A theoretical and experimental investigation of indirectly excited roll motion in ships

The phenomenon of indirectly exciting the roll motion of a vessel due to no nlinear couplings of the heave, pitch and roll modes is investigated theore tically and analytically. Two nonlinear mechanisms that cause large-amplitu de rolling motions in a head or following sea are investigated. The first m echanism is internal or autoparametric resonance and the second is parametr ic resonance. The energy put into the pitch and heave modes by the wave exc itations may be transferred into the roll mode by means of nonlinear coupli ng among these modes; thus, the roll can be indirectly excited. As a result , a ship in a head or following sea can spontaneously develop severe rollin g motion. In the analytical approach, the method of multiple scales is used to determine a system bf nonlinear first-order equations governing the mod ulation of the amplitudes and phases of the system. The fixed-point solutio ns of these equations are determined and their bifurcations are investigate d. Hopf bifurcations are found in the case of two-to-one internal resonance . Numerical simulations are used to investigate the bifurcations of the ens uing limit cycles and how they produce chaos. Experiments are conducted wit h tanker and destroyer models. They demonstrate some of the nonlinear effec ts, such as the jump phenomenon, the subcritical instability, and the coexi stence of multiple solutions. The experimental results are in good qualitat ive agreement with the results predicted theoretically.