Comparison of stochastic stability boundaries for parametrically forced systems with application to ship rolling motion

TL;DR

This paper investigates the stability boundaries of ship rolling motion under stochastic parametric excitation, offering new theoretical insights and validating existing formulas through numerical examples.

Contribution

It introduces a novel theoretical explanation for instability mechanisms in stochastic seas and confirms the applicability of existing formulas with numerical validation.

Findings

New theoretical explanation for instability mechanisms

Validation of Roberts and Dostal's formulas

Numerical confirmation of stability boundaries

Abstract

Numerous accidents caused by parametric rolling have been reported on container ships and pure car carriers (PCCs). A number of theoretical studies have been performed to estimate the occurrence condition of parametric rolling in both regular and irregular seas. Some studies in random wave conditions have been the approximate extension of the occurrence conditions for regular waves (e.g. Maki et al). Furthermore, several researches have been based on the stochastic process in ocean engineering (Roberts and Dostal). This study tackled the parametric rolling in irregular seas from the stability of the system's origin. It provided a novel theoretical explanation of the instability mechanism for two cases: white noise parametric excitation and colored noise parametric excitation. The authors then confirmed the usefulness of the previously provided formulae by Roberts and Dostal through numerical examples.