Scattering of a Plane Elastic Wave From Objects Near an Interface

1972 ◽  
Vol 39 (4) ◽  
pp. 1019-1026 ◽  
Author(s):  
Stephen B. Bennett
Keyword(s):  
Elastic Wave ◽  
Electromagnetic Waves ◽  
Three Dimensions ◽  
Circular Cylinders ◽  
Scattering Problems ◽  
Reflection And Refraction ◽  
Time Harmonic ◽  
Incident Plane ◽  
Boundary Curves ◽  
Consistent Formulation

The displacement field generated by the reflection and refraction of plane (time harmonic) elastic waves by finite obstacles of arbitrary shape, in the neighborhood of a plane interface between two elastic media, is investigated. The technique employed allows a consistent formulation of the problem for both two and three dimensions, and is not limited either to boundary shapes which are level surfaces in appropriate coordinate systems, i.e., circular cylinders, spheres, etc., or to closed boundary curves or surfaces. The approach is due to Twersky, and has been applied to many problems of the scattering of electromagnetic waves. The method consists of expressing the net field due to all multiple scattering in terms of the field reflected from each boundary in isolation when subjected to an incident plane elastic wave. Thus the technique makes use of more elemental scattering problems whose solutions are extant. By way of illustration, a numerical solution to the scattering of a plane elastic wave by a rigid circular cylindrical obstacle adjacent to a plane free surface is considered.

scholarly journals Mathematical interpretation of seismic wave scattering and refraction on tunnel structures of circular cross-section

2020 ◽  
Vol 18 (3) ◽  
pp. 241-260
Author(s):  
Elefterija Zlatanovic ◽  
Vlatko Sesov ◽  
Dragan Lukic ◽  
Zoran Bonic
Keyword(s):  
Elastic Wave ◽  
Wave Scattering ◽  
Scattering Problem ◽  
Circular Cross Section ◽  
Circular Cylinders ◽  
Elastic Wave Scattering ◽  
Incident Plane ◽  
Seismic Wave Scattering ◽  
Basic Equations ◽  
Mathematical Interpretation

Mathematical interpretation of the elastic wave diffraction in circular cylinder coordinates is in the focus of this paper. Firstly, some of the most important properties of Bessel functions, pertinent to the elastic wave scattering problem, have been introduced. Afterwards, basic equations, upon which the method of wave function expansions is established, are given for cylindrical coordinates and for plane-wave representation. In addition, steady-state solutions for the cases of a single cavity and a single tunnel are presented, with respect to the wave scattering and refraction phenomena, considering both incident plane harmonic compressional and shear waves. The last part of the work is dealing with the translational addition theorems having an important role in the problems of diffraction of waves on a pair of circular cylinders.

Scattering Problems: Beltrami Fields and Solvability

2012 ◽  
Author(s):  
G. F. Roach ◽  
I. G. Stratis ◽  
A. N. Yannacopoulos
Keyword(s):  
Integral Equation ◽  
Electromagnetic Wave ◽  
Electromagnetic Waves ◽  
Boundary Integral ◽  
Scattering Problems ◽  
Electromagnetic Wave Scattering ◽  
Beltrami Fields ◽  
Integral Equation Methods ◽  
Time Harmonic ◽  
Surrounding Space

This chapter deals with the solvability of time-harmonic electromagnetic wave scattering by an obstacle: either the obstacle or the environment in which it is embedded, or both, is (are) occupied by a chiral material. It assumes that the scatterer and its surrounding space are homogeneous: thus allowing the use of the boundary integral equation methods for the study of the considered problems. This chapter considers two kinds of problems: first, the scattering of plane electromagnetic waves propagating in chiral space by a perfectly conducting obstacle, and second, the scattering of plane electromagnetic waves by a penetrable obstacle; either the scatterer or the surrounding space, or both, may be filled with a chiral material.

Multiple scattering of electromagnetic waves by finitely many point-like obstacles

2014 ◽  
Vol 24 (05) ◽  
pp. 863-899 ◽  
Author(s):  
Durga Prasad Challa ◽  
Guanghui Hu ◽  
Mourad Sini
Keyword(s):  
Multiple Scattering ◽  
Electromagnetic Scattering ◽  
Electromagnetic Waves ◽  
Plane Waves ◽  
Field Measurements ◽  
Scattered Wave ◽  
Three Dimensions ◽  
Music Algorithm ◽  
Scattering Problems ◽  
Scattering Coefficients

This paper is concerned with the direct and inverse time-harmonic electromagnetic scattering problems for a finite number of isotropic point-like obstacles in three dimensions. In the first part, we show that the representation of scattered fields obtained using the Foldy physical assumption "on the proportionality of the strength of the scattered wave on a given scatterer to the external field on it" is the same as the one derived from the model corresponding to the scattering by Dirac-like refraction indices. Using the regularization approach known in quantum mechanics, we rigorously deduce the solution operator (Green's tensor) of the last model in appropriate weighted spaces. Intermediate levels of the scattering between the Born and Foldy models are also described. In the second part, we apply the MUSIC algorithm to the inverse problem of detecting both the position of point-like scatterers and the scattering coefficients attached to them from the far-field measurements of finitely many incident plane waves, with an emphasis on discussing the effect of multiple scattering.

RECIPROCITY RELATIONS FOR A CONDUCTIVE SCATTERER WITH A CHIRAL CORE IN QUASI-STATIC FORM

2018 ◽  
Vol 60 (1) ◽  
pp. 86-94
Author(s):  
C. E. ATHANASIADIS ◽  
E. S. ATHANASIADOU ◽  
S. DIMITROULA
Keyword(s):  
Electromagnetic Waves ◽  
Scattering Problem ◽  
Spherical Wave ◽  
Point Sources ◽  
Scattering Problems ◽  
Spherical Waves ◽  
Incident Plane ◽  
Reciprocity Relations ◽  
Static Form ◽  
Stationary Approximation

We analyse a scattering problem of electromagnetic waves by a bounded chiral conductive obstacle, which is surrounded by a dielectric, via the quasi-stationary approximation for the Maxwell equations. We prove the reciprocity relations for incident plane and spherical electric waves upon the scatterer. Mixed reciprocity relations have also been proved for a plane wave and a spherical wave. In the case of spherical waves, the point sources are located either inside or outside the scatterer. These relations are used to study the inverse scattering problems.

STRONG AND WEAK FORMS OF THE METHOD OF MOMENTS AND THE COUPLED DIPOLE METHOD FOR SCATTERING OF TIME-HARMONIC ELECTROMAGNETIC FIELDS

1992 ◽  
Vol 03 (03) ◽  
pp. 583-603 ◽  
Author(s):  
AKHLESH LAKHTAKIA
Keyword(s):  
Electromagnetic Fields ◽  
Method Of Moments ◽  
Electromagnetic Scattering ◽  
Final Section ◽  
The Other ◽  
Numerical Techniques ◽  
Scattering Problems ◽  
Time Harmonic

Algorithms based on the method of moments (MOM) and the coupled dipole method (CDM) are commonly used to solve electromagnetic scattering problems. In this paper, the strong and the weak forms of both numerical techniques are derived for bianisotropic scatterers. The two techniques are shown to be fully equivalent to each other, thereby defusing claims of superiority often made for the charms of one technique over the other. In the final section, reductions of the algorithms for isotropic dielectric scatterers are explicitly given.

Topological sensitivity analysis revisited for time-harmonic wave scattering problems. Part I: the free space case

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Frédérique Le Louër ◽  
María-Luisa Rapún
Keyword(s):  
Free Space ◽  
Order Term ◽  
Harmonic Wave ◽  
Dirichlet Condition ◽  
Point Sources ◽  
Neumann Condition ◽  
Scattering Problems ◽  
Content Type ◽  
Time Harmonic ◽  
Topological Gradient

PurposeIn this paper, the authors revisit the computation of closed-form expressions of the topological indicator function for a one step imaging algorithm of two- and three-dimensional sound-soft (Dirichlet condition), sound-hard (Neumann condition) and isotropic inclusions (transmission conditions) in the free space.Design/methodology/approachFrom the addition theorem for translated harmonics, explicit expressions of the scattered waves by infinitesimal circular (and spherical) holes subject to an incident plane wave or a compactly supported distribution of point sources are available. Then the authors derive the first-order term in the asymptotic expansion of the Dirichlet and Neumann traces and their surface derivatives on the boundary of the singular medium perturbation.FindingsAs the shape gradient of shape functionals are expressed in terms of boundary integrals involving the boundary traces of the state and the associated adjoint field, then the topological gradient formulae follow readily.Originality/valueThe authors exhibit singular perturbation asymptotics that can be reused in the derivation of the topological gradient function that generates initial guesses in the iterated numerical solution of any shape optimization problem or imaging problems relying on time-harmonic acoustic wave propagation.

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