Multiple scattering of elastic waves by cylinders of arbitrary cross section. II. Pair‐correlated cylinders

1985 ◽  
Vol 78 (5) ◽  
pp. 1874-1878 ◽  
Author(s):  
V. K. Varadan ◽  
V. V. Varadan ◽  
Y. Ma
Keyword(s):  
Multiple Scattering ◽  
Cross Section ◽  
Elastic Waves ◽  
Arbitrary Cross Section ◽  
Scattering Of Elastic Waves

Multiple scattering of elastic waves by a distribution of identical spheres

1990 ◽  
Vol 31 (11) ◽  
pp. 2619-2625 ◽  
Author(s):  
D. D. Phanord ◽  
N. E. Berger
Keyword(s):  
Multiple Scattering ◽  
Elastic Waves ◽  
Scattering Of Elastic Waves

scholarly journals Monte Carlo simulation of multiple scattering of elastic waves

2000 ◽  
Vol 105 (B4) ◽  
pp. 7873-7892 ◽  
Author(s):  
Ludovic Margerin ◽  
Michel Campillo ◽  
Bart Van Tiggelen
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Multiple Scattering ◽  
Elastic Waves ◽  
Scattering Of Elastic Waves

scholarly journals Multiple Scattering Theory for Heterogeneous Elastic Continua with Strong Property Fluctuation: Theoretical Fundamentals and Applications

2019 ◽  
Author(s):  
Huijing He
Keyword(s):  
Nondestructive Evaluation ◽  
Multiple Scattering ◽  
Elastic Waves ◽  
Scattering Theory ◽  
New Model ◽  
First Order ◽  
Weak Property ◽  
Strong Property ◽  
Scattering Of Elastic Waves ◽  
Dispersion And Attenuation

Scattering of elastic waves in heterogeneous media has become one of the most important problems in the field of wave propagation due to its broad applications in seismology, natural resource exploration, ultrasonic nondestructive evaluation and biomedical ultrasound. Nevertheless, it is one of the most challenging problems because of the complicated medium inhomogeneity and the complexity of the elastodynamic equations. A widely accepted model for the propagation and scattering of elastic waves, which properly incorporates the multiple scattering phenomenon and the statistical information of the inhomogeneities is still missing. In this work, the author developed a multiple scattering model for heterogeneous elastic continua with strong property fluctuation and obtained the exact solution to the dispersion equation under the first-order smoothing approximation. The model establishes an accurate quantitative relation between the microstructural properties and the coherent wave propagation parameters and can be used for characterization or inversion of microstructures. Starting from the elastodynamic differential equations, a system of integral equation for the Green functions of the heterogeneous medium was developed by using Green’s functions of a homogeneous reference medium. After properly eliminating the singularity of the Green tensor and introducing a new set of renormalized field variables, the original integral equation is reformulated into a system of renormalized integral equations. Dyson’s equation and its first-order smoothing approximation, describing the ensemble averaged response of the heterogeneous system, are then derived with the aid of Feynman’s diagram technique. The dispersion equations for the longitudinal and transverse coherent waves are then obtained by applying Fourier transform to the Dyson equation. The exact solution to the dispersion equations are obtained numerically. To validate the new model, the results for weak-property-fluctuation materials are compared to the predictions given by an improved weak-fluctuation multiple scattering theory. It is shown that the new model is capable of giving a more robust and accurate prediction of the dispersion behavior of weak-property-fluctuation materials. Numerical results further show that the new model is still able to provide accurate results for strong-property-fluctuation materials while the weak-fluctuation model is completely failed. As applications of the new model, dispersion and attenuation curves for coherent waves in the Earth’s lithosphere, the porous and two-phase alloys, and human cortical bone are calculated. Detailed analysis shows the model can capture the major dispersion and attenuation characteristics, such as the longitudinal and transverse wave Q-factors and their ratios, existence of two propagation modes, anomalous negative dispersion, nonlinear attenuation-frequency relation, and even the disappearance of coherent waves. Additionally, it helps gain new insights into a series of longstanding problems, such as the dominant mechanism of seismic attenuation and the existence of the Mohorovičić discontinuity. This work provides a general and accurate theoretical framework for quantitative characterization of microstructures in a broad spectrum of heterogeneous materials and it is anticipated to have vital applications in seismology, ultrasonic nondestructive evaluation and biomedical ultrasound.

scholarly journals Mathematical modeling on the propagation of guided elastic waves

2020 ◽  
Vol 11 (2) ◽  
pp. 135-139
Author(s):  
Sara Teidj
Keyword(s):  
Cross Section ◽  
Elastic Waves ◽  
Electromagnetic Induction ◽  
Eddy Currents ◽  
Composite Plates ◽  
Arbitrary Cross Section ◽  
Train Derailment ◽  
The Subject ◽  
Wave Propagation In Waveguides ◽  
Inspection Techniques

AbstractThe main cause of train derailment is related to transverse defects that arise in the railhead. These consist typically of opened or internal flaws that develop generally in a plane that is orthogonal to the rail direction. Most of the actual inspection techniques of rails relay on eddy currents, electromagnetic induction, and ultrasounds. Ultrasounds based testing is performed according to the excitation-echo procedure [1]. It is conducted conventionally by using a contact excitation probe that rolls on the railhead or by a contact-less system using a laser as excitation and air-coupled acoustic sensors for wave reception. The ratio of false predictions either positive or negative is yet too high due to the low accuracy of the actual devices. The inspection rate is also late; new numerical method has been developed in this context: The semi-analytical finite element method SAFE. This method has been applied in the case of anisotropic media [2], composite plates [3] and media in contact with fluids [4]. This method has been used successfully for several structures and especially in the case of beams of any cross-section such as rails that are the subject of this work and we were interested in wave propagation in waveguides of any arbitrary cross-section in the case of beams or rails.

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