Theoretical and Experimental Study of the Nonlinearly Coupled Heave, Pitch, and Roll Motions of a Ship in Longitudinal Waves

Abstract The loss of dynamic stability and the resulting large-amplitude roll of a vessel in a head or following sea were studied theoretically and experimentally. A ship model with three degrees of freedom (roll, pitch, heave) was considered. The governing equations for the heave and pitch modes were linearized and their harmonic solutions were coupled with the nonlinear equation governing roll. The resulting equation, which has time-varying coefficients, was used to predict the response in roll. The principal parametric resonance was considered in which the excitation frequency is twice the natural frequency in roll. Force-response curves were obtained. The existence of jump phenomena and multiple stable solutions for the case of subcritical instability was observed in the experiments and found to be in good qualitative agreement with the results predicted by the theory. The experiments also revealed that the large-amplitude roll is dependent on the location of the model in the standing waves.