Analysis and validation of ad hoc nonlinear roll motion models

Abstract

To study the subject of nonlinear roll motion, which is the most difficult one to formulate, a number of mathematical models are used. These models emphasize different aspects of the motion and concentrate on particular characteristics of the phenomenon. Most of the time nonlinearities are introduced to the equation of motion through restoring and damping moments. In general, it is assumed that linearity of the inertia and exciting moment terms are not violated. In this study, an ad hoc nonlinear equation of nonlinear roll motion describing a ship’s rolling in beam waves at the resonance condition has been analyzed. By changing the nonlinear damping and restoring terms in the equation, ten different expressions are derived and solved by a form of harmonic balance method. Validity of the estimated nonlinear roll amplitudes obtained from the derived expressions are investigated through comparison with the experimental results of three ship models, which have been published previously.