Wave motion due to the rolling of flexible porous structures

Generation of surface waves due to the rolling motion of a thin flexible porous plate, either partially immersed or fully submerged in deep water, is analyzed in this study. The plate is modeled as either an elastic porous plate or a tensioned porous membrane of finite length. The original physical problem in the half-plane is modeled as a mixed boundary value problem for the Laplace equation with higher-order structural boundary conditions. To address the problem, it is decomposed into a pair of quarter-plane problems by introducing a symmetric function and a special connection in the form of integro-differential relations. The involved connection links the original solution potentials with rigid and newly defined auxiliary potentials. These latter problems are reduced to Fredholm integral equations of the first kind, which are solved using the Galerkin technique. The technique involves the basis functions as simple polynomials multiplied by appropriate weight functions whose forms are dictated by the plate edge conditions. This methodology yields highly accurate closed bounds for the radiated wave amplitude. Numerical results are presented and analyzed to examine how the radiated wave amplitude varies with different physical and structural parameters.