Low-frequency responses of compliant offshore structures associated with both slowly varying wave drift forces and nonlinearities of the mooring system are investigated by numerical simulation. An idealized model corresponding to a single degree of freedom system with a piecewise-linear restoring force function is considered. The characteristics of the response and the dependence of the response amplitude on various. governing parameters are discussed. The response often exhibits subharmonic and chaotic motions, which are characteristics of a nonlinear system, and which make the response curves completely different from those of a linear system.
Large offshore structures, such as semi-submersibles or tankers, moored in random seas often exhibit large amplitude low-frequency motions in the horizontal modes of motion - surge, sway and yaw. Mooring line forces due to such low-frequency motions can be critical in the design of the mooring systems of these structures. Two main causes of such low-frequency motions in waves have been Identified and investigated individually. One is the low-frequency component of the wave force acting on the structure, the so-called slowly varying wave drift force; and the other is the nonlinearities of the mooring system. This has been investigated in a large number of theoretical and experimental studies (reported, for example, in ITTC, 1990), and useful approximate methods for predicting the slowly varying drift force are available (e.g. Pinkster, 1974; Agnon and Mei, 1985). More recently, attention has been focused on particular aspects of this problem such as the effects of wave grouping and low-frequency damping. However, almost all such studies have been restricted to a mooring system with linear restoring characteristics. On the other hand, it has been also reported that low-frequency, subharmonic oscillations often occur in the motion of a structure with nonlinear moorings (e.g., Lean, 1971).