On the natural frequencies and modal shapes in two-dimensional moonpools with recesses in finite water depth

In this paper, the theoretical model proposed in Zhang et al. (2019) is extended to compute the natural frequencies and modal shapes for two-dimensional moonpools with one or two recesses in finite water depth. In the framework of linear potential flow theory, the boundary value problem is solved by using a domain decomposition method, assuming the velocity potential at the outer boundaries to be nil. In particular, a new and efficient approximation method, double-mode approximations (DMA), is derived to estimate the natural frequencies and modal shapes for both piston-mode and sloshing-mode resonances. The present results using the derived DMA formulas are compared with the experimental results by Ravinthrakumar et al. (2019) and the solutions using the frozen-mode approximation (FMA). The comparisons show satisfactory agreement with the experimental data. In particular, it is shown that, in contrast to FMA, DMA can well predict the non-flat modal shape of the free surface at piston-mode resonance. Moreover, extensive parametric studies are performed to examine the effects of the moonpool geometry on natural frequencies and free-surface modal shapes.