Resonances of enclosed shallow water basins with slender floating elastic bodies

A model for the hydroelastic response of enclosed shallow water basins with floating slender plates of large span, in variable bathymetry is presented. The eigenproblem for the system's resonant behaviour is formulated in the strong and variational form. Based on the variational form, and special hydroelastic finite elements, a quadratic eigenvalue problem is derived for the eigenfrequencies and eigenmodes of the basin-floating body system. Benchmark examples, for simplified configurations, are used to study the effects of parameters like the plate's span, position, draft, mass, stiffness and depth of the basin. It is observed that the presence of the plate can alter significantly the eigenstates of the pond if the depth of the basin is relatively small, compared to the plate draft. In such cases the plate span and position play a crucial role. The hydroelastic analysis can be important even in cases where the depth increases and the upper surface elevation differences, in the presence or absence of the floating plate, appear to be less significant. This is due to the importance in accurately calculating the curvature and hence bending moments inside the plate. The proposed model could be relevant to the seiche formation analysis in reservoirs with floating photovoltaic platforms or ice-covered lakes.