Acoustic Diffraction by a Rigid Annular Spherical Cap

1972 ◽  
Vol 39 (1) ◽  
pp. 139-147 ◽  
Author(s):  
D. L. Jain ◽  
R. P. Kanwal
Keyword(s):  
Cross Section ◽  
Acoustic Waves ◽  
Circular Disk ◽  
Polar Axis ◽  
Field Amplitude ◽  
Far Field ◽  
Axially Symmetric ◽  
Spherical Cap ◽  
Time Harmonic ◽  
Acoustic Diffraction

The problem of the diffraction of time-harmonic axially symmetric acoustic waves by a perfectly rigid annular spherical cap is solved approximately by an integral equation technique. Formulas are derived for the far-field amplitude as well as the scattering cross section when the incident wave is a plane wave traveling along the polar axis. By taking appropriate limits, the solutions for the corresponding problems for an annular circular disk and a whole spherical cap are also presented.

Acoustic Diffraction of a Plane Wave by Two Coplanar Parallel Perfectly Soft or Rigid Strips

1972 ◽  
Vol 50 (9) ◽  
pp. 928-939 ◽  
Author(s):  
D. L. Jain ◽  
R. P. Kanwal
Keyword(s):  
Magnetic Field ◽  
Cross Section ◽  
Normal Derivative ◽  
Field Amplitude ◽  
Far Field ◽  
Soft Or ◽  
Transmission Coefficients ◽  
Incident Plane ◽  
Acoustic Diffraction ◽  
Conducting Screen

The problem of diffraction of a normally incident plane acoustic wave by two parallel and coplanar infinite strips is considered. The assumed boundary conditions on the strips are the vanishing of either the total wave function or its normal derivative. Expressions are obtained for the first few terms of the series for the far-field amplitude and the scattering cross section when the wavelength is much larger than the distance between the outer edges of the strips. The corresponding results for two parallel and coplanar infinite slits in a soft or a rigid screen follow by applying Babinet's principle. This analysis also gives the transmission coefficients for the case of two infinite parallel slits in a thin conducting screen when the electric or magnetic field vectors of the incident plane monochromatic waves are polarized parallel to the edges of the slits.

The low frequency scalar diffraction by an elliptic disc

1967 ◽  
Vol 63 (4) ◽  
pp. 1273-1280 ◽  
Author(s):  
B. D. Sleeman
Keyword(s):  
Plane Wave ◽  
Cross Section ◽  
Scattered Field ◽  
Low Frequency ◽  
Field Amplitude ◽  
Wave Number ◽  
Series Expansions ◽  
Far Field ◽  
Scalar Diffraction ◽  
Scattering Cross

SummaryThe problem of scalar Dirichlet diffraction of a plane wave by an elliptic disc is discussed. A scheme is given whereby the low frequency expansion of the scattered field may be readily obtained. Series expansions are obtained for the far-field amplitude up to and including the second order in the wave number. The first two terms of the scattering cross-section are also derived.

scholarly journals The determination of the surface impedance of an obstacle

1993 ◽  
Vol 36 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Andrzej W. Kȩdzierawski
Keyword(s):  
Acoustic Waves ◽  
Surface Impedance ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Inverse Scattering Problem ◽  
Far Field ◽  
Field Patterns ◽  
Time Harmonic ◽  
Scattered Fields

The inverse scattering problem we consider is to determine the surface impedance of a three-dimensional obstacle of known shape from a knowledge of the far-field patterns of the scattered fields corresponding to many incident time-harmonic plane acoustic waves. We solve this problem by using both the methods of Kirsch-Kress and Colton-Monk.

Dense sets and far field patterns for acoustic waves in an inhomogeneous medium

1988 ◽  
Vol 31 (3) ◽  
pp. 401-407 ◽  
Author(s):  
David Colton
Keyword(s):  
Inhomogeneous Medium ◽  
Inverse Scattering ◽  
Acoustic Waves ◽  
Scattering Problem ◽  
Plane Waves ◽  
Related Result ◽  
Wave Number ◽  
Far Field ◽  
Field Patterns ◽  
Time Harmonic

In this paper, we shall obtain two results on the class of far field patterns corresponding to the scattering of time harmonic acoustic plane waves by an inhomogeneous medium of compact support. Although the problem of characterizing the class of far field patterns is of basic importance in inverse scattering theory, very little is known about this class other than the fact that the far field patterns are entire functions of their independent (complex) variables for each positive fixed value of the wave number. In particular, the class of far field patterns is not all of L2(∂Ω) where ∂Ω is the unit sphere and this implies that the inverse scattering problem is improperly posed since the far field patterns are, in practice, determined from inexact measurements. The purpose of this paper is to show that while the class of far field patterns corresponding to the scattering of time harmonic plane waves by an inhomogeneous medium is not all of L2(∂Ω), it is dense in L2(∂Ω) for sufficiently small values of the wave number. In addition, a related result will be obtained for a special translation of the class of far field patterns. Analogous results for the scattering of time harmonic acoustic waves by a homogeneous scattering obstacle have recently been obtained by Colton [1], Colton and Kirsch [2], Colton and Monk [3, 4] and Kirsch [8].

The inverse elastic scattering by an impenetrable obstacle and a crack

2020 ◽  
Author(s):  
Jianli Xiang ◽  
Guozheng Yan
Keyword(s):  
Mixed Type ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Field Operator ◽  
Integral Equation Method ◽  
Factorization Method ◽  
Boundary Integral ◽  
Far Field ◽  
Direct Scattering ◽  
Time Harmonic

Abstract This paper is concerned with the inverse scattering problem of time-harmonic elastic waves by a mixed-type scatterer, which is given as the union of an impenetrable obstacle and a crack. We develop the modified factorization method to determine the shape of the mixed-type scatterer from the far field data. However, the factorization of the far field operator $F$ is related to the boundary integral matrix operator $A$, which is obtained in the study of the direct scattering problem. So, in the first part, we show the well posedness of the direct scattering problem by the boundary integral equation method. Some numerical examples are presented at the end of the paper to demonstrate the feasibility and effectiveness of the inverse algorithm.

Structural Analysis and Internal Force Calculation of Variable Cross-Section Silo

2012 ◽  
Vol 446-449 ◽  
pp. 429-434
Author(s):  
Rui Ting Ma
Keyword(s):  
Cross Section ◽  
Variable Cross Section ◽  
Internal Force ◽  
Variable Cross ◽  
Axially Symmetric ◽  
Internal Forces ◽  
Differential Element ◽  
Symmetric Load ◽  
Force Calculation ◽  
Constant Section

In this paper, the differential element of constant-section silo wall suffering from axially symmetric load is analyzed. From the results of constant-section silo, the author derives the displacements and internal forces of variable cross-section silo. Through a specific example, this paper compares the displacements , internal forces and concrete consumption of variable cross-section silo with those of constant-section silo, and discusses the merits of variable cross-section silo.

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