Coupled dynamic analysis between floating marine structures and flexible members such as mooring lines and risers, is a challenging work in the ocean engineering field. Coupled analysis on mooring-buoy interactions has been paid more and more concern for recent years. For floating offshore structures at sea, the motions driven by environmental loads are inevitable. The movement of mooring lines occurs due to the excitation on the top by floating structures. Meanwhile the lines restrict the buoy’s motion by forces acting on the fareleads. Positioning is the main function of mooring system, its orientation effects can’t be ignored for floating structures such as semi-submersible, FPS, and TLP, especially when the buoy’s equilibrium position shifting to another place. Similar as hydrostatic restoring forces, mooring force related with the buoy’s displacement can be transformed into mooring stiffness and can be added in the differential equations of motion, which is calculated at its equilibrium point. For linear hydrodynamic analysis in frequency domain, any physical quantity should be linear or be linearized, however mooring stiffness is nonlinear in essence, so the tangent or differential stiffness is used. Steel chains are widely used in catenary mooring system. An explicit formulation of catenary mooring stiffness is derived in this article, which consists of coupled relations between horizontal and vertical mooring forces. The effects of changing stiffness due to the shift of equilibrium position on the buoy’s hydrodynamic performance are investigated.

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