Nonlinear and Stochastic Aspects of Parametric Rolling Modeling

This paper addresses, starting from an extensive series of tests in longitudinal regular waves (already done) and irregular waves (in progress), the problems connected with the threshold formulation for para- metric rolling and its amplitude modeling above threshold. Both head and following waves have been considered, also in view of the greater attention to head sea conditions called for during International Maritime Organisation Subcommittee on Stability and Load Lines, and on Fishing Vessels Safety (IMO/ SLF) discussion on the revision of the Intact Stability Code. Particular attention is given in the regular wave case to the nonlinear damping, nonlinear restoring, and nonlinear parametric excitation terms. The math- ematical models so developed are "compared" with experimental results by means of an ad hoc parameter estimation technique. It is, on the other hand, well known that several different thresholds can be proposed in the case of irregular waves and that the nonlinear modeling of roll motion variance above threshold is at present not properly addressed. Here, too, a series of experiments will be conducted in the presence of narrow band irregular waves having the bandwidth as parameter. A mathematical description of the nonlinear parametric rolling can be obtained with the use of approximate analytical techniques.