Computing leaky Lamb waves for waveguides between elastic half-spaces using spectral collocation

TL;DR

This paper introduces a spectral collocation method for accurately computing leaky Lamb waves in elastic waveguides embedded in elastic half-spaces, overcoming challenges faced by traditional numerical approaches.

Contribution

The authors develop a spectral collocation approach that effectively computes leaky wave modes by using domain mappings to complex paths, enabling accurate dispersion and attenuation analysis.

Findings

Successfully retrieves dispersion and attenuation curves for leaky Lamb waves.

Validates results against DISPERSE software and finite element simulations.

Provides an efficient alternative to existing numerical methods for complex waveguide problems.

Abstract

In non-destructive evaluation guided wave inspections, the elastic structure to be inspected is often embedded within other elastic media and the ensuing leaky waves are complex and non-trivial to compute; we consider the canonical example of an elastic waveguide surrounded by other elastic materials that demonstrates the fundamental issues with calculating the leaky waves in such systems. Due to the complex wavenumber solutions required to represent them, leaky waves pose significant challenges to existing numerical methods, with methods that spatially discretise the field to retrieve them suffering from the exponential growth of their amplitude far into the surrounding media. We present a spectral collocation method yielding an accurate and efficient identification of these modes, leaking into elastic half-spaces. We discretise the elastic domains and, depending on the exterior bulk wavespeeds, select appropriate mappings of the discretised domain to complex paths, in which the numerical solution decays and the physics of the problem are preserved. By iterating through all possible radiation cases, the full set of dispersion and attenuation curves are successfully retrieved and validated, where possible, against the commercially available software DISPERSE. As an independent validation, dispersion curves are obtained from finite element simulations of time-dependent waves using Fourier analysis.