speed and course resulting in potential synchronous rolling. Nowadays, according to the IMO Intact Stability Code the natural period of roll is determined with the use of very simplified GM-based formula. The paper deals with the problem of more sophisticated prediction of ship’s natural rolling frequency with the use of the one degree-of-freedom roll equation with regard to nonlinear restoring moment. A special emphasis is put on the damping coefficient modelling which remains one of the crucial issues in terms of rolling simulation. Two typical approaches to the damping coefficient estimation are tested, the linear and the nonlinear one according to Ikead’s method. The set of ship roll simulations is carried out for a wide range of excitation frequency and a variety of exciting moment. The results of computation focused on the natural frequency of ship roll prediction are compared to assess the influence of damping model selection.