Wave interaction with multiple floating elastic plates with arbitrary constraints near a sloping beach

The problem of wave interaction with multiple elastic plates floating near a sloping beach is considered, particularly resembling the case of a floating solar farm near a coast. The linearized shallow water theory is adopted to describe the motion of fluid. The Kirchhoff–Love plate theory is used to model the elastic plates. A highly efficient domain decomposition approach is applied to derive the solution. Particularly, the eigenfunction expansions are employed to establish the velocity potential in free surface fluid domains, while the Green function method is used to construct the velocity potential of the fluid domain covered by floating elastic plates. This approach can significantly reduce the number of unknowns in the velocity potential, especially when a large number of plates are involved. Extensive results and discussions are provided for the wave run-up on the beach, maximum deflection, and principal strain on the elastic plates. In particular, based on a wide space approximated solution, the oscillatory behaviour of the wave run-up vs the incident wavenumber is analysed, along with the corresponding physical mechanisms. Furthermore, apart from the frequency-domain results, time-domain analyses are also conducted based on a Fourier transform approach. Two different types of incident impulses are considered to interact with floating elastic plates near a beach, namely a Gaussian wave packet and a storm-type incident wave.