Nonlinear Coupled Motions for a Given Two-Point Tension Mooring System

The nonlinear behaviors of plane coupled motions for a given two-point tension mooring system, are discussed in the present paper. For a cylinder moored by two taut lines under the action of gravity, buoyance and forces due to wave-current and mooring lines, a mathematical model of motions with three degrees of freedom is established. The steady solution and stability are analyzed. By integrating the equations of motions, history, phase map and Poincare map are obtained. The Liapunov exponents are also computed. The numerical results show that: the horizontal movement will increase, and stability will also increase as the steady force increases. The amplitude of responses will decrease as time-dependent forces decrease. Because of the geometric 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 nonsymmetrical but still symmetrical statistically.