Fully nonlinear analysis of second-order sloshing resonance in a three-dimensional tank

The 3D boundary element method (BEM) based on the potential flow theory is developed to study the second-order resonance problems in rectangular sloshing tanks. Fully-nonlinear free-surface boundary conditions are considered. A local surface fitting method is used to calculate tangential derivatives. A shared-memory parallel procedure based on OpenMP is adopted for the efficiency improvement. Both 2D and 3D sloshing cases are studied. It is found that the second-order resonance may occur due to the interaction among natural frequencies and excitations frequencies. The second-order resonance becomes obvious after a sufficient long time length. After increasing the excitation amplitude, the second-order resonance emerges much earlier. For 3D situations, the second-order resonance in rectangular tanks with either equal or unequal length and width sides are investigated. The second-order resonances due to the interaction of two orthogonal plane waves in length and width directions are observed.