Computer-aided simulations of large amplitude roll motions of ships in waves and of dynamic stability

Abstract

The paper deals with analytical-numerical and computer-aided methods to simulate large amplitude roll motions and to evaluate the dynamic stability of ships in waves.

A simplified but fundamental equation of roll motion is set up accounting for the characteristic nonlinearities in the damping and restoring term, the latter including the coupling with heave motion, a constant bias and regular wave excitation.

The methods employed for studying the roll response and the stability of the formulated nonlinear differential equation are a second-order perturbation expansion, a Runge-Kutta numerical procedure and alternatively an analog-digital computer code, namely CSMP (Continuous System Modelling Program). The latter is herein applied in the framework of a Computer-Aided Ship Design Procedure.

Comparisons are made with published experimental and numerical results for a frigate model, known from W.B. Marshfield and others. It is shown that the presented methods are valuable tools in evaluating the dynamic stability and in predicting the capsizing of ships in waves. However, the mathematical model implied for the roll motions needs further refinement.