New insight into the wave-induced nonlinear vertical load effects of ultra-large container ships based on experiments

Abstract

Accurate estimation of the wave-induced extreme hogging vertical bending moment (VBM) is of vital importance for the design of container ships because container ships are normally under hogging conditions in still water. According to the empirical formulas proposed by the classification society rules, the design hogging VBM can be approximately 20 % smaller than the design sagging VBM for vessels with small block coefficients. High-order harmonic components in the vertical load effects, which are induced by the nonlinearities in the hydrodynamic forces and ship hull geometry, contribute to the asymmetry. Previous studies have shown that the nonlinear hydrostatic and Froude–Krylov forces increase the sagging VBM significantly. Current numerical tools are able to reveal this asymmetry to a certain extent. There is, however, little focus on the nonlinear pressure under the bow bottom, which is a more likely contributor to the hogging VBM. Several unexpected phenomena have been observed for large container ships. The wave-frequency sagging and hogging VBMs followed each other closely, and hence did not reflect the significant nonlinear factors as expected. In this paper, the test data of two (8600-TEU and 13000-TEU) ultra-large containership models in both regular and irregular head waves are systematically studied. In regular waves, the influence of the second and third harmonics on the fundamental hogging peaks and sagging troughs is estimated by comparing both the amplitude and phase difference relative to the first harmonic peaks. In irregular waves, the focus is on the statistical characteristics of the wave-induced nonlinear vertical load effects. To achieve a balance between results in regular and irregular waves, the influence of the second harmonics is evaluated through bispectral analysis.