Leaky wave characterisation using spectral methods

TL;DR

This paper presents a spectral collocation method for accurately and efficiently identifying leaky wave dispersion properties in elastic waveguides immersed in fluids, overcoming traditional root-finding and numerical challenges.

Contribution

It introduces a novel spectral method with a mapping technique to find exponentially growing leaky wave solutions, improving accuracy and efficiency over existing methods.

Findings

Successfully applied to leaky Lamb waves in fluid-embedded waveguides

Validated results against commercial software Disperse

Demonstrated fast convergence and robustness of the spectral approach

Abstract

Leaky waves are an important class of waves, particularly for guiding waves along structures embedded within another medium; a mismatch in wavespeeds often leads to leakage of energy from the waveguide, or interface, into the medium, which consequently attenuates the guided wave. The accurate and efficient identification of theoretical solutions for leaky waves is a key requirement for the choices of modes and frequencies required for non-destructive evaluation inspection techniques. We choose a typical situation to study: an elastic waveguide with a fluid on either side. Historically, leaky waves are identified via root-finding methods that have issues with conditioning, or, numerical methods` that struggle with the exponential growth of solutions at infinity. By building upon a spectral collocation method, we show how it can be adjusted to find exponentially growing solutions, i.e. leaky waves, leading to an accurate, fast and efficient identification of their dispersion properties. The key concept required is a mapping, in the fluid region, that allows for exponential growth of the physical solution at infinity, whilst the mapped numerical setting decays. We illustrate this by studying leaky Lamb waves in an elastic waveguide immersed between two different fluids and verify this using the commercially available software Disperse.