Springing Response Due to Directional Wave Field Excitation

This paper analyses the wave-induced high-frequency bending moment response of ships, denoted springing. The aim is to predict measured severe springing responses in a large bulk carrier. It is shown that the most important springing contribution is due to the resultant second order excitation in multidirectional sea.

The incident pressure field from the second order bidirectional wave field is derived, including the non-linear cross-coupling terms between the two wave systems (e.g. wind driven waves and swell). The resulting effect of the super-harmonic cross-coupling interaction terms on the springing response is discussed.

An example with opposing waves is given, representing probably the 'worst' case for energy exchange between the wave systems. Theoretical predictions of standard deviation of wave- and springing-induced stress amidships are compared with full-scale measurements for a bulk carrier.