Stability Criteria for the Slow Motion Nonlinear Dynamics of Towing and Mooring Systems

Abstract

Analytical expressions for the necessary and sufficient conditions for stability of towing and mooring systems with several lines are derived based on the Routh stability criteria. These expressions are combined to provide physics-based relations for the bifurcation boundaries occurring in towing and mooring systems as a parameter is varied, and thus can be used for design of mooring and towing systems. Further, these expressions prove that several rules of thumb generally are not applicable. The special case of symmetric towing/mooring systems is covered as well. In this particular case, the analytical expressions can be simplified to derive a number of rules that can be implemented readily in design. The mathematical model consists of the horizontal plane maneuvering equations (surge, sway, yaw) of the towed/moored vessel without memory under steady current excitation, and a quasistatic model for the mooring/towing lines. The line static behavior is modeled by (i) nonlinear elastic strings (nylon, polyester); or (ii) heavy, inextensible catenaries. Other mooring line models (i.e. three-dimensional extensible finite element model) and external excitations (i.e. wind and second order mean drift forces) can be incorporated in the model.