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Water wave scattering by a surface-mounted rectangular anisotropic elastic plate

Ben Wilks, Michael H. Meylan, Zachary J. Wegert, Vivien J. Challis, Ngamta Thamwattana

TL;DR

The paper addresses water-wave scattering by a surface-mounted rectangular anisotropic elastic plate in a three-dimensional fluid. It develops a coupled hydroelastic model by expanding the total potential into a diffraction component for a rigid plate and radiation potentials tied to plate vibration modes, with the plate’s dry modes computed via a Rayleigh–Ritz method and the coupled problem solved through boundary-integral equations discretized by a constant-panel method. An energy-balance identity based on the optical theorem verifies the computations, and the results reveal resonant plate responses and symmetry-induced mode suppression under various forcing scenarios. This framework enables accurate analysis of anisotropic hydroelastic interactions with potential applications to large floating structures and piezoelectric wave-energy converters in three dimensions.

Abstract

This paper considers the problem of water wave scattering by a rectangular anisotropic elastic plate mounted on the ocean surface, with either free or clamped edges. The problem is obtained as an expansion over the dry modes of the elastic plate, which are computed using a Rayleigh--Ritz method. In turn, the component diffraction and radiation problems are solved by formulating a boundary integral equation and solving numerically using a constant panel method. The results are presented to highlight the resonant responses of the plate under different forcing scenarios. In particular, we illustrate how the excitation of certain modes can be forbidden due to symmetry.

Water wave scattering by a surface-mounted rectangular anisotropic elastic plate

TL;DR

The paper addresses water-wave scattering by a surface-mounted rectangular anisotropic elastic plate in a three-dimensional fluid. It develops a coupled hydroelastic model by expanding the total potential into a diffraction component for a rigid plate and radiation potentials tied to plate vibration modes, with the plate’s dry modes computed via a Rayleigh–Ritz method and the coupled problem solved through boundary-integral equations discretized by a constant-panel method. An energy-balance identity based on the optical theorem verifies the computations, and the results reveal resonant plate responses and symmetry-induced mode suppression under various forcing scenarios. This framework enables accurate analysis of anisotropic hydroelastic interactions with potential applications to large floating structures and piezoelectric wave-energy converters in three dimensions.

Abstract

This paper considers the problem of water wave scattering by a rectangular anisotropic elastic plate mounted on the ocean surface, with either free or clamped edges. The problem is obtained as an expansion over the dry modes of the elastic plate, which are computed using a Rayleigh--Ritz method. In turn, the component diffraction and radiation problems are solved by formulating a boundary integral equation and solving numerically using a constant panel method. The results are presented to highlight the resonant responses of the plate under different forcing scenarios. In particular, we illustrate how the excitation of certain modes can be forbidden due to symmetry.
Paper Structure (6 sections, 19 equations, 1 figure)

This paper contains 6 sections, 19 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Problem outline
  3. Preliminaries
  4. Time harmonic formulation
  5. Diffraction by a rigid plate
  6. Green's function

Figures (1)

  • Figure 1: (a) Side and (b) plan views of the scattering problem. The rectangular plate, labelled $\Gamma$, has side lengths $a$ and $b$ and the fluid is of depth $H$. The incident wave $\phi^{\rm inc}$ excites the plate into motion, generating scattered waves $\phi^{\rm sc}$.