An approach to the non-linear solution of the oscillating water column

Abstract

The non-linear solution of the resonant moon-pool/oscillating water column problem is discussed. The problem is given in 2-D, and the non-linear free surface effects inside the oscillator, as well as a simplified model for non-linear damping effects at the outlet, are introduced. The solution of the problem is shown to be quite dependent on the non-linearities and shows response similar to that of a Duffing oscillator with a hardening spring, in terms of multiple solutions close to resonance and subharmonic resonance. The physical restriction introduced by the finite height of the oscillator introduces a considerable restriction to the possibility of finding steady state, periodic solutions. The non-linear free surface effects and the non-linear damping effects are found to be of equivalent importance, but influencing the solution in different ways. The response amplitude, for steady state, periodic solutions seems to be slightly more influenced by the non-linear free surface effects than by the non-linear damping effect.