Analytical expressions of the bifurcation boundaries for symmetric spread mooring systems

Abstract

For a general symmetric Spread Mooring System .(SMS), the five necessary and sufficient conditions for stability are derived analytically. It is shown that only two conditions are dominant in symmetric ship moorings. The equations derived in this paper provide analytical means for determining static and dynamic loss of stability, as well as elementary singularities and roots to chaos, of symmetric SMS configurations, such as those recommended by the American Petroleum Institute. Thus, first it becomes easy to identify the morphogenesis occurring when a bifurcation boundary is crossed; and second, it is possible to determine the dependence of a symmetric SMS on any design parameter—such as mooring line length, orientation, pretension, etc. Theoretical results are verified by comparison to numerical results generated with nonlinear dynamics and codimension one and two bifurcation theory. The mathematical model of the SMS consists of the nonlinear third order manoeuvring equations without memory of the horizontal plane slow motion dynamics—surge, sway, and yaw—of a vessel moored to several terminals. Mooring lines are modeled as synthetic nylon ropes, chains, or steel cables. External excitation consists of time independent current, wind, and mean wave drift forces.