A simplified 2½-degree of freedom time-domain model with non-linearity for the simulation of parametric roll

Abstract

In this paper, a simplified 2½-degree of freedom time-domain numerical method with non-linearity is developed, presented in detail and validated for simulating parametric roll. The method is termed 2½-degree of freedom since; it first linearly couples heave and pitch via a three-dimensional frequency-domain pulsating source method. The roll equation of motion is – then – solved in the time domain with, non-linear damping and non-linear parametric excitation taken into account and formulated in terms of heave-pitch-wave profile influence on roll. In other words, heave and pitch motions influence roll but roll motion does not influence heave and pitch back hence, the term 2½-degree of freedom. The mathematical formulation of the proposed method is presented in detail and has been developed into an in-house numerical model. Subsequently, the numerical model is applied to a modern container ship. Experimental results from the literature are utilized for validation. Predicted results show very good agreement with experiments and demonstrate the ability of the proposed method to accurately capture the influence of various parameters affecting parametric roll.