Evaluation of Green’s function for vertical point-load excitation applied to the surface of a layered semi-infinite elastic medium

2006 ◽  
Vol 76 (7-8) ◽  
pp. 465-479 ◽  
Author(s):  
Andrej Strukelj ◽  
Tomaz Plibersek ◽  
Andrej Umek
Keyword(s):  
Green’S Function ◽  
Elastic Medium ◽  
Green's Function ◽  
Point Load

scholarly journals Green's function of the clamped punctured disk

1977 ◽  
Vol 20 (2) ◽  
pp. 175-181 ◽  
Author(s):  
Mitsuru Nakai ◽  
Leo Sario
Keyword(s):  
Green’S Function ◽  
Circular Plate ◽  
Green's Function ◽  
American Mathematical Society ◽  
Point Load ◽  
Thin Elastic Plate ◽  
Constant Sign ◽  
Boundary Circle ◽  
Simply Supported ◽  
Image Position

If a thin elastic circular plate B: ∣z∣ < 1 is clamped (simply supported, respectively) along its edge ∣z∣ = 1, its deflection at z ∈ B under a point load at ζ ∈ B, measured positively in the direction of the gravitational pull, is the biharmonic Green's function β(z, ζ) of the clamped plate (γ(z, ζ) of the simply supported plate, respectively). We ask: how do β(z, ζ) and γ(z, ζ) compare with the corresponding deflections β0(z, ζ) and γ0(z, ζ) of the punctured circular plate B0: 0 < ∣ z ∣ < 1 that is “clamped” or “simply supported”, respectively, also at the origin? We shall show that γ(z, ζ) is not affected by the puncturing, that is, γ(·, ζ) = γ0(·, ζ), whereas β(·, ζ) is:on B0 × B0. Moreover, while β((·, ζ) is of constant sign, β0(·, ζ) is not. This gives a simple counterexmple to the conjecture of Hadamard [6] that the deflection of a clampled thin elastic plate be always of constant sign:The biharmonic Gree's function of a clampled concentric circular annulus is not of constant sign if the radius of the inner boundary circle is sufficiently small.Earlier counterexamples to Hadamard's conjecture were given by Duffin [2], Garabedian [4], Loewner [7], and Szegö [9]. Interest in the problem was recently revived by the invited address of Duffin [3] before the Annual Meeting of the American Mathematical Society in 1974. The drawback of the counterexample we will present is that, whereas the classical examples are all simply connected, ours is not. In the simplicity of the proof, however, there is no comparison.

ON VOLTERRA'S DISLOCATIONS IN A SEMI-INFINITE ELASTIC MEDIUM

1958 ◽  
Vol 36 (2) ◽  
pp. 192-205 ◽  
Author(s):  
J. A. Steketee
Keyword(s):  
Green’S Function ◽  
Elastic Medium ◽  
Green's Function ◽  
Displacement Field ◽  
General Problem ◽  
Function Method ◽  
Green’S Functions ◽  
Boundary Surface ◽  
Green’S Function Method ◽  
Plane Parallel

In this paper a Green's function method is developed to deal with the problem of a Volterra dislocation in a semi-infinite elastic medium in such a way that the boundary surface of the medium remains free from stresses. (A Volterra dislocation is here defined as a surface across which the displacement components show a discontinuity of the type Δu = U + Ω ×r, where U and Ω are constant vectors.) It is found that the general problem requires the construction of six sets of Green's functions. The method for the construction is outlined and applied to one of the six sets, which is of the type of two double forces with moments in a plane parallel with the boundary. The displacement field thus generated is computed. Several of the results obtained are believed to be of geophysical interest, but a more detailed discussion of these applications is postponed to a further communication which is being prepared.

On estimating the impulse response between receivers in a controlled ultrasonic experiment

Geophysics ◽  
2006 ◽  
Vol 71 (4) ◽  
pp. SI79-SI84 ◽  
Author(s):  
K. van Wijk
Keyword(s):  
Data Processing ◽  
Laboratory Experiment ◽  
Green’S Function ◽  
Detailed Analysis ◽  
Elastic Medium ◽  
Impulse Response ◽  
Green's Function ◽  
Geophysical Data ◽  
Seismic Interferometry ◽  
Band Limited

A controlled ultrasonic laboratory experiment provides a detailed analysis of retrieving a band-limited estimate of the Green's function between receivers in an elastic medium. Instead of producing a formal derivation, this paper appeals to a series of intuitive operations, common to geophysical data processing, to understand the practicality of seismic interferometry. Whereas the retrieval of the full Green's function is based on the crosscorrelation of receivers in the presence of equipartitioned signal, an estimate of the impulse response is recovered successfully with 40 sources in a line covering six wavelengths at the surface.

Green’s function for the scattered field near the surface of a dissipative elastic medium.

2010 ◽  
Vol 127 (3) ◽  
pp. 2012-2012 ◽  
Author(s):  
Evgenia A. Zabolotskaya ◽  
Yurii A. Ilinskii ◽  
Mark F. Hamilton
Keyword(s):  
Green’S Function ◽  
Elastic Medium ◽  
Green's Function ◽  
Scattered Field

Green's function for an infinite pre-stressed elastic medium

1976 ◽  
Vol 31 (2) ◽  
pp. 183-194
Author(s):  
E. Boschi ◽  
E. Di Curzio
Keyword(s):  
Green’S Function ◽  
Elastic Medium ◽  
Green's Function

Dynamic 2.5-D Green's function for a point load or a point fluid source in a layered poroelastic half-space

2017 ◽  
Vol 77 ◽  
pp. 123-137 ◽  
Author(s):  
Chao He ◽  
Shunhua Zhou ◽  
Peijun Guo ◽  
Honggui Di ◽  
Junhua Xiao
Keyword(s):  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Point Load ◽  
Fluid Source

Green's function for a two–dimensional exponentially graded elastic medium

2004 ◽  
Vol 460 (2046) ◽  
pp. 1689-1706 ◽  
Author(s):  
Youn-Sha Chan ◽  
L. J. Gray ◽  
T. Kaplan ◽  
Glaucio H. Paulino
Keyword(s):  
Green’S Function ◽  
Elastic Medium ◽  
Green's Function ◽  
Two Dimensional ◽  
Exponentially Graded
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