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Scattering of Elastic Waves by an Anisotropic Sphere with Application to Polycrystalline Materials.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Scattering of Elastic Waves by an Anisotropic Sphere with Application to Polycrystalline Materials./
Author:	Jafarzadeh, Ata.
Description:	1 online resource (49 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 85-06, Section: B.
Contained By:	Dissertations Abstracts International85-06B.
Subject:	Propagation. -
Online resource:	click for full text (PQDT)
ISBN:	9798381022650

Scattering of Elastic Waves by an Anisotropic Sphere with Application to Polycrystalline Materials.
Jafarzadeh, Ata.

Scattering of Elastic Waves by an Anisotropic Sphere with Application to Polycrystalline Materials. - 1 online resource (49 pages)

Source: Dissertations Abstracts International, Volume: 85-06, Section: B.

Thesis (Ph.D.)--Chalmers Tekniska Hogskola (Sweden), 2023.

Includes bibliographical references

Scattering of a plane wave by a single spherical obstacle is the archetype of many scattering problems in various branches of physics. Spherical objects can provide a good approximation for many real objects, and the analytic formulation for a single sphere can be used to investigate wave propagation in more complex structures like particulate composites or grainy materials, which may have applications in non-destructive testing, material characterization, medical ultrasound, etc. The main objective of this thesis is to investigate an analytical solution for scattering of elastic waves by an anisotropic sphere with various types of anisotropy. Throughout the thesis a systematic series expansion approach is used to express displacement and traction fields outside and inside the sphere. For the surrounding isotropic medium such an expansion is made in terms of the traditional vector spherical wave functions. However, describing the fields inside the anisotropic sphere is more complicated since the classical methods are not applicable. The first step is to describe the anisotropy in spherical coordinates, then the expansion inside the sphere is made in the vector spherical harmonics in the angular directions and power series in the radial direction. The governing equations inside the sphere provide recurrence relations among the unknown expansion coefficients. The remaining expansion coefficients outside and inside the sphere can be found using the boundary conditions on the sphere. Thus, this gives the scattered wave coefficients from which the transition (T) matrix can be found. This is convenient as the T matrix fully describes the scattering by the sphere and is independent of the incident wave. The expressions of the general Tmatrix elements are complicated, but in the low frequency limit it is possible to obtain explicit expressions.The Tmatrices may be used to solve more complex problems like the wave propagation in polycrystalline materials. The attenuation and wave velocity in a polycrystalline material with randomly oriented anisotropic grains are thus investigated. These quantities are calculated analytically using the simple theory of Foldy and show a very good correspondence for low frequencies with previously published results and numerical computations with FEM. This approach is then utilized for an inhomogeneous medium with local anisotropy, incorporating various statistical information regarding the geometrical and elastic properties of the inhomogeneities.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2024

Mode of access: World Wide Web

ISBN: 9798381022650Subjects--Topical Terms:

1372600
Propagation.
Index Terms--Genre/Form:

554714
Electronic books.

Scattering of Elastic Waves by an Anisotropic Sphere with Application to Polycrystalline Materials.
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500 $a Source: Dissertations Abstracts International, Volume: 85-06, Section: B.
502 $a Thesis (Ph.D.)--Chalmers Tekniska Hogskola (Sweden), 2023.
504 $a Includes bibliographical references
520 $a Scattering of a plane wave by a single spherical obstacle is the archetype of many scattering problems in various branches of physics. Spherical objects can provide a good approximation for many real objects, and the analytic formulation for a single sphere can be used to investigate wave propagation in more complex structures like particulate composites or grainy materials, which may have applications in non-destructive testing, material characterization, medical ultrasound, etc. The main objective of this thesis is to investigate an analytical solution for scattering of elastic waves by an anisotropic sphere with various types of anisotropy. Throughout the thesis a systematic series expansion approach is used to express displacement and traction fields outside and inside the sphere. For the surrounding isotropic medium such an expansion is made in terms of the traditional vector spherical wave functions. However, describing the fields inside the anisotropic sphere is more complicated since the classical methods are not applicable. The first step is to describe the anisotropy in spherical coordinates, then the expansion inside the sphere is made in the vector spherical harmonics in the angular directions and power series in the radial direction. The governing equations inside the sphere provide recurrence relations among the unknown expansion coefficients. The remaining expansion coefficients outside and inside the sphere can be found using the boundary conditions on the sphere. Thus, this gives the scattered wave coefficients from which the transition (T) matrix can be found. This is convenient as the T matrix fully describes the scattering by the sphere and is independent of the incident wave. The expressions of the general Tmatrix elements are complicated, but in the low frequency limit it is possible to obtain explicit expressions.The Tmatrices may be used to solve more complex problems like the wave propagation in polycrystalline materials. The attenuation and wave velocity in a polycrystalline material with randomly oriented anisotropic grains are thus investigated. These quantities are calculated analytically using the simple theory of Foldy and show a very good correspondence for low frequencies with previously published results and numerical computations with FEM. This approach is then utilized for an inhomogeneous medium with local anisotropy, incorporating various statistical information regarding the geometrical and elastic properties of the inhomogeneities.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2024
538 $a Mode of access: World Wide Web
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650 4 $a Partial differential equations. $3 1102982
650 4 $a Nondestructive testing. $3 592680
650 4 $a Symmetry. $3 569115
650 4 $a Decomposition. $3 1372547
650 4 $a Restrictions. $3 1467589
650 4 $a Anisotropy. $3 744114
650 4 $a Energy. $3 784773
650 4 $a Integral equations. $3 527971
650 4 $a Deformation. $3 1328788
650 4 $a Radiation. $3 673044
650 4 $a Composite materials. $3 561730
650 4 $a Industrial engineering. $3 679492
650 4 $a Materials science. $3 557839
650 4 $a Mathematics. $3 527692
655 7 $a Electronic books. $2 local $3 554714
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