Nonlinear Response of a Moored Ship to Sea Oscillations

Abstract

A possible mooring line suspension system for a large vessel is shown in Figure 13.1. Consider the longitudinal motion of this ship in a harbor basin under a simple harmonic disturbing force F(t) = F cos ωt. This disturbing force, which is caused by the harbor waves impinging on the ship’s hull, often has a frequency ω which is close to the natural frequency of oscillation of the water within the harbor basin. This problem is also discussed by Wilson (1951) and Abramson (1955). In reality, neither ω or the force amplitude F are constant; ω may cover a spectrum of frequencies; and both may vary with time. In the following analysis, however, the motion of the ship in the direction of F(t) only is considered, where ω and F are constant. In addition, it is assumed that the composite effect of all seven mooring lines on ship’s motion is essentially the same as that for just two equivalent horizontal lines, as shown in Figure 13.2. It will be shown that these assumptions lead to a nonlinear differential equation of motion which is a special form of the more general one derived by Wilson (1951).