Subharmonic Response in the Nonlinear Oscillation of Moored Ships

ABSTRACT Ship and mooring line responses are studied for spread mooring systems and for ships moored parallel to a quay. subharmonic responses are studied in detail, where the equations of ship motion are uncoupled and where wave excitation is harmonic. This model represents surge and sway for ships moored in bays or harbor basins where wind generated waves or seiches exist. Conditions for mooring line resonance under transverse and parametric excitation by the ship are investigated. Peak ship responses due to subharmonic resonances are predicted near the natural frequency of the moored ship, at fractional values of the dominant forcing frequency of the waves. Results of sea tests for an LST moored in the Gulf of Mexico confirm the calculations, and show the importance of considering subharmonic ship responses in the design of effective mooring configurations. Introduction Vessels or floating platforms moored in bays and harbors can undergo very complex motions brought about by wave action. In some instances, the motions of the surrounding body of water, and the wave forces impinging on the ships' hulls, become nearly harmonic. The waves themselves may cover a wide range of frequencies and amplitudes, as shown by measurements and spectral analysis. Storms in the adjacent ocean give rise to oscillations of the water masses (seiches). Waves of short periods (3 to 30 sec) generated by winds also cause ship motion. A ship moored in these waters may undergo troublesome motion, even in relatively mild seas, and under certain critical conditions may break adrift from its moorings. These critical conditions depend on a combination of factors, including the wave size and frequency, mooring line configuration, and the ship's size and draft. A ship's motion in surge, sway and yaw (longitudinal, transverse, and rotational motion in the plane of the sea, respectively) can be effectively controlled by proper choice and positioning of the mooring lines. An effective "spread" mooring system, consisting of heavy anchor chain lines fastened to stake pile anchors, is sketched in Figure 1. O'Brien and Muga [1], who describe such a system in detail, found that this mooring system is ineffective against heave, roll, and pitch (vertical motion and rotations about the longitudinal and transverse axes, respectively). This suggests that the differential equations describing the surge, sway, and yaw motions may be uncoupled, to a first approximation; from the equations involving the latter three degrees of freedom. For the special case of spread moorings in which the dominant wave action is beam on (transverse) and the longitudinal constraint forces are balanced, surge and yaw can also be neglected so that only sway motion exists.