Wave scattering by an elastic plate in a viscous fluid of finite depth

Abstract

This work examines a two-dimensional wave scattering problem in a viscous, incompressible fluid of finite depth over an impermeable bottom by a semi-infinite and finite floating elastic plate. Weakly viscous potential theory is utilized to frame the problem using the velocity potential and stream function. The paper addresses three main objectives: first, it analyzes the behavior of the distorted positive real root of the dispersion relation in both the water region and the region covered by the plate; second, the boundary value problem is solved separately for both semi-infinite and finite elastic plates using the matched eigenfunction expansion method; third, the impact of different parameters on various hydrodynamic coefficients is examined through several numerical plots. We find that the viscosity affects the low-frequency waves more than the high-frequency ones in the plane progressive wave analysis. Further, it seems that the effect of viscosity increases with a decreasing water depth. From the wave scattering problem with varying viscosity, it is noted that, at low viscosity levels, the wave energy absorption by the medium is minimal, resulting in a reflection coefficient close to 1. With an increase in the viscosity to moderate levels, more wave energy is dissipated due to viscous effects, reducing the reflection coefficient to nearly 0.