Ultrasonic Wave Scattering by a Subsurface Flaw in Joined Fluid-Solid Half Spaces

The scattering of waves by a flaw (cavity or inclusion) that is embedded in an elastic half space at a finite depth below the interface with a fluid half space is studied using the T-matrix approach. Expressions are derived for the scattered fields generated in the fluid and solid half spaces as well as the asymptotic form of the field in the fluid at a large distance from the interface. Numerical results are presented for spherical voids and steel inclusions embedded in epoxy as well as oblate spheroidal voids in a metal for various flaw depths, scattering geometries, and frequency of the incident wave. The results obtained by keeping different orders of multiple scattering between the flaw and the interface are critically discussed.

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The Transition Matrix Formalism for the Scattering of an Alluvium on an Elastic Half-Space

Volume 8: Seismic Engineering ◽

10.1115/pvp2007-26116 ◽

2007 ◽

Author(s):

Wen-I Liao ◽

Tsung-Jen Teng ◽

Shiang-Jung Wang

Keyword(s):

Half Space ◽

Transition Matrix ◽

Plane Waves ◽

Three Dimensional ◽

Scattering Matrix ◽

Elastic Half Space ◽

Basis Functions ◽

Matrix Formalism ◽

T Matrix ◽

Singular Wave

This paper develops the transition matrix formalism for scattering from an three-dimensional alluvium on an elastic half-space. Betti’s third identity is employed to establish orthogonality conditions among basis functions that are Lamb’s singular wave functions. The total displacements and associated tractions exterior and interior to the surface are expanded in a Rayleigh series. The boundary conditions are applied and the T-matrix is derived. A linear transformation is utilized to construct a set of orthogonal basis functions. The transformed T-matrix is related to the scattering matrix and it is shown that the scattering matrix is symmetric and unitary and that the T-matrix is symmetric. Typical numerical results obtained by incident plane waves for verification are presented.

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Wave Scattering by Crack Under Shock P-Wave in an Elastic Half-Space

Journal of Vibration Engineering & Technologies ◽

10.1007/s42417-021-00385-9 ◽

2021 ◽

Author(s):

Hai Zhang ◽

Tianyu Zhao ◽

Dai Wang ◽

Qiang Pei ◽

Ying Xu ◽

...

Keyword(s):

Half Space ◽

Wave Scattering ◽

Elastic Half Space ◽

P Wave

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An efficient TCS formula for rainfall microwave attenuation: T-matrix approach and 3-D fitting for oblate spheroidal raindrops

IEEE Transactions on Antennas and Propagation ◽

10.1109/8.718572 ◽

1998 ◽

Vol 46 (8) ◽

pp. 1176-1181 ◽

Cited By ~ 6

Author(s):

Yong-Lee Seow ◽

Le-Wei Li ◽

Mook-Seng Leong ◽

Pang-Shyan Kooi ◽

Tat-Soon Yeo

Keyword(s):

Matrix Approach ◽

Oblate Spheroidal ◽

Microwave Attenuation ◽

T Matrix

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On Evaluation of Lamb's Integrals for Waves in a Two-Dimension Elastic Half-Space

Journal of Mechanics ◽

10.1017/s1727719100001684 ◽

2000 ◽

Vol 16 (2) ◽

pp. 109-124 ◽

Cited By ~ 9

Author(s):

Chau-Shioung Yeh ◽

Tsung-Jen Teng ◽

Wen-I Liao

Keyword(s):

Half Space ◽

Phase Function ◽

Wave Scattering ◽

Elastic Half Space ◽

Steepest Descent ◽

Inverse Mapping ◽

Lamb’S Problem ◽

Admissible Path ◽

Formal Solutions ◽

Steepest Descent Path

ABSTRACTIn this paper, a modified version of the method of steepest descent is proposed for the evaluation of Lamb's integrals which can be considered as basis functions dealing with the development of the transition matrix method which can be used to study the wave scattering in a two-dimensional elastic half-space. The formal solutions of the generalized Lamb's problem are studied and evaluated on the basis of the proposed method. After defining a phase function which presents in wavenumber integral, an exact mapping and an inverse mapping can be obtained according to the phase function. Thus, the original integration path can be deformed into an equivalent admissible path, namely, steepest descent path which passed through the saddle point, and then mapped onto a real axis of mapping plane, finally, resulted in an integral of Hermite type. This integral can be efficiently evaluated numerically in spite of either near- to far-field or low to high frequency. At the same time, the asymptotic value can easily be obtained by applying the proposed method. The numerical results for generalized Lamb's solutions are calculated and compared with analytic, asymptotic or other existing data, the excellent agreements are found. The properties of generalized Lamb's solutions are studied and discussed in details. Their possible applications for wave scattering in elastic half-space are also pointed out.

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