Theoretical Research On Parametric Rolling Of Ships In Head Seas

Parametric rolling is a kind of the resonance phenomena of ship motions, caused by the periodical fluctuations of stability parameters of ships in waves. Parametric rolling is one of ship non-linear motions, which has negative effects on ship running efficiency and strongly imperils passenger and cargo on board and ship hull structure. Research for parametric rolling was early taken in 1930s, and in recently ten years, parametric ship rolling motion in a real sea has been a hot topic. In the present thesis, parametric rolling of ships in regular waves and irregular long-crest waves is investigated by time-domain simulation on the base of frequency-domain potential theory of ship motions. Second-order non-linear equations of ship motions in waves including the coupling of the heave, roll and pitch motions are established. Parametric resonance and incidence wave coefficients in the equations are analyzed by the Taylor expansion. Irregular long-crested waves, wave exciting forces and metacentric height fluctuation are simulated by the method of linear superposition. Based on the theoretical model, computational code'PARR'program is developed and a 4000teu Panamax container ship is selected as an example for the parametric rolling resonance investigation. The effects of wave height, wave length, ship speed, and the relation between wave frequency and roll nature frequency on parametric rolling in regular waves are discussed. The threshold boundaries for parametric rolling are presented, and the influence of parametric rolling on the velocities and accelerations at specified locations on the ship hull are investigated. For the cases in irregular waves, the indirect spectrum method is presented in the purpose of measuring the probability of parametric rolling; and the effects of wave group are specially considered.