scholarly journals Ultrasonic Scattered Field Distribution of One and Two Cylindrical Solids with Phased Array Technique

2019 ◽  
Vol 32 (1) ◽  
Author(s):  
Xiaozhou Liu ◽  
Jian Ma ◽  
Haibin Wang ◽  
Sha Gao ◽  
Yifeng Li ◽  
...  
Keyword(s):  
Plane Wave ◽  
Field Distribution ◽  
Scattered Field ◽  
Phased Array ◽  
Simulation Analysis ◽  
Plane Waves ◽  
Theoretical Solution ◽  
Steel Matrix ◽  
Field Distributions ◽  
Scattered Fields

AbstractThe scattered fields of plane waves in a solid from a cylinder or sphere are critical in determining its acoustic characteristics as well as in engineering applications. This paper investigates the scattered field distributions of different incident waves created by elastic cylinders embedded in an elastic isotropic medium. Scattered waves, including longitudinal and transverse waves both inside and outside the cylinder, are described with specific modalities under an incident plane wave. A model with a scatterer embedded in a structural steel matrix and filled with aluminum is developed for comparison with the theoretical solution. The frequency of the plane wave ranged from 235 kHz to 2348 kHz, which corresponds to scaling factors from 0.5 to 5. Scattered field distributions in matrix materials blocked by an elastic cylindrical solid have been obtained by simulation or calculated using existing parameters. The simulation results are in good agreement with the theoretical solution, which supports the correctness of the simulation analysis. Furthermore, ultrasonic phased arrays are used to study scattered fields by changing the characteristics of the incident wave. On this foundation, a partial preliminary study of the scattered field distribution of double cylinders in a solid has been carried out, and the scattered field distribution at a given distance has been found to exhibit particular behaviors at different moments. Further studies on directivities and scattered fields are expected to improve the quantification of scattered images in isotropic solid materials by the phased array technique.

A method for the exact solution of a class of two-dimensional diffraction problems

1951 ◽  
Vol 205 (1081) ◽  
pp. 286-308 ◽  
Keyword(s):  
Integral Equation ◽  
Plane Wave ◽  
Integral Equations ◽  
Scattered Field ◽  
Plane Waves ◽  
Angular Spectrum ◽  
Diffraction Theory ◽  
General Interest ◽  
Two Dimensional ◽  
Dual Integral Equations

In the last few years Copson, Schwinger and others have obtained exact solutions of a number of diffraction problems by expressing these problems in terms of an integral equation which can be solved by the method of Wiener and Hopf. A simpler approach is given, based on a representation of the scattered field as an angular spectrum of plane waves, such a representation leading directly to a pair of ‘dual’ integral equations, which replaces the single integral equation of Schwinger’s method. The unknown function in each of these dual integral equations is that defining the angular spectrum, and when this function is known the scattered field is presented in the form of a definite integral. As far as the ‘radiation’ field is concerned, this integral is of the type which may be approximately evaluated by the method of steepest descents, though it is necessary to generalize the usual procedure in certain circumstances. The method is appropriate to two-dimensional problems in which a plane wave (of arbitrary polarization) is incident on plane, perfectly conducting structures, and for certain configurations the dual integral equations can be solved by the application of Cauchy’s residue theorem. The technique was originally developed in connexion with the theory of radio propagation over a non-homogeneous earth, but this aspect is not discussed. The three problems considered are those for which the diffracting plates, situated in free space, are, respectively, a half-plane, two parallel half-planes and an infinite set of parallel half-planes; the second of these is illustrated by a numerical example. Several points of general interest in diffraction theory are discussed, including the question of the nature of the singularity at a sharp edge, and it is shown that the solution for an arbitrary (three-dimensional) incident field can be derived from the corresponding solution for a two-dimensional incident plane wave.

THE SCATTERING OF ELECTROMAGNETIC WAVES BY A CORRUGATED SHEET

1959 ◽  
Vol 37 (7) ◽  
pp. 787-797 ◽  
Author(s):  
T. B. A. Senior
Keyword(s):  
Plane Wave ◽  
Current Distribution ◽  
Scattered Field ◽  
Electromagnetic Waves ◽  
Plane Waves ◽  
Physical Optics ◽  
Integral Expression ◽  
Conducting Sheet

The physical optics method is used to determine the scattering of a plane wave by a perfectly conducting sheet having sinusoidal corrugations. The only approximation concerns the current distribution on the sheet and the scattered field then appears as a spectrum of plane waves whose amplitudes are given by a simple integral expression.

Electromagnetic waves

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Plane Wave ◽  
Electromagnetic Waves ◽  
Maxwell Equations ◽  
Plane Waves ◽  
Geometrical Optics ◽  
Particle Detection ◽  
Spatial Coordinates ◽  
A Charge

This chapter examines solutions to the Maxwell equations in a vacuum: monochromatic plane waves and their polarizations, plane waves, and the motion of a charge in the field of a wave (which is the principle upon which particle detection is based). A plane wave is a solution of the vacuum Maxwell equations which depends on only one of the Cartesian spatial coordinates. The monochromatic plane waves form a basis (in the sense of distributions, because they are not square-integrable) in which any solution of the vacuum Maxwell equations can be expanded. The chapter concludes by giving the conditions for the geometrical optics limit. It also establishes the connection between electromagnetic waves and the kinematic description of light discussed in Book 1.

scholarly journals Plane Wave Imaging through Interfaces

Sensors ◽  
2021 ◽  
Vol 21 (15) ◽  
pp. 4967
Author(s):  
Guillermo Cosarinsky ◽  
Jorge F. Cruza ◽  
Jorge Camacho
Keyword(s):  
Image Quality ◽  
Plane Wave ◽  
Phased Array ◽  
Mathematical Formulation ◽  
Non Destructive Testing ◽  
Arbitrary Geometry ◽  
Destructive Testing ◽  
Wave Imaging ◽  
Imaging Strategy ◽  
Non Destructive

Plane Wave Imaging (PWI) has been recently proposed for fast ultrasound inspections in the Non-Destructive-Testing (NDT) field. By using a single (or a reduced number) of plane wave emissions and parallel beamforming in reception, frame rates of hundreds to thousands of images per second can be achieved without significant image quality losses with regard to the Total Focusing Method (TFM) or Phased Array (PA). This work addresses the problem of applying PWI in the presence of arbitrarily shaped interfaces, which is a common problem in NDT. First, the mathematical formulation for generating a plane wave inside a component of arbitrary geometry is given, and the characteristics of the resultant acoustic field are analyzed by simulation, showing plane wavefronts with non-uniform amplitude. Then, an imaging strategy is proposed, accounting for this amplitude effect. Finally, the proposed method is experimentally validated, and its application limits are discussed.

Surface and interfacial anti-plane waves in micropolar solids with surface energy

2020 ◽  
pp. 108128652096564
Author(s):  
Mriganka Shekhar Chaki ◽  
Victor A Eremeyev ◽  
Abhishek K Singh
Keyword(s):  
Surface Wave ◽  
Plane Wave ◽  
Numerical Study ◽  
Plane Waves ◽  
Angular Frequency ◽  
Elastic Half Space ◽  
Surface Strain ◽  
Theoretical Frameworks ◽  
Algebraic Form ◽  
New Type

In this work, the propagation behaviour of a surface wave in a micropolar elastic half-space with surface strain and kinetic energies localized at the surface and the propagation behaviour of an interfacial anti-plane wave between two micropolar elastic half-spaces with interfacial strain and kinetic energies localized at the interface have been studied. The Gurtin–Murdoch model has been adopted for surface and interfacial elasticity. Dispersion equations for both models have been obtained in algebraic form for two types of anti-plane wave, i.e. a Love-type wave and a new type of surface wave (due to micropolarity). The angular frequency and phase velocity of anti-plane waves have been analysed through a numerical study within cut-off frequencies. The obtained results may find suitable applications in thin film technology, non-destructive analysis or biomechanics, where the models discussed here may serve as theoretical frameworks for similar types of phenomena.

Study of wave attenuation in concrete

1993 ◽  
Vol 8 (9) ◽  
pp. 2344-2353 ◽  
Author(s):  
J-M. Berthelot ◽  
Souda M. Ben ◽  
J.L. Robert
Keyword(s):  
Experimental Study ◽  
Plane Wave ◽  
Wave Attenuation ◽  
Plane Waves ◽  
Propagation Distance ◽  
Experimental Results ◽  
The Other ◽  
Wave Frequency ◽  
Concrete Composition ◽  
Analytical Expression

The experimental study of wave attenuation in concrete has been achieved in the case of the propagation of plane waves in concrete rods. Different mortars and concretes have been investigated. A transmitter transducer coupled to one of the ends of the concrete rod generates the propagation of a plane wave in the rod. The receiver transducer, similar to the previous one, is coupled to the other end of the rod. The experimental results lead to an analytical expression for wave attenuation as function of the concrete composition, the propagation distance, and the wave frequency.

Rigorous accounting diffraction on non-plane gratings irradiated by non-planar waves

2021 ◽  
Author(s):  
Leonid I. Goray
Keyword(s):  
Plane Wave ◽  
Wave Diffraction ◽  
Plane Waves ◽  
Three Dimensional ◽  
Integral Equation Method ◽  
Transverse Magnetic ◽  
Incident Field ◽  
Boundary Integral ◽  
Cylindrical Waves ◽  
Plane Wave Diffraction

Abstract The modified boundary integral equation method (MIM) is considered a rigorous theoretical application for the diffraction of cylindrical waves by arbitrary profiled plane gratings, as well as for the diffraction of plane/non-planar waves by concave/convex gratings. This study investigates two-dimensional (2D) diffraction problems of the filiform source electromagnetic field scattered by a plane lamellar grating and of plane waves scattered by a similar cylindrical-shaped grating. Unlike the problem of plane wave diffraction by a plane grating, the field of a localised source does not satisfy the quasi-periodicity requirement. Fourier transform is used to reduce the solution of the problem of localised source diffraction by the grating in the whole region to the solution of the problem of diffraction inside one Floquet channel. By considering the periodicity of the geometry structure, the problem of Floquet terms for the image can be formulated so that it enables the application of the MIM developed for plane wave diffraction problems. Accounting of the local structure of an incident field enables both the prediction of the corresponding efficiencies and the specification of the bounds within which the approximation of the incident field with plane waves is correct. For 2D diffraction problems of the high-conductive plane grating irradiated by cylindrical waves and the cylindrical high-conductive grating irradiated by plane waves, decompositions in sets of plane waves/sections are investigated. The application of such decomposition, including the dependence on the number of plane waves/sections and radii of the grating and wave front shape, was demonstrated for lamellar, sinusoidal and saw-tooth grating examples in the 0th & –1st orders as well as in the transverse electric and transverse magnetic polarisations. The primary effects of plane wave/section partitions of non-planar wave fronts and curved grating shapes on the exact solutions for 2D and three-dimensional (conical) diffraction problems are discussed.

Sign in / Sign up

Export Citation Format

Share Document