Scattering of flexural--gravity waves by a group of elastic plates floating on a stratified fluid

TL;DR

This paper develops a mathematical framework to analyze how multiple elastic floating plates in a stratified fluid scatter flexural--gravity waves, extending previous models to account for layered density profiles and inhomogeneous covers.

Contribution

It introduces a generalized method for modeling wave scattering by multiple elastic plates on stratified fluids, incorporating multi-layer matching and energy conservation for improved accuracy.

Findings

Eigenfunction expansion method effectively models multi-layer interactions.

Stratification significantly influences elastic plates' hydrodynamic responses.

High convergence rates validate the numerical approach.

Abstract

A hydroelastic problem of flexural--gravity waves scattering by a demarcation between two floating elastic plates is investigated within the frame of linear potential-flow theory, where the method of matched eigenfunction expansions is employed for analysis. A generalized extension is subsequently derived to promote the formulae to the case of multiple elastic plates on a stratified fluid with multiple layers, which is helpful to study the hydrodynamic behaviors of inhomogeneous floating covers as well as the effects of density stratification in seawater. The eigenfunction expansions are numerically calculated by an inner product technique, in which an orthogonal definition involving an explicit differential term exhibits the effectiveness in dealing with the multi-layer matching relations between adjacent regions covered by different elastic plates. By use of Green's theorem, an energy conversation relation is deduced to assure the convergence of the calculation to the physical reality, and the high converging rates are exhibited afterwards. The correctness of numerical results are also verified by comparing with a previous analytical method. The details of the hydrodynamic responses of the generalized extension, especially the impact of the fluid stratification on the inner forces of the elastic plates, are discussed under different situations.