Wave-induced Ship Hull Vibrations in Stochastic Seaways

A theoretical Study is undertaken on the determination of wave-induced loads in flexible ship hulls. The calculations are performed within the framework of a non-linear, quadratic strip theory formulated in the frequency domain. Included are non-linear effects due to changes in added mass, hydrodynamic damping and water line breadth with sectional immersion in waves. The study is limited to continuous excitations from the waves and thus transient so-called whipping vibrations due to slamming loads are not considered.Because of the non-linearities the ship hull responses become non-Gaussian in stationary stochastic seaways. The statistical properties of a response are here described by the first four statistical moments through a Hermite series approximation to the probability density function. The peak value distributions of the low and high frequency responses are treated independently, due to the large separation between dominating wave frequencies and the lowest two-node frequency of the hull beam. Both extreme value predictions and fatigue damage are considered.For a fast container ship the rigid body and two-node (springing) vertical wave-induced bending moments amidship are calculated in stationary and non-stationary seaways. In the long term analysis due account is taken of speed reduction in heavy seas, different heading angles, operational areas and clustering effects in the peak value statistics.The main result is that springing is, relatively, most pronounced in head or near head sea in lighter sea states where the zero-crossing periods are small. It is also found that the non-linear contributions to the springing response are at least as important as the linear contribution. However, for the long-term extreme peak responses the springing vibrations become less important. This indicates that a design wave bending moment probably can be derived without considering springing for normal merchant ship types. For the example ship, a factor of approximately two is found between the calculated sagging and hogging moments at the same probability level. This is in reasonable agreement with the current rule requirements for the wave bending moment.