Determination of Roll Motion for a Floating Body in Regular Waves

Abstract

This paper deals with the mathematical modelling of the roll motion of a floating body in regular waves in beam seas for non-restrained conditions. The hydrodynamic forces are computed with the application of strip theory, and frequency dependent sectional added mass moment of inertia and damping are integrated over the length of the body by using the Frank close fit method. The governing equation that arises after balancing the hydrodynamic and exciting forces is reduced to non-dimensional form prior to converting it into the frequency domain by applying the Laplace transform technique. Numerical experiments have been carried out for a vessel of 19 190 t displacement under the action of a small amplitude sinusoidal wave of 11.2 s periodicity to obtain the roll response. This has been done in order to check the roll response computed numerically by developing a numerical model, SHIPMOT-R, where the Runge-Kutta-Gill method is adopted. A good agreement has been achieved between the time histories of roll motions computed numerically and derived analytically for zero and nonzero forward speeds. It is observed that the roll amplitude increases with the increase of vessel speed. This modelling technique would be very useful for ascertaining a vessel's safety requirements in the early stages of design.