Dynamic instability of a parametrically excited ship rolling model

Abstract

This paper investigated the nonlinear interaction behavior of the heave-excited rolling of ships. The coupled heave-roll system is shown to have two coupling terms due to parametric excitation: A linear term, usually included in most roll stability analyses, which causes Mathieu's type of instability, and a quadratic term which is often ignored. the significance of including the quadratic coupling effect of heave is studied. The analytical conditions of heave-excited ship rolling are derived using the harmonic balance method. It is shown that, from the viewpoint of dynamic stability analysis, the quadratic coupling term is not a high order term and should be included in the governing equation of motion. the parametrically excited heave-roll behavior should be modelled by a Hill's equation instead of a Mathieu's equation. Comparisons of the instability regions predicted by these two models are made. The important factors affecting the instability regions are also discussed.