A non-linear mathematical model of higher order for strong parametric resonance of the roll motion of ships in waves

Non-linear equations of ship motions in waves describing the couplings between heave, roll and pitch are investigated. A third order mathematical model is introduced, aimed at describing strong parametric excitation associated with cyclic changes in the ship restoring characteristics. A derivative model is employed to describe the coupled restoring actions up to third order. Non-linear coupling coefficients are derived in terms of hull form characteristics. In the present investigation, experimental results corresponding to excessive motions of a transom stern fishing vessel in head seas are compared to numerical simulations obtained from the derived third order non-linear mathematical model. It is shown that this enhanced model gives good results and a better comparison with the experiments than a second order model.