Wave-induced hydrodynamic responses of a rigid body connected with elastic plates floating on a two-layer fluid

A novel physical model of Very Large Floating Structures (VLFSs) is investigated for a two-layer fluid. This model is composed of a semi-immersed module rigidly connected with two elastic plates, which may provide basic knowledge for the study of multi-module floating structures in a stratified ocean. Under the hypothesis of small-amplitude wave theory, the case with the coupling effects among the wave motion, the vertical deformation of the elastic plates and the rigid body's oscillation is solved by only considering a scattering problem and a radiation one. New inner product relations with orthogonality are suggested to calculate the undetermined coefficients in eigenfunction expansions, which is eligible to yield a convergent result. By this approach, the matching relations are simplified and the numerical calculation speed is remarkably promoted. Exciting forces (caused by the scattering potential), hydrodynamic coefficients for added mass and radiation damping (caused by the direct act of radiation potential) and additional coefficients for added stiffness and added damping (caused by the indirect act of radiation potential via the elastic plates) are obtained. Numerical representations for amplitudes, exciting forces, hydrodynamic coefficients, and additional coefficients are shown, in which Green's theorem is used for ensuring convergence.