Analysis of scattered fields by an impedance discontinuity of a planar surface by using Helmholtz-Kirchhoff integral theorem

2012 ◽  
Author(s):  
Toru Kawano ◽  
Keiji Goto ◽  
Toyohiko Ishihara
Keyword(s):  
Planar Surface ◽  
Integral Theorem ◽  
Scattered Fields ◽  
Kirchhoff Integral ◽  
Impedance Discontinuity

Reconstruction of diffraction patterns by using the Helmholz–Kirchhoff integral theorem

2003 ◽  
Vol 36 (6) ◽  
pp. 1368-1371 ◽  
Author(s):  
Miloš Kopecký ◽  
Edoardo Busetto ◽  
Andrea Lausi
Keyword(s):  
Diffuse Scattering ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Laue Pattern ◽  
Integral Theorem ◽  
Thermal Diffuse Scattering ◽  
Position Sensitive ◽  
Diffraction Patterns ◽  
Thermal Diffuse ◽  
Kirchhoff Integral

A new method to obtain three-dimensional information on atomic arrangement from a monochromatic Laue pattern based on the Helmholz–Kirchhoff integral theorem is presented and experimentally proved by applying the algorithm to the thermal diffuse scattering from a single crystal. The advantage given by the possibility of collecting all the required data on a position-sensitive detector in one shot opens new perspectives for studies of fast physical or chemical processes in three dimensions. The reduced exposure time can also avoid radiation damage of organic specimens, and, in conjunction with an ultra-bright beam from the next generation of X-ray free-electron lasers, makes the method suitable for structural studies with individual atomic clusters. This approach can also be used, by observing the thermal diffuse scattering or order diffuse scattering from both non-crystalline samples and `imperfect' crystals, for the investigation of short-range ordered arrangements of atoms.

Determination of Acoustic Scattering From a Two-Dimensional Finite Phononic Crystal Using Bloch Wave Expansion

2014 ◽  
Author(s):  
Jason A. Kulpe ◽  
Michael J. Leamy ◽  
Karim G. Sabra
Keyword(s):  
Internal Pressure ◽  
Half Space ◽  
Pressure Field ◽  
Phononic Crystal ◽  
Acoustic Scattering ◽  
Bloch Wave ◽  
Two Dimensions ◽  
Integral Theorem ◽  
Wave Expansion ◽  
Kirchhoff Integral

In this study the acoustic scattering is determined from a finite phononic crystal through an implementation of the Helmholtz-Kirchhoff integral theorem. The approach employs the Bloch theorem applied to a semi-infinite phononic crystal (PC) half-space. The internal pressure field of the half-space, subject to an incident acoustic monochromatic plane wave, is formulated as an expansion of the Bloch wave modes. Modal coefficients of reflected (diffracted) plane waves are arrived at via boundary condition considerations on the PC interface. Next, the PC inter-facial pressure, as determined by the Bloch wave expansion (BWE), is employed along with the Helmholtz-Kirchhoff integral equation to compute the scattered pressure from a large finite PC. Under a short wavelength limit approximation (wavelength much smaller than finite PC dimensions), the integral approach is employed to calculate the scattered pressure field for a large PC subject to an incident wave with two distinct incident angles. In two dimensions we demonstrate good agreement of scattered pressure results of large finite PC when compared against detailed finite element calculations. The work here demonstrates an efficient and accurate uniform computational framework for modeling the scattered and internal pressure fields of a large finite phononic crystal.

scholarly journals Flaws in classical proofs of vector Kirchhoff integral theorem and its new strict proof

2017 ◽  
Vol 66 (16) ◽  
pp. 164201
Author(s):  
Huang Xiao-Wei ◽  
Sheng Xin-Qing
Keyword(s):  
Integral Theorem ◽  
Kirchhoff Integral

Uniqueness of Solutions to Variationally Formulated Acoustic Radiation Problems

1990 ◽  
Vol 112 (2) ◽  
pp. 263-267 ◽  
Author(s):  
Xiao-Feng Wu ◽  
Allan D. Pierce
Keyword(s):  
Acoustic Radiation ◽  
Axial Direction ◽  
Acoustic Power ◽  
Normal Derivative ◽  
Surface Velocity ◽  
Finite Cylinder ◽  
Uniqueness Of Solutions ◽  
Integral Theorem ◽  
Kirchhoff Integral

Determination of the surface acoustic pressure given the surface velocity of a vibrating body can be formulated in various ways. However, for some such formulations such as the surface Helmholtz integral equation, solutions are not unique at certain discrete frequencies. Such uniqueness problems can also be present for variational formulations of the problem, but the variational formulation based on the normal derivative of the Kirchhoff integral theorem has unique solutions for vibrating disks and plate-like bodies. For bodies of finite volume, but for which each surface point is vibrating in phase, the total radiated acoustic power is always unique, even though the pressure may not be. The latter conclusion is supported by numerical calculations based on the Rayleigh-Ritz technique for the case of a finite cylinder vibrating as a rigid body in the axial direction.

scholarly journals Scale Model Evaluation and Optimization of Sodar Acoustic Baffles

2015 ◽  
Vol 32 (3) ◽  
pp. 507-517
Author(s):  
Adrien Chabbey ◽  
Stuart Bradley ◽  
Fernando Porté-Agel
Keyword(s):  
Numerical Model ◽  
Phased Array ◽  
Scale Model ◽  
Scaled Model ◽  
Integral Theorem ◽  
Bench Testing ◽  
Beam Patterns ◽  
Kirchhoff Integral ◽  
Shield Design ◽  
Model Approach

AbstractA 21:1 scaled sodar, operating at 40 kHz, has been built and tested in the laboratory. Sodars, which use sound scattered by turbulence to profile the lowest few hundred meters of the atmosphere, need good acoustic shielding to diminish annoyance and to reduce unwanted reflections from nearby objects. Design of the acoustic shielding is generally inhibited by the difficulty of testing on full-scale systems and uncertainty as to accuracy of models. In contrast, the scale model approach described allows for “bench testing” of many designs under controlled conditions, and efficient comparison with models. Measured beam patterns from the scale model were compared with those from a numerical model based on the Kirchhoff integral theorem. Satisfactory agreement has allowed using the numerical model to optimize the acoustic shield design, both for the gross acoustic baffle geometry and for the geometry of rim modulations known as thnadners. Optimization was performed in the specific case of a scaled model of a commercial phased array sodar.

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