Nonlinear coupled motions for a given two-point tension mooring system

The nonlinear behaviors of plane coupled motions for a given two-point tens ion mooring system, are discussed in the present paper. For a cylinder moor ed by two taut lines under the action of gravity, buoyance and forces due t o wave-current and mooring lines, a mathematical model of motions with thre e degrees of freedom is established. The steady solution and stability are analyzed. By integrating the equations of motions, history, phase map and P oincare map are obtained. The Liapunov exponents are also computed. The num erical results show that: the horizontal movement will increase, and stabil ity will also increase as the steady force increases. The amplitude of resp onses will decrease as time-dependent forces decrease. Because of the geome tric nonlinearity, there exist many windows bifurcating to pseudo-periodic or multi-periodic solution. The bifurcating patterns may be different. The behaviors are very complex. Under wave excitation alone, the motions are no nsymmetrical but still symmetrical statistically.