The diffraction of SH waves by an arbitrary shaped crack in two dimensions

1992 ◽  
Vol 340 (1659) ◽  
pp. 503-529 ◽  
Keyword(s):  
Function Method ◽  
Scattering Problem ◽  
Elastic Solid ◽  
Two Dimensions ◽  
General Shape ◽  
Sh Waves ◽  
Green Function Method ◽  
Rigid Barrier ◽  
Shaped Crack ◽  
Scalar Scattering

In this paper we consider the two-dimensional scalar scattering problem for Helmholtz’s equation exterior to a smooth open arc of general shape. The problem has a number of physical applications including the diffraction of sound by a rigid barrier immersed in a compressible fluid and by a crack in an elastic solid which supports a state of anti-plane strain (SH-motion). The mathematical method used here is the crack Green function method introduced by G. R. Wickham. This enables the scattering problem to be reduced to the solution of a Fredholm integral equation of the second kind with a continuous kernel. The numerical solution of this equation is discussed and a number of examples are computed.

Scattering of SH-Waves to Semi-Cylindrical Canyon and Rectangular Elastic Hill on the Ground

2012 ◽  
Vol 610-613 ◽  
pp. 2544-2551
Author(s):  
Wen Pu Shi
Keyword(s):  
Half Space ◽  
Function Method ◽  
Expansion Method ◽  
Free Boundaries ◽  
Sh Waves ◽  
Green Function Method ◽  
Common Boundary ◽  
Wave Function Expansion Method ◽  
The Common ◽  
The Given

Wave function expansion method and Green function method were employed to study thescattering problem of SH-waves to the semi-cylindrical canyon and rectangular hill on the gr ound. First, the displacements in the half space and rectangular hill were given which can santisfy the stress-free conditions on the free boundaries. Then, the first kind of Fredholm integration equation of the unknown distribution stress was obtained by using the displacement conditions on the common boundary between the half-space and the rectangular hill, and Gauss-Legendre integration formula was used to solve the equation. The given example results show the feasibility and practicability of the method here.

The Green function method for the two-surface problem

1970 ◽  
Vol 8 (13) ◽  
pp. 1069-1071 ◽  
Author(s):  
F. Flores ◽  
F. Garcia-Moliner ◽  
J. Rubio
Keyword(s):  
Green Function ◽  
Function Method ◽  
Green Function Method ◽  
The Green Function

Theory of Electron Diffraction by Crystals

1967 ◽  
Vol 22 (4) ◽  
pp. 422-431 ◽  
Author(s):  
Kyozaburo Kambe
Keyword(s):  
Integral Equation ◽  
Electron Diffraction ◽  
General Theory ◽  
Green’S Function ◽  
Green's Function ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Two Dimensions ◽  
The Third ◽  
Third Dimension

A general theory of electron diffraction by crystals is developed. The crystals are assumed to be infinitely extended in two dimensions and finite in the third dimension. For the scattering problem by this structure two-dimensionally expanded forms of GREEN’S function and integral equation are at first derived, and combined in single three-dimensional forms. EWALD’S method is applied to sum up the series for GREEN’S function.

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