Development of a semi-analytical method for the efficient prediction of parametric roll

• A semi-analytic method for parametric roll simulation is introduced.
• The nonlinear restoring component is formulated in a simplified form for nonlinear roll.
• The concept of the transfer function is validated for the leading component of metacentric height.
• The simulation results for parametric roll of modern containerships are compared with those of IRF simulation.
• The accuracy of efficiency of the semi-analytic formulation is validated by comparative study.

A semi-analytical approach to the simulation of the parametric roll motions of container ships in head seas is presented. In the proposed 1.5-degree of freedom model, the nonlinear change in the transverse stability induced by the vertical motions and wave elevation is approximated by investigating the relationship between the restoring lever (GZ) and the metacentric height (GM) in waves. In particular, the variations in the GM in irregular waves are modeled by the transfer functions of the mean value and first harmonic component on the basis of the assumption of superposition. Using the derived formula, the quantitative prediction of parametric roll motion as well as the susceptibility to such motion in regular and irregular waves is conducted. A comparison with the results of a weakly nonlinear time-domain method, namely, the impulse response function method based on the hydrodynamic coefficients of strip theory, is carried out to validate the proposed model. Not only the accuracy and efficiency of the present approach but also the stochastic properties of parametric roll in random seas are examined considering the sensitivities and uncertainties in the computations.