SCATTERING OF ELASTIC WAVES BY SMALL INHOMOGENEITIES

Geophysics ◽  
1960 ◽  
Vol 25 (3) ◽  
pp. 642-648 ◽  
Author(s):  
John W. Miles
Keyword(s):  
Shear Modulus ◽  
Elastic Wave ◽  
Wave Field ◽  
General Result ◽  
Elastic Waves ◽  
Isotropic Medium ◽  
Scattering Theory ◽  
Rayleigh Scattering ◽  
S Waves ◽  
Scattering Of Elastic Waves

Rayleigh scattering theory is extended to determine the perturbation on an arbitrarily prescribed elastic wave field produced by small inhomogeneities in an otherwise homogeneous, isotropic medium. The general result is applied to the specific problems of the scattering of both plane P- and S-waves. It is found that a change in compressibility acts at a distance as a simple source and a change in density as a dipole, as in the acoustical problem, while a change in shear modulus contributes both simple‐source and quadrapole fields.

Rayleigh scattering of elastic waves from cracks

1979 ◽  
Vol 50 (2) ◽  
pp. 818-824 ◽  
Author(s):  
J. E. Gubernatis ◽  
E. Domany
Keyword(s):  
Elastic Waves ◽  
Rayleigh Scattering ◽  
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.

Application of the Singularity Expansion Method to Elastic Wave Scattering

1990 ◽  
Vol 43 (10) ◽  
pp. 235-249 ◽  
Author(s):  
Herbert U¨berall ◽  
P. P. Delsanto ◽  
J. D. Alemar ◽  
E. Rosario ◽  
Anton Nagl
Keyword(s):  
Elastic Wave ◽  
Elastic Waves ◽  
Wave Scattering ◽  
Scattering Amplitude ◽  
Scattering Problem ◽  
Expansion Method ◽  
Complex Frequency ◽  
Elastic Wave Scattering ◽  
Physical Measurements ◽  
Scattering Of Elastic Waves

The singularity expansion method (SEM), established originally for electromagnetic-wave scattering by Carl Baum (Proc. IEEE 64, 1976, 1598), has later been applied also to acoustic scattering (H U¨berall, G C Gaunaurd, and J D Murphy, J Acoust Soc Am 72, 1982, 1014). In the present paper, we describe further applications of this method of analysis to the scattering of elastic waves from cavities or inclusions in solids. We first analyze the resonances that appear in the elastic-wave scattering amplitude, when plotted vs frequency, for evacuated or fluid-filled cylindrical and spherical cavities or for solid inclusions. These resonances are interpreted as being due to the phase matching, ie, the formation of standing waves, of surface waves that encircle the obstacle. The resonances are then traced to the existence of poles of the scattering amplitude in the fourth quadrant of the complex frequency plane, thus establishing the relation with the SEM. The usefulness of these concepts lies in their applicability for solving the inverse scattering problem, which is the central problem of NDE. Since for the case of inclusions, or of cavities with fluid fillers, the scattering of elastic waves gives rise to very prominent resonances in the scattering amplitude, it will be of advantage to analyze these with the help of the resonance scattering theory or RST (first formulated by L Flax, L R Dragonette, and H U¨berall, J Acoust Soc Am 63, 1978, 723). These resonances are caused by the proximity of the SEM poles to the real frequency axis, on which the frequencies of physical measurements are located. A brief history of the establishment of the RST is included here immediately following the Introduction.

Conversion of Elastic Wave Polarization in Calcium Molybdate Layer

2018 ◽  
Vol 284 ◽  
pp. 95-100
Author(s):  
Yu.N. Belyayev ◽  
E.I. Yashin ◽  
O.Y. Yashina
Keyword(s):  
Elastic Wave ◽  
Elastic Waves ◽  
Wave Polarization ◽  
Anisotropic Layer ◽  
Calcium Molybdate ◽  
Algebraic Problem ◽  
Scattering Of Elastic Waves ◽  
Conversion Coefficients ◽  
Beam Diffraction ◽  
Incident Wave Energy

Scattering of elastic waves in calcium molybdate films is considered. The transformation of elastic waves as a result of six-beam diffraction in an anisotropic layer is analyzed. This analysis is based on the transfer matrix method. The distribution of incident wave energy between six scattered waves is characterized by conversion coefficients. The method for conversion coefficients calculations is presented. It does not require solving algebraic problem on eigenvalues for waves in an anisotropic layer. Features of dependencies of conversion coefficients of CaMoO4 layers on angles of incidence, frequency and the thickness of the layer are demonstrated.

scholarly journals Discrete scattering and meta-arrest of locally resonant elastic wave metamaterials with a semi-infinite crack

2021 ◽  
Vol 477 (2253) ◽  
pp. 20210356
Author(s):  
Kuan-Xin Huang ◽  
Guo-Shuang Shui ◽  
Yi-Ze Wang ◽  
Yue-Sheng Wang
Keyword(s):  
Elastic Wave ◽  
Elastic Waves ◽  
Structural Parameters ◽  
Internal Mass ◽  
Mass Spring Model ◽  
Scattering Of Elastic Waves ◽  
Specific Frequency ◽  
Release Ratio ◽  
Hopf Method ◽  
Mass Spring

Previous investigations on wave scattering and crack propagation in the discrete periodic structure are concentrated on the conditional mass–spring model, in which the internal mass is not included. In this work, elastic wave metamaterials with local resonators are studied to show the scattering of elastic waves by a semi-infinite crack and the arrest behaviour. The influences of internal mass–spring structure are analysed and the discrete Wiener–Hopf method is used to obtain the displacement solution. Numerical calculations are performed to show that the dynamic negative effective mass and band gaps can be observed owing to the local resonance of the internal mass. Therefore, the scattering of an elastic wave with a specific frequency by a semi-infinite crack can be avoided by tuning the structural parameters. Moreover, the energy release ratio which characterizes the splitting resistance is presented and the meta-arrest performance is found. It is expected that this study will increase understanding of how to control the scattering characteristics of elastic waves by a semi-infinite crack in locally resonant metamaterials and also help to improve their fracture resistance.

scholarly journals Numerical Modelling and Optimization of Two-Dimensional Phononic Band Gaps in Elastic Metamaterials with Square Inclusions

2021 ◽  
Vol 11 (7) ◽  
pp. 3124
Author(s):  
Alya Alhammadi ◽  
Jin-You Lu ◽  
Mahra Almheiri ◽  
Fatima Alzaabi ◽  
Zineb Matouk ◽  
...  
Keyword(s):  
Elastic Wave ◽  
Tungsten Carbide ◽  
Composite Structure ◽  
Elastic Waves ◽  
Wave Attenuation ◽  
Low Frequency ◽  
Filling Fraction ◽  
Carbide Composite ◽  
Elastic Metamaterials ◽  
Tungsten Carbide Composite

A numerical simulation study on elastic wave propagation of a phononic composite structure consisting of epoxy and tungsten carbide is presented for low-frequency elastic wave attenuation applications. The calculated dispersion curves of the epoxy/tungsten carbide composite show that the propagation of elastic waves is prohibited inside the periodic structure over a frequency range. To achieve a wide bandgap, the elastic composite structure can be optimized by changing its dimensions and arrangement, including size, number, and rotation angle of square inclusions. The simulation results show that increasing the number of inclusions and the filling fraction of the unit cell significantly broaden the phononic bandgap compared to other geometric tunings. Additionally, a nonmonotonic relationship between the bandwidth and filling fraction of the composite was found, and this relationship results from spacing among inclusions and inclusion sizes causing different effects on Bragg scatterings and localized resonances of elastic waves. Moreover, the calculated transmission spectra of the epoxy/tungsten carbide composite structure verify its low-frequency bandgap behavior.

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