Elastic wave propagation and scattering in heterogeneous, anisotropic media

Textured polycrystalline materials

Research output: Contribution to journalArticle

66 Citations (Scopus)

Abstract

The propagation of elastic waves through heterogeneous, anisotropic media is considered. Appropriate ensemble averaging of the elastic wave equation leads to the Dyson equation which governs the mean response of the field. The Dyson equation is given here in terms of anisotropic elastic Green's dyadics for the medium with and without heterogeneities. The solution of the Dyson equation for the mean response is given for heterogeneities that are weak. The formalism is further specified for the case of equiaxed cubic polycrystalline metals with a single aligned axis. The Green's dyadics in this case are those for a transversely isotropic medium. Simple expressions for the attenuations of the shear horizontal, quasicompressional, and quasishear waves are given in terms of integrations on the unit circle. The derived expressions are limited to frequencies below the geometric optics limit, but give the attenuations in a direct manner. Comparisons with previous results are also discussed. It is anticipated that a similar approach is necessary for the study of wave propagation in complex anisotropic materials such as fiber, reinforced composites. In addition, the results are applicable to diffuse ultrasonic inspection of textured polycrystalline media.

Original languageEnglish (US)
Pages (from-to)541-552
Number of pages12
JournalJournal of the Acoustical Society of America
Volume106
Issue number2
DOIs
StatePublished - Aug 20 1999

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anisotropic media
wave scattering
elastic waves
wave propagation
dyadics
elastic scattering
attenuation
isotropic media
wave equations
inspection
ultrasonics
optics
formalism
shear
composite materials
fibers
propagation
metals
Waves
Equations

ASJC Scopus subject areas

  • Arts and Humanities (miscellaneous)
  • Acoustics and Ultrasonics

Cite this

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title = "Elastic wave propagation and scattering in heterogeneous, anisotropic media: Textured polycrystalline materials",
abstract = "The propagation of elastic waves through heterogeneous, anisotropic media is considered. Appropriate ensemble averaging of the elastic wave equation leads to the Dyson equation which governs the mean response of the field. The Dyson equation is given here in terms of anisotropic elastic Green's dyadics for the medium with and without heterogeneities. The solution of the Dyson equation for the mean response is given for heterogeneities that are weak. The formalism is further specified for the case of equiaxed cubic polycrystalline metals with a single aligned axis. The Green's dyadics in this case are those for a transversely isotropic medium. Simple expressions for the attenuations of the shear horizontal, quasicompressional, and quasishear waves are given in terms of integrations on the unit circle. The derived expressions are limited to frequencies below the geometric optics limit, but give the attenuations in a direct manner. Comparisons with previous results are also discussed. It is anticipated that a similar approach is necessary for the study of wave propagation in complex anisotropic materials such as fiber, reinforced composites. In addition, the results are applicable to diffuse ultrasonic inspection of textured polycrystalline media.",
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PY - 1999/8/20

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N2 - The propagation of elastic waves through heterogeneous, anisotropic media is considered. Appropriate ensemble averaging of the elastic wave equation leads to the Dyson equation which governs the mean response of the field. The Dyson equation is given here in terms of anisotropic elastic Green's dyadics for the medium with and without heterogeneities. The solution of the Dyson equation for the mean response is given for heterogeneities that are weak. The formalism is further specified for the case of equiaxed cubic polycrystalline metals with a single aligned axis. The Green's dyadics in this case are those for a transversely isotropic medium. Simple expressions for the attenuations of the shear horizontal, quasicompressional, and quasishear waves are given in terms of integrations on the unit circle. The derived expressions are limited to frequencies below the geometric optics limit, but give the attenuations in a direct manner. Comparisons with previous results are also discussed. It is anticipated that a similar approach is necessary for the study of wave propagation in complex anisotropic materials such as fiber, reinforced composites. In addition, the results are applicable to diffuse ultrasonic inspection of textured polycrystalline media.

AB - The propagation of elastic waves through heterogeneous, anisotropic media is considered. Appropriate ensemble averaging of the elastic wave equation leads to the Dyson equation which governs the mean response of the field. The Dyson equation is given here in terms of anisotropic elastic Green's dyadics for the medium with and without heterogeneities. The solution of the Dyson equation for the mean response is given for heterogeneities that are weak. The formalism is further specified for the case of equiaxed cubic polycrystalline metals with a single aligned axis. The Green's dyadics in this case are those for a transversely isotropic medium. Simple expressions for the attenuations of the shear horizontal, quasicompressional, and quasishear waves are given in terms of integrations on the unit circle. The derived expressions are limited to frequencies below the geometric optics limit, but give the attenuations in a direct manner. Comparisons with previous results are also discussed. It is anticipated that a similar approach is necessary for the study of wave propagation in complex anisotropic materials such as fiber, reinforced composites. In addition, the results are applicable to diffuse ultrasonic inspection of textured polycrystalline media.

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