Resonances of Floating Elastic Structures in Enclosed Shallow-Water Basins

Water wave interactions with floating deformable bodies is an interesting coupled problem finding important applications, as in the case of the responses of large floating structures and platforms of shallow draft and wave-ice sheet interaction. In this work we consider interactions of waves with floating elastic structures in enclosed or partially enclosed basins, as e.g. lakes, bays, reservoirs and harbors. Related applications include the wave induced deflection of floating marinas, solar energy platforms, ice covered lakes, etc. When enclosed or partially enclosed basins are considered, the hydroelastic interactions may be triggered due to the formation of standing waves. These standing waves or seiches have been documented in several occasions. In many cases the seiche effects in terms of wave amplitudes are small, but extreme catastrophic seiches have also occured. This fact suggests that the integrity of a floating structure might be compromised due to an extreme seiche. The main aim of this study is the analysis and simulation of hydroelastic standing waves. Towards this aim a configuration comprising of a constant depth basin, partially covered by a large, thin, floating elastic plate is studied. Shallow-water conditions, typical for the analysis of long waves are considered. The study focuses on the identification of the main resonant frequencies, which is important concerning the design of the considered floating structures. The problem is treated by a semi-analytical method based on the shallow water model by Stoker (1957), in conjunction with modal series expansions. Indicative results are presented illustrating the effects of the main parameters characterising the system, like the dimensions and rigidity of the structure, the clearances and the bathymetry.