This paper deals with the interaction of sea waves with a moored floating rectangular structure. The problem is of interest in various practical situations such as the design of floating breakwaters and of artificial islands, and the modelling of wave-ice sheet interaction. In the paper the incident wave field is modelled as a Gaussian stochastic process of a specified spectrum. In this context a diffraction problem and a radiation problem are posed. The related boundary value problem is discussed and solved by an eigen-functions expansion matching method. The method renders an estimate of the velocity potential at the first order in a Stokes’ expansion and, thus, of the wave pressure and of the wave forces. Several hydrodynamic quantities of interest are investigated. Specifically, reflection and transmission coefficients are derived and represented as a function of the structural dimensions. Further, the added mass and radiation damping terms are estimated. Then, the dynamics of the floating structure is examined by considering a 3-D-O-F system. Next, the wave-structure interaction is investigated in the context of a Quasi-Determinism theory. It is shown that the developed approach can be employed to account for both the dynamic and hydrodynamic effects of a structure in which diffraction is not negligible. The theoretical results are supplemented with data from pertinent Monte Carlo simulations.

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