Reduction of hydroelastic response of a flexible floating structure by an annular flexible permeable membrane

Abstract

In the present study, hydroelastic response mitigation of a very large floating circular structure by an annular flexible permeable membrane is studied under the assumption of the linearized theory of water waves and small amplitude structural response. The very large floating structure is modeled based on small amplitude plate theory, while the flexible annular membrane is modeled using the two-dimensional string equation. Darcy’s law is used to model wave past the permeable annular membrane. To keep the structures in position, both the floating structures are assumed to be moored on the circular boundaries. The velocity potentials are expanded in terms of the Fourier–Bessel series in the open water, membrane-, and plate-covered regions. The solution of the physical problem is obtained using the matched eigenfunction expansion method along with the orthogonality of the vertical eigenfunctions in the open water region. On the other hand, orthogonal mode–coupling relation, satisfied by the vertical eigenfunctions in the floating flexible plate-covered region, is used when there is no spacing between the outer and the inner structures. The wave forces exerted on the inner and outer structures, deflection of the plate, and flow distribution around the inner plate are analyzed using numerical computations to understand the hydroelastic response of the inner elastic plate in the presence of the outer porous membrane. The effects of various wave and structural parameters such as wavenumber, porous-effect parameter, tensile force, width of the outer membrane, spring constants associated with the mooring joints, and the spacing between the structures are examined. The study reveals that the porous-effect parameter and the width of the annular membrane play an important role in reducing the wave forces on the inner plate. Moreover, due to the reflection and dissipation of a major part of the wave energy concentrating near the free surface, the inner floating structure experiences negligible wave loads in the case of deep water.