Surface gravity wave interaction with circular flexible structures

Abstract

Surface gravity wave interaction with circular floating elastic plates of finite radius is analyzed in both the cases of single and two-layer fluids in finite water depth. The problems are analyzed under the assumption of small amplitude water wave theory and structural response. Further, gravity wave diffraction by circular elastic plates is studied under shallow water approximation based on linearized long wave theory. In the present analysis, the flexible structures are namely flexible circular plates and membranes of negligible draft. From the general formulation of the floating elastic plates, the results associated with the flexible membranes are obtained as special cases. Fourier–Bessel series type expansion formulae for the velocity potentials are obtained in the open water surface region and flexible plate/membrane covered region by the method of separation of variables. Suitable orthogonal mode-coupling relations are used along with the matching of velocity and pressure to obtain system of equations for the determination of the unknowns in the expansion formulae. Numerical results on structural deflection are computed and plotted to understand the hydrodynamic characteristics of the floating structures under water action. In order to understand the flow distribution around the floating circular flexible structures, contour plots are provided.