An asymptotic solution of wave interaction with a spatially varying elastic plate

Abstract

The present article addresses a coupled potential flow and thin plate model of water-wave scattering influenced by an elastic plate with spatial variations. The scattering problem is solved mathematically using asymptotic expansion and the Fourier transform approach. The paper develops a first-order asymptotic solution, which significantly illustrates the hydrodynamic coefficients and emphasizes wave diffraction phenomena. Based on the real-life scenarios, we consider the sinusoidal ripple-type shape function of the elastic plate and analyze the Bragg resonance in wave reflection. The number of ripples and the wavenumber of the shape function affect the most reflected wave components, and the energy of reflected waves is increased due to wave action conservation. A deeper understanding of resonance phenomena, the influence of plate geometry, the roles of compressive force, and flexural rigidity, as well as the intricate interplay between wave characteristics and structural parameters, is obtained through the combined numerical analyses conducted in this study. Examining plate deflection reveals that the deflection amplitude is substantially higher near the variation region of the elastic plate. Findings of this study can assist in the design and optimization of very large floating structures and coastal protection systems by enabling the prediction and control of wave amplification, suppression, and transmission through the strategic tuning of structural geometry, rigidity, and compressive force.