Bifurcations in ship rolling: experimental results and parameter identification technique

Abstract

The steady rolling response in a regular beam sea of a 1 : 50 scale model of a destroyer in the bare hull condition has been studied. The restoring moment of the hull features strongly softening characteristics. This has led to the experimental evidence of bifurcations with jump in amplitude and phase during the tests at two different wave frequencies. The high quality measurements allowed the analysis of the gathered data through a single-degree-of-freedom roll motion equation. Exact numerical solutions have been used to obtain reliable values of the coefficients of the mathematical model to be used for the roll motion simulation. Approximate perturbative solutions have then been used to obtain a description of the domains of attraction of the system. An analysis of the stability of the steady state solutions in the range of frequencies where bifurcations and jumps were detected coupled with the analysis of the change of shape of the domains of attraction with the frequency allowed the differences found between the two physical situations to be explained.