Validation of Volterra Series Approach for Modelling Parametric Rolling of Ships
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. Although a lot of analytical techniques are available on the assessment of parametric roll in regular excitation, not many investigations have explored its occurrence in irregular seas. A consensus on the stability criteria to assess the danger due to this phenomenon in actual ocean has not yet been reached making it an active area of investigation.
A precursor to the development of stability criteria is a simple model to capture the phenomenon of parametric rolling. However, it is important that the model is not over simplified and ignores important dynamics of the process. Therefore it is necessary to perform validation studies between the simplified model and the complete nonlinear model capturing all the physics of the phenomenon.
This paper provides the validation studies of a 1-DOF (degree of freedom) simplified model for roll motion against a standard 6-DOF time domain simulation approach. The 1-DOF model is based on the Volterra series representation of the hydrostatic stiffness in waves while accounting for the heave and pitch motions of the model. It also includes a nonlinear damping model capturing the radiation and the viscous damping. The 6-DOF model solves for the nonlinear equations of motion based on Euler angles and also includes the nonlinear Froude Krylov excitations and nonlinear hydrostatic forces on the vessel. Details of the modeling in the two approaches are described and comparisons are performed to assess the validity of 1-DOF simplified model.
Keywords: GM variation; Volterra series; metacentric height; 6-DOF time domain; Large-amplitude motion; Simulation tool; Parametric roll resonance