Numéro : 2076 - Year : 1988
Jump phenomena in nonlinear rolling in a stochastic beam sea
A.FRANCESCUTTO, Professor Associato, Instituto di Architettura Navale , Universita di Trieste, I.
The extensive analysis carried out in last years nonlinear rolling, allowed many researchers to discover some very particular features of this motion. In a deterministic beam sea, it appeared the possibility of resonance conditions different from synchronism, in particular subharmonic oscillations in both the upright and heeled condition. The resonance peaks as a function of tuning ratio are bent, mainly as a consequence of righting arm nonlinearity, so that in a suitable range of frequencies the oscillation can have three steady states of very different amplitude. The appearance of different states belonging to the same excitation intensity can play an important role in seakeeping and stability.
An open problem was constituted, until now, by the nonlinear rolling in a stochastic beam sea, always treated as a process with sufficiently broad band to have no possibility of jump phenomena. To clarify this puzzling aspect, a nonlinear model with the excitation represented by white noise filtered through a linear filter was studied in detail. Applying the method of Gaussian closure of moments, the roll variance has been obtained. The bandwidth was allowed to vary SO as to represent roughly ITTC spectrum and then decreased progressively.
The global behaviour is similar to that of deterministic excitation, but here referred to the roll variance, with the characteristic bending of the curves. If the excitation is sufficiently narrow band, the possibility of multiple states is conserved. The results show that it is not necessary a monochromatic sea to have the possibility of jump phenomena, that could appear, for example, in the case of swells. Similar results are to be expected in the case of subharmonic resonances.
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