TY - JOUR

T1 - A probabilistic approach to modelling ultrasonic shear wave propagation in locally anisotropic heterogeneous media

AU - Ferguson, Alistair S.

AU - Tant, Katherine M. M.

AU - Foodun, Mohammud

AU - Mulholland, Anthony J.

PY - 2024/4/16

Y1 - 2024/4/16

N2 - 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.

AB - 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.

KW - Fokker-Planck

KW - probabilistic

KW - layered

KW - anisotropic

KW - ultrasound

KW - elastic

KW - moments

UR - https://www.tandfonline.com/journals/twrm20

U2 - 10.1080/17455030.2024.2341283

DO - 10.1080/17455030.2024.2341283

M3 - Article

SN - 1745-5030

SP - 1

EP - 24

JO - Waves in Random and Complex Media

JF - Waves in Random and Complex Media

ER -