Radiation of ultrasound into an anisotropic solid

Q. C. Guo; J. D. Achenbach

doi:10.1016/0041-624X(95)00060-G

Radiation of ultrasound into an anisotropic solid

Q. C. Guo^*, J. D. Achenbach

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

A half-space, x₃ ≤ 0, of a transversely isotropic solid whose axis of symmetry makes an angle α with the x₃-axis, is subjected to a spatially uniform time-harmonic distribution of normal surface tractions over a circular area of the plane x₃ = 0. The wave motion radiated into the half-space is investigated. Using an integral representation for the displacement components the problem is first reduced to a system of singular integral equations for the displacements on the surface x₃ = 0. This system is solved by the boundary element method over a truncated area, where use is made of recently derived simplified forms of the Green's functions. The results show the skewing of the beam as the angle between the axis of symmetry of the transversely isotropic solid and the normal to the surface of the solid is increased.

Original language	English (US)
Pages (from-to)	449-456
Number of pages	8
Journal	Ultrasonics
Volume	33
Issue number	6
DOIs	https://doi.org/10.1016/0041-624X(95)00060-G
State	Published - Nov 1995

Funding

A FORTRAN programf or the numericalc alculationo f the Green’s functions,p rovided by Andres Saez-Perez and CanyunW ang,w asu seda s one part of the program that we developedf or solving the numericale xamples presentedin this paper.T his work wasc arriedo ut in the course of researchs ponsoredb y the Office of Naval Research.

Keywords

Green's functions
anisotropy
beam skewing
boundary element method

ASJC Scopus subject areas

Acoustics and Ultrasonics

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10.1016/0041-624X(95)00060-G

Cite this

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title = "Radiation of ultrasound into an anisotropic solid",

abstract = "A half-space, x3 ≤ 0, of a transversely isotropic solid whose axis of symmetry makes an angle α with the x3-axis, is subjected to a spatially uniform time-harmonic distribution of normal surface tractions over a circular area of the plane x3 = 0. The wave motion radiated into the half-space is investigated. Using an integral representation for the displacement components the problem is first reduced to a system of singular integral equations for the displacements on the surface x3 = 0. This system is solved by the boundary element method over a truncated area, where use is made of recently derived simplified forms of the Green's functions. The results show the skewing of the beam as the angle between the axis of symmetry of the transversely isotropic solid and the normal to the surface of the solid is increased.",

keywords = "Green's functions, anisotropy, beam skewing, boundary element method",

author = "Guo, {Q. C.} and Achenbach, {J. D.}",

note = "Funding Information: A FORTRAN programf or the numericalc alculationo f the Green{\textquoteright}s functions,p rovided by Andres Saez-Perez and CanyunW ang,w asu seda s one part of the program that we developedf or solving the numericale xamples presentedin this paper.T his work wasc arriedo ut in the course of researchs ponsoredb y the Office of Naval Research.",

year = "1995",

month = nov,

doi = "10.1016/0041-624X(95)00060-G",

language = "English (US)",

volume = "33",

pages = "449--456",

journal = "Ultrasonics",

issn = "0041-624X",

publisher = "Elsevier B.V.",

number = "6",

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TY - JOUR

T1 - Radiation of ultrasound into an anisotropic solid

AU - Guo, Q. C.

AU - Achenbach, J. D.

N1 - Funding Information: A FORTRAN programf or the numericalc alculationo f the Green’s functions,p rovided by Andres Saez-Perez and CanyunW ang,w asu seda s one part of the program that we developedf or solving the numericale xamples presentedin this paper.T his work wasc arriedo ut in the course of researchs ponsoredb y the Office of Naval Research.

PY - 1995/11

Y1 - 1995/11

N2 - A half-space, x3 ≤ 0, of a transversely isotropic solid whose axis of symmetry makes an angle α with the x3-axis, is subjected to a spatially uniform time-harmonic distribution of normal surface tractions over a circular area of the plane x3 = 0. The wave motion radiated into the half-space is investigated. Using an integral representation for the displacement components the problem is first reduced to a system of singular integral equations for the displacements on the surface x3 = 0. This system is solved by the boundary element method over a truncated area, where use is made of recently derived simplified forms of the Green's functions. The results show the skewing of the beam as the angle between the axis of symmetry of the transversely isotropic solid and the normal to the surface of the solid is increased.

AB - A half-space, x3 ≤ 0, of a transversely isotropic solid whose axis of symmetry makes an angle α with the x3-axis, is subjected to a spatially uniform time-harmonic distribution of normal surface tractions over a circular area of the plane x3 = 0. The wave motion radiated into the half-space is investigated. Using an integral representation for the displacement components the problem is first reduced to a system of singular integral equations for the displacements on the surface x3 = 0. This system is solved by the boundary element method over a truncated area, where use is made of recently derived simplified forms of the Green's functions. The results show the skewing of the beam as the angle between the axis of symmetry of the transversely isotropic solid and the normal to the surface of the solid is increased.

KW - Green's functions

KW - anisotropy

KW - beam skewing

KW - boundary element method

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DO - 10.1016/0041-624X(95)00060-G

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SN - 0041-624X

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SP - 449

EP - 456

JO - Ultrasonics

JF - Ultrasonics

IS - 6

ER -

Radiation of ultrasound into an anisotropic solid

Abstract

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Keywords

ASJC Scopus subject areas

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