A semi-analytic method for predicting local instability, global bifurcation, and the onset of chaotic motion in a multi-point mooring system is developed. Large geometric nonlinearities and combined periodic waves and steady current are considered. It is shown that a stability analysis based on the approximate solution of the strongly nonlinear ocean system can serve as an efficient predictor for the nonlinear behavior, thus reducing numerical search efforts for global instability and chaotic response regions.
With the increasing depth in exploration and production of oil and gas, there is a compelling need for compliant ocean systems. Chaotic response has been recently observed in various nonlinear single-point mooring systems [Thompson, et al. 1984; Papoulias and Bernistas 1988]. Multipoint or spread mooring systems in deep water, in addition to material discontinuities have a distinct planar geometric nonlinearity associated with large mooring line angles. These systems are characterized by a unique equilibrium position and a strong nonlinearity described by a monotone increasing restoring force. While weakly nonlinear systems have been studied extensively using both classical and modern approaches [Nayfeh and Mook 1979; Guckenheimer and Holmes 1983], studies of complex single equilibrium point systems with strong nonlinearities are limited. Some numerical investigations of systems exhibiting similar nonlinear properties have revealed complex behavior including bifurcations, coexistence of attractors, and sensitivity to initial conditions. Examples of such systems are the biased hardening Duffing equation [Ueda 1980] and single equilibrium systems in which the restoring force is described by a power series or an exponential function [Bishop and Virgin 1988]. This paper describes the analysis of a floating structure with a symmetric multi-point mooring assembly (Fig. 1). In order to isolate the effect of geometric nonlinearity, linearized drag is employed and stiffness of a taut continuous form is assumed.