Analytical Expressions of the Stability and Bifurcation Boundaries for General Spread Mooring Systems

Abstract

Spread mooring systems (SMS) are labeled as general when they are not restricted by conditions of symmetry. The six necessary and sufficient conditions for stability of general SMS are derived analytically. The boundaries where static and dynamic loss of stability occur also are derived in terms of the system eigenvalues, thus providing analytical means for defining the morphogenesis that occurs when a bifurcation boundary is crossed. The equations derived in this paper provide analytical expressions of elementary singularities and routes to chaos for general mooring system configurations. Catastrophe sets are generated first by the derived expressions and then numerically using nonlinear dynamics and codimension-one and -two bifurcation theory; agreement is excellent. The mathematical model consists of the nonlinear, third-order maneuvering equations without memory of the horizontal plane, slow-motion dynamics—surge, sway, and yaw—of a vessel moored to several terminals. Mooring lines can be modeled by synthetic nylon ropes, chains, or steel cables. External excitation consists of time-independent current, wind, and mean wave drift forces. The analytical expressions derived in this paper apply to nylon ropes and current excitation. Expressions for other combinations of lines and excitation can be derived.