A study on the interaction of waves with a submerged vertical elastic plate present in either layer of a two-layer fluid

Abstract

The problems of interactions between an elastic plate and surface as well as interface waves are considered and analyzed using the theory of linearized water waves. Considering the ocean’s multilayered nature, a two-layered fluid system that serves as the foundation for a more complex multilayered fluid model is examined. It is taken into consideration when an elastic plate is present in either layer of the two-layered water domain. Applying Green’s function technique on the boundary value problem related to the flexible plate and its end conditions, an expression of the normal derivative of the potential function is derived. Employing Green’s identity on the fundamental potential function and the scattered potential, an alternative expression for the normal derivative of the potential function is obtained. Comparison of alternative expressions of the normal derivative of the potential function allows the deduction of a Hypersingular Integral Equation (HSIE) in terms of the unknown potential difference across the plate. Then, using the Expansion-Collocation approach, the HSIE is resolved. The resulting solution provides insights into the reflection coefficient and plate deflection as they vary with different parameters.