Non-linear Springing Excitation Due to a Bidirectional Wave Field

Significant springing vibrations in ships have recently been measured in a large ocean-going bulk carrier. So far calculations using various linear and non-linear hydrodynamic procedures have not been able to predict the measured responses. In the present paper it is shown that the springing response depends strongly on second order (sum frequency) terms involving cross-coupling terms from the combined wind- and swell-driven wave system.

The calculations are based on the second order strip theory formulation and thus no three-dimensional effects are accounted for. The agreement with measured springing responses is found to be greatly improved when these second-order cross-coupling terms are included.