DYNAMIC INSTABILITY IN QUARTERING SEAS .3. NONLINEAR EFFECTS ON PERIODIC MOTIONS

The loss of stability of the horizontal-plane periodic motion of a ste ered ship in waves is investigated. In earlier reports we referred to the possibility of a broaching mechanism that will be intrinsic to the periodic mode, whereby there will exist no need for the ship to go th rough the surf-riding stage. However, about this point the discussion was essentially conjectural, In order to provide substance we present here a theoretical approach that is organized in two stages: Initially , we demonstrate the existence of a mechanism of parametric instabilit y of yaw on the basis of a rudimentary, single-degree model of maneuve ring motion in waves. Then, with a more elaborate model, we identify t he underlying nonlinear phenomena that govern the large-amplitude hori zontal ship motions, considering the ship as a multi-degree, nonlinear oscillator. Our analysis brings to light a very specific sequence of phenomena leading to cumulative broaching that involves a change in th e stability of the ordinary periodic motion on the horizontal plane, a transition towards subharmonic response and, ultimately, a sudden jum p to resonance. Possible means for controlling the onset of such undes irable behavior are also investigated.