ANALYTICAL EXPRESSIONS FOR STABILITY AND BIFURCATIONS OF TURRET MOORING SYSTEMS

The eight necessary and sufficient conditions for stability of turret mooring systems (TMS) are derived analytically. Analytical expressions for TMS bifurcation boundaries where static nd dynamic loss of stabil ity occur are also derived. These analytical expressions provide physi cs-based means to evaluate the stability properties of TMS, find eleme ntary singularities, and describe the morphogeneses occurring as a par ameter (or design variable) or group of parameters are varied. They el iminate the need to compute numerically the TMS eigenvalues. Analytica l results are verified by comparison to numerical results generated by direct computation of eigenvalues and their bifurcations. Catastrophe sets (design charts) are constructed in the two-dimensional parametri c design space to show the dependence of design variables on the stabi lity of the system. The TMS mathematical model consists of the nonline ar horizontal plane-surge, sway and yaw-fifth-order, large drift, low speed maneuvering equations. Mooring lines are modeled quasistatically by catenaries. External excitation consists of time independent curre nt, steady wind, and second-order mean drift forces.