Dynamic Analysis of Mooring Systems (Bifurcations).

Abstract

The dynamic response of autonomous mooring systems under time independent external excitation is studied. The mathematical model of the system accounts for important elements of motions such as higher order hydrodynamic derivatives, external excitation and mooring line nonlinearities. Three qualitatively different mooring line models are developed and used to cover a wide range of applications ranging from an extensible taut nonlinear string to an inextensible heavy cable. A nonlinear, three dimensional, large deformation, nonlinear elastic strain finite element model is used for all intermediate cases. Numerical solution of the latter problem is achieved through a global Newton iteration. Differential equations of motion are analyzed in six dimensional state space. Stability of equilibria in the sense of Lyapunov captures essential characteristics of the nonlinear flow. Topological considerations assist in constructing global properties of solutions. A numerical integration pitfall, namely convergence to unstable equilibrium is explained. Study of codimension one and two bifurcations establishes that both static bifurcations (solution branching) and dynamic loss of stability (flutter) may occur. The universal unfolding of a generalized pitchfork bifurcation and its persistent perturbations are studied. Bifurcation sets of parametrized families of the system equations take the form of generic fold and cusp singularities. Periodic solutions are predicted and computed based on occurrence of subtle Hopf bifurcations. Orbital stability of periodic solutions is assessed by means of their Floquet characteristic exponents. Catastrophic Hopf bifurcations are shown to occur creating pathways to chaos. Chaotic response and fractal dimensions of associated strange attractors are quantified using computations of Lyapunov characteristic exponents. It is shown that static bifurcations do not depend on the type or model of the mooring line, whereas dynamic bifurcations may change drastically for a qualitatively different mooring line. The thesis results offer possible explanations for instabilities often observed in mooring systems. The main geometric parameters of a system affecting its motions are identified. Therefore, rational design decisions and proper selection of these parameters are possible in order to achieve a maximum operating window within safety limits for a particular system.