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.