Influence of righting moment curve on parametric roll motion in regular longitudinal waves

Parametric roll is a phenomenon which typically occurs in longitudinal waves. Although its theoretical existence has been known for decades, parametric roll attracted a great deal of interest in recent years. Stability accidents result from parametric roll make the topic more important because of the potential risks to money and human lives. In the present study, parametrically excited roll motion is modeled as a single degree of freedom system incorporating heave and pitch effects by means of restoring moment variations. The nonlinear roll model is solved by the averaging technique to avoid viable correlation between the responses and area under restoring moment curves. Nonlinear effects like discontinuous bifurcations were also introduced into the results. As a result, risk free regions, risky regions, risky regions due to discontinue bifurcations and extremely risky regions were determined.