Study on Roll Characteristics of Small Fishing Vessel : (Part 2) An Approximate Method of Solution for Nonlinear Lateral Equations

Abstract

A calculation method of solving the nonlinear coupled equations for ship sway, roll and yaw is proposed, in which the nonlinear terms of restoring moment, damping and cross-coupling dampings are taken into account. The nonlinear dampings are replaced by equivalent linearized forms with amplitude-dependent coefficients. The restoring roll moment is represented by an odd-power polynomial of roll angle. A perturbation method is applied to obtain the first-Order solution by extending Wright's method to the multi-degree ship lateral motions. The validity of the present method is confirmed through the comparisons with the roll experiments of two cylindrical models having strongly nonlinear GZ curves. Numerical examples are also presented to show that the coupling term of sway into roll has a considerable effect on the nonlinear roll response.