On natural frequencies and modal shapes in two-dimensional asymmetric and symmetric moonpools in finite water depth

In this paper theoretical models are proposed for computing the natural frequencies and modal shapes of two-dimensional asymmetric and symmetric moonpools in the finite water depth. The boundary value problem is solved by using a domain decomposition approach. On the outer vertical boundary bounded by the beam of the two bodies, linearized velocity potential is assumed to be nil. Eigenvalue problem is formulated by matching the velocity potential and fluid flux on the common boundaries to obtain the natural frequencies and modal shapes of the free surface elevation. In the symmetric moonpool cases, so-called single mode approximations (SMA) have been derived and can be adopted for rapid estimation of the natural frequencies for both piston and sloshing modes. The present results have been extensively compared with the solutions using the two-dimensional infinite water depth model developed by Molin 1], the numerical solutions and experimental data by Faltinsen et al. 2]. It is found that the solutions have been improved from the infinite water depth model. It is demonstrated that the proposed models can well predict the resonance frequencies and modal shapes for the two-dimensional asymmetric and symmetric moonpools.