An analytical study on generation of waves due to the rolling of flexible porous barriers

Abstract

Complete analytical solution for generation of waves due to rolling of a partially immersed vertical elastic porous plate or a tensioned membrane is obtained. The originally defined boundary value problem in the half-plane has been decomposed first into a couple of flexible porous wave potential problems in the quarter-plane. Then, a pair of integral relations are introduced to establish a connection among the flexible porous wave potentials, solid wave potentials, and auxiliary wave potentials. By utilizing the connection, the flexible porous wave potentials can be determined in terms of the solid and the auxiliary wave potentials. The problems for the latter two types of potentials are easier to handle mathematically than the problems for the flexible porous wave potentials because of the involved structural boundary condition. Thus, the solid and the auxiliary wave potentials have been obtained analytically by the existing methods of solutions. Explicit analytical expressions are derived for the radiated wave amplitudes and velocity potentials. These radiated wave amplitudes are numerically computed and analyzed for different parameters involved. The results are validated with those derived for the problem involving a solid plate.