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

  • Alistair Ferguson

Student thesis: Doctoral Thesis

Abstract

In this thesis the propagation of high-frequency elastic waves in a spatially heterogeneous, randomly layered material is reported upon. The material is locally anisotropic and a smooth function describes the spatial variation in the rotation of the associatedslowness surface in the plane of wave propagation. The layer thicknesses and the rotation of their associated slowness curves 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, additively manufactured metallic components and carbon fibre reinforced polymer (CFRP) composites. The model for wave propagation set out in later sections captures the attenuation and deformation of the input wave as it interacts with the internal material microstructure via multiple scattering. In early Chapters, a key parameter emerges which captures the degree ofanisotropy in the medium and it is shown how this affects the transmitted and reflected energy. 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 equations that emerge. Using these stochastic equations allows derivation of infinitesimal generators which encode information about the random processes in the wave propagation problem, which affords for studies into the probabilitydensity functions of the coherent wave via the use of Fokker-Planck equations. Later Chapters use diffusion approximations to study a broadband ultrasonic pulse via Ricatti equations; in particular a line source. The incoherent component of the wave is characterised via the autocorrelation of the reflection coefficient and an expression for the reflected intensity of the wave at different lateral observation points is derived.
Date of Award31 May 2022
Original languageEnglish
Awarding Institution
  • University Of Strathclyde
SponsorsUniversity of Strathclyde
SupervisorKatherine Margaret Mary Tant (Supervisor) & Anthony Mulholland (Supervisor)

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