Non-linear Dynamics of Parametric Roll of Container Ship in Irregular Seas
Abhilash Somayajula and Jeffrey Falzarano
Parametric motion is the phenomenon where a structure is excited into large amplitude motion even when there is no direct excitation. A well-known example of this type of motion is the parametric roll of ships in head or following seas. Parametric roll of container ships in head seas is relatively a new problem which has gained much importance after the catastrophic incidence of APL China in 1998. Many studies have investigated this phenomenon in the case of a ship being excited in regular waves. However, ships do not encounter regular waves in the actual ocean. So, it is imperative to study the importance of parametric roll in irregular seas.
In this paper the analysis of roll equation of motion is performed by nonlinear modeling. The problem of parametric roll is approached as a non-linear dynamics problem with due consideration to nonlinear time varying hydrostatics as well as the nonlinear damping. A nonlinear damping model is used to approximate the actual viscous damping in the system. The variation of the roll righting arm with time has been modeled using a Volterra series representation which includes the hydrostatic non-linearity.
Various realizations of the roll motion have been simulated and analyzed to study the ergodic behavior of the phenomenon. The paper also discusses future ideas of how to analyze parametric roll in irregular seaways.
Keywords: GM variation; Volterra series; metacentric height; Parametric roll resonance