Nonlinear modes of large-amplitude ship motion with roll-pitch coupling

Abstract

This research pertains to the dynamics of a ship taking into account the nonlinear coupling of roll and pitch degrees of freedom. Such nonlinearity has critical implications for large-amplitude ship motion, and can thus be useful in understanding conditions leading to capsize. The nonlinear normal modes of the conservative system are determined numerically and are displayed in a frequency-energy plot, which clarifies the bifurcations that connect the various branches of periodic orbits. Numerical simulations show that, although the solutions on most branches result in capsize if their energy is beyond a common critical value, a few branches contain stable solutions at higher energies that do not lead to capsize, suggesting possible methods of capsize mitigation. We study a class of solutions analytically using a complexification-averaging technique. Finally, we run a simulation in the case of light damping in roll with high-energy initial conditions, illustrating transitions between branches that occur in the direction of decreasing energy on the frequency-energy plot.