Bouncing-Ball Model of ‘Dry’ Motions of a Tethered Buoy

Abstract

The motions of a buoy moored to the sea floor by a cable are considered. The buoy is modeled both as a point mass and as a sphere. It is assumed that the mooring line has no effect when it is slack, and that when it becomes taut it exerts an instantaneous impulsive force on the buoy, analogous to the impact of a ball bouncing on a rigid surface. The magnitude of the axial component of the velocity is reduced at this time. Fluid inertia and damping are not included, and the wave forces are assumed to be harmonic. The effects of the coefficient of restitution and the forcing frequency on two types of critical force are examined. Trajectories of the motion are plotted and the impact velocities are computed and analyzed. Knowledge of the number and magnitude of these impacts is useful in assessing fatigue of the mooring line.