Another form of 3D Green’s function for an elastic solid with exponential inhomogeneity

2017 ◽  
Vol 229 (2) ◽  
pp. 455-473
Author(s):  
Kazumi Watanabe
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Elastic Solid ◽  
Exponential Inhomogeneity

Defect Green’s Function of Multiple Point-Like Inhomogeneities in a Multilayered Anisotropic Elastic Solid

2004 ◽  
Vol 71 (5) ◽  
pp. 672-676
Author(s):  
B. Yang
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Elastic Solid ◽  
Anisotropic Elasticity ◽  
Matrix Inversion ◽  
Numerical Results ◽  
Multiple Point ◽  
Present Formulation ◽  
Anisotropic Elastic ◽  
The Continuum

Defect Green’s function (GF) of multiple point-like inhomogeneities in a multilayered solid has been derived within the theory of linear anisotropic elasticity. It is related to the (reference) GF of the multilayered matrix excluding the inhomogeneities through the continuum Dyson’s equation. While the reference GF is available, the defect GF can be solved. The expressions are first analytically reduced by realizing the point-likeness of the inhomogeneities. The subsequent procedure involves the solution of the response of each individual inhomogeneity to a far-field straining in the multilayered matrix and a matrix inversion on the order of the number of inhomogeneities. Furthermore, the defect GF is applied to derive the field induced by inhomogeneous substitutions in a multilayered solid. Numerical results are reported for arrays of cubic and semispherical Ge inclusions in a Si/Ge superlattice. The numerical results have demonstrated the validity and efficiency of the present formulation.

Diffraction of sound by a surface scratch on an elastic solid

1990 ◽  
Vol 1 (4) ◽  
pp. 353-369 ◽  
Author(s):  
M. S. Howe
Keyword(s):  
Green’S Function ◽  
Cross Section ◽  
Green's Function ◽  
Plane Surface ◽  
Circular Cross Section ◽  
Elastic Solid ◽  
Sound Waves ◽  
Limited Region ◽  
Rayleigh Approximation ◽  
Approximate Form

An analysis is made of the diffraction of sound by a scratch (or groove) in the nominally plane surface of a fluid-loaded elastic solid. The solid is modelled as an isotropic half-space, and an exact representation of the diffracted sound is obtained as an integral over the surface of the scratch involving a Green's function and the acoustic field for the homogeneous solid. The restriction of the range of integration to the surface of the scratch permits the use of an approximate form of Green's function which is valid for source positions confined to a limited region of space. Details are worked out for the case in which the acoustic wavelength is much larger than the diameter of the scratch cross-section (Rayleigh approximation). The results are illustrated by application to sound waves in water inicident on a rectilinear scratch of circular cross-section in steel or rubber. In the former case an important rôle in diffraction is played by leaky Rayleigh waves on the fluid-solid interface.

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