A probabilistic approach to modelling ultrasonic shear wave propagation in locally anisotropic heterogeneous media

Ferguson, Alistair S. and Tant, Katherine M. M. and Foodun, Mohammud and Mulholland, Anthony J. (2024) A probabilistic approach to modelling ultrasonic shear wave propagation in locally anisotropic heterogeneous media. Waves in Random and Complex Media. pp. 1-24. ISSN 1745-5049 (https://doi.org/10.1080/17455030.2024.2341283)

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Abstract

This article considers the propagation of a high-frequency time harmonic, elastic wave in a spatially heterogeneous, randomly layered material. The material is locally anisotropic, and the material properties change from one layer to the next by a random rotation of the associated slowness surface in the plane of wave propagation. The layer thicknesses and this rotation follow a stochastic (Markovian) process. This situation is found in ultrasonic wave propagation in polycrystalline materials; for example, in the ultrasonic non-destructive testing of welds and additively manufactured metallic components. This work focuses on monochromatic shear waves propagating in a two-dimensional plane. Using the differences in length scales between the ultrasound wavelength, the mean layer size, and the wave propagation distance, a small parameter is identified in the stochastic differential equation that emerges. Its infinitesimal generator leads to a Fokker-Planck equation via limit theorems involving this small parameter. A weak form of the Fokker-Planck equation is derived and then solved via a finite element package. The numerical solution to the Fokker-Planck equation is used to compute statistical moments of the power transmission coefficient. Finally, a parametric study on the effect of the degree of anisotropy (asphericity of the slowness surface) of the material on the transmitted energy is performed.

ORCID iDs

Ferguson, Alistair S., Tant, Katherine M. M. ORCID logoORCID: https://orcid.org/0000-0003-4345-7054, Foodun, Mohammud and Mulholland, Anthony J.;
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