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A strategy of spatial distortion to make an anisotropic problem become isotropic has been previously validated in two-dimensional transverse isotropic (TI) viscoelastic cases. Here, the approach is extended to the three-dimensional problem by considering the time-harmonic point force response (Green's function) in a TI viscoelastic material. The resulting wave field, exactly solvable using a Radon transform with numerical integration, is approximated via spatial distortion of the closed form analytical solution to the isotropic case. Different distortions are used, depending on whether the polarization of the wave motion is orthogonal to the axis of isotropy, with the approximation yielding differing levels of accuracy.
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Converging super-elliptic torsional shear waves in a bounded transverse isotropic viscoelastic material with nonhomogeneous outer boundary
A theoretical approach was recently introduced [Guidetti and Royston, J. Acoust. Soc. Am. 144, 2312–2323 (2018)] for the radially converging slow shear wave pattern in transverse isotropic materials subjected to axisymmetric excitation normal to the axis of isotropy at the outer boundary of the material. This approach is enabled via transformation to an elliptic coordinate system with isotropic properties. The approach is extended to converging fast shear waves driven by axisymmetric torsional motion polarized in a plane containing the axis of isotropy. The approach involves transformation to a super-elliptic shape with isotropic properties and use of a numerically efficient boundary value approximation.
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- Award ID(s):
- 1852691
- PAR ID:
- 10594007
- Publisher / Repository:
- Acoustical Society of America (ASA)
- Date Published:
- Journal Name:
- The Journal of the Acoustical Society of America
- Volume:
- 146
- Issue:
- 5
- ISSN:
- 0001-4966
- Format(s):
- Medium: X Size: p. EL451-EL457
- Size(s):
- p. EL451-EL457
- Sponsoring Org:
- National Science Foundation
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