Impedance eigenvalues in linear elasticity

TL;DR

This paper investigates impedance eigenvalues in linear elasticity, exploring their properties, relation to inverse scattering, and methods for approximation from fluid-structure interaction data.

Contribution

It introduces impedance eigenvalues as elastic analogues of Steklov eigenvalues and analyzes their role in inverse scattering and approximation techniques.

Findings

Impedance eigenvalues relate to fluid-solid interaction signatures.

They can be approximated from far field measurements.

Methods are illustrated for an isotropic elastic disk.

Abstract

This paper is devoted to studying impedance eigenvalues (that is, eigenvalues of a particular Dirichlet-to-Neumann map) for the time harmonic linear elastic wave problem, and their potential use as target-signatures for fluid-solid interaction problems. We first consider several possible families of eigenvalues of the elasticity problem, focusing on certain impedance eigenvalues that are an analogue of Steklov eigenvalues. We show that one of these families arises naturally in inverse scattering. We also analyse their approximation from far field measurements of the scattered pressure field in the fluid, and illustrate several alternative methods of approximation in the case of an isotropic elastic disk.