Resonance mechanism of hydroelastic response of multi-patch floating photovoltaic structure in water waves over stepped seabed

This paper investigates the hydroelastic response of a multi-patch floating photovoltaic (FPV) structure in water waves over a stepped seabed. The resonance conditions and underlying mathematical mechanism of FPV patches are explored based on the linear potential-flow theory and the thin-plate model. An implicit function of the open-water wavelength and the FPV patch's structural wavelength is derived. Resonance conditions occur in the FPV patch when the patch length and structural wavelength (rather than the water wavelength, as commonly believed) satisfy certain proportions. Mathematical derivations are conducted to interpret the value of each proportion. Two resonance conditions are recognized based on the mathematical structure of the solution. The effects of a stepped seabed and adjacent patches on the resonance conditions and hydroelastic behavior of FPV structures are also investigated. For a given stiffness parameter, the resonance conditions of FPV patches are solely determined by the water depth. The distance between adjacent patches does not alter the resonance conditions of each patch. Resonance occurs in the water body between two patches when the ratio of patch distance to water wavelength takes certain proportional values. A resonant water body tends to amplify the oscillation amplitude of both patches. However, when two FPV patches and a constrained water body reach their theoretical resonance conditions at the same time, the oscillation amplitudes of both the seaward patch and the constrained free surface are evidently suppressed. The transmitted waves of an FPV structure are largely determined by the dynamics of the leeward patch.