Parametric Rolling at Main Resonance

The parametric resonance of the induced rolling is a typical dangerous situation for the transversal stability of ships operating in longitudinal waves. In this paper are presented the results of experimental tests regarding the seakeeping performances of a 2700 dwt cargo model at full loading, in regular longitudinal waves. It was observed the induced roll motion, in the second instability domain, both at zero and design speed. There were analyzed the conditions for occurrence of the parametric resonance and there were identified the instability domains of motion. The theoretical analysis of the heave and pitch motions in longitudinal waves, in frequency domain, was performed by using a computer code based on Frank-close fit method. A satisfactory correlation between the theoretical and experimental results was found for heave and pitch motions. In order to simulate the induced rolling a typical differential coupled equations system for heave, induced roll and pitch motions was used. The numerical solution was obtained using the Runge-Kutta method. The simulation results for the ship motions at zero speed, in following regular waves, are presented. A good agreement was obtained between the numerical and experimental results in time domain.