Computation of leaky waves in layered structures coupled to unbounded media by exploiting multiparameter eigenvalue problems

TL;DR

This paper introduces a semi-analytical method leveraging multiparameter eigenvalue problems to accurately compute leaky wave modes in layered structures coupled with unbounded media, relevant for ultrasound and seismic wave simulations.

Contribution

It develops a novel approach that transforms complex nonlinear eigenvalue problems into multiparameter eigenvalue problems solvable with advanced algorithms, improving wave mode computation accuracy.

Findings

Effective computation of leaky wave modes in layered media.

Demonstrated applicability to ultrasound and seismic wave modeling.

Enhanced numerical stability and accuracy in eigenvalue solutions.

Abstract

We present a semi-analytical approach to compute quasi-guided elastic wave modes in horizontally layered structures radiating into unbounded fluid or solid media. This problem is of relevance, e.g., for the simulation of guided ultrasound in embedded plate structures or seismic waves in soil layers over an elastic half-space. We employ a semi-analytical formulation to describe the layers, thus discretizing the thickness direction by means of finite elements. For a free layer, this technique leads to a well-known quadratic eigenvalue problem for the mode shapes and corresponding horizontal wavenumbers. Rigorously incorporating the coupling conditions to account for the adjacent half-spaces gives rise to additional terms that are nonlinear in the wavenumber. We show that the resulting nonlinear eigenvalue problem can be cast in the form of a multiparameter eigenvalue problem whose solutions represent the wave numbers in the plate and in the half-spaces. The multiparameter eigenvalue problem is solved numerically using recently developed algorithms.