Subharmonic oscillations in nonlinear rolling

In this paper the rolling motion of a ship is examined with particular regard to the possibility of obtaining oscillations which are subharmonic to the excitation frequency. Three different mechanisms are found to be responsible for this phenomenon, the importance of which has already been recognized in the context of ship stability. The first is related to a strong symmetric or non-symmetric nonlinearity in the righting arm. The second is linked to the harmonic composition of sea waves and the third to the well known parametric excitation caused by coupling between different ship motions in a following sea.The onset of subharmonics is related to a threshold value for the excitation strongly depending on damping. The more appropriate analytical methods for a theoretical study of each mechanism are suggested.