Interaction of surface water waves with an elastic plate over an arbitrary bottom topography

Abstract

In the present paper, the problem involving the transformation of incident wave energy by floating elastic structure situated at a finite distance from an arbitrary bottom topography is studied. Here, both symmetric and asymmetric bottom profiles, which are arbitrary in nature, are considered . The successive steps are used to approximate the uneven bottom profile. The method of step approximation along with matched eigenfunction expansion is employed by which a system of linear algebraic equations is obtained and solved to determine the hydrodynamic quantities, namely transmission and reflection coefficients, plate deflection, strain and shear force on the plate. The present results are validated with the known results of literature for the case of rigid floating structure over the uniform finite depth as a particular case. The energy identity is obtained through Green integral theorem and is checked in towards the accuracy of present results. The effect of various structural and system parameters such as elastic plate length, angle of incidence, depth ratios, distance between the bottom topography and elastic plate on transmission and reflection coefficients, shear force and strain, plate deflection is investigated through different graphs and tables. This problem will give useful information to create the desirable tranquility zone near the seashore.