Catenary is increasingly used as mooring-line and riser system as the water depth gets larger due to its lower cost and easier installment. Its dynamic response and restoring performance become more complicated, as the length of the mooring-line become larger, and the structural and fluid dynamics the mooring-line become consequently more obvious. Compared to the quasi-static method where the static restoring force is mainly involved, the dynamic behaviors and its hysteresis of the catenary mooring-line are considered here so as to comprehensively examine the non-linearly restoring performance of mooring-lines. Based on the 3d dynamic vector equations along with the modified FEM simulations, the hysteresis character of the restoring stiffness and the influences of the catenary dynamics on its restoring performance are presented and discussed.

It is found that, principally owing to the damping and inertial effect coming from the fluid and structural dynamics, the restoring force of the mooring-line depends on both the structural displacement and velocity. Moreover, the dynamic stiffness behaves as a hysteresis loop, instead of a curve. Our numerical results show that the energy consumption during one period rises nonlinearly with the increase of the body frequency ωd and amplitude A0. And, the influence of nonlinear restoring stiffness on the structural response along with the slack-taut phenomenon caused by structural /hydrodynamic inertia and damping is discussed.

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