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.

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.

Calculation of the Six-Beam Diffraction in Layered Media Using Polynomials of Principal Minors

2018 ◽  
Vol 26 (02) ◽  
pp. 1850017 ◽  
Author(s):  
Yuriy N. Belyayev
Keyword(s):  
Shear Wave ◽  
Elastic Waves ◽  
Wave Equations ◽  
Functional Dependencies ◽  
Sh Wave ◽  
Sh Waves ◽  
The Matrix ◽  
Conversion Coefficients ◽  
Incident Waves ◽  
Beam Diffraction

The scattering of plane elastic waves by an anisotropic layered medium in the case of the six-beam diffraction is considered. The matrix method for solving wave equations is developed. The conversion coefficients [Formula: see text] for the three types of incident waves (horizontally polarized shear wave, vertically polarized shear wave and longitudinal wave) are defined. Representations of coefficients [Formula: see text] through elements of transfer matrix are found. The method for coefficients [Formula: see text] calculations is presented. It does not require the solving of algebraic problem on eigenvalues for waves in an anisotropic layer. Some features of the functional dependencies of [Formula: see text] on the angles of incidence, wave frequency and layer thickness are demonstrated on several examples of the crystals in a three-layer model. It is shown that the conversions SH wave into SV waves and SV wave into SH waves are equivalent.

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.

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.

Fast and slow interaction of elastic waves with platonic clusters

2011 ◽  
Vol 467 (2136) ◽  
pp. 3509-3529 ◽  
Author(s):  
Michael H. Meylan ◽  
Ross C. McPhedran
Keyword(s):  
Elastic Waves ◽  
Early Time ◽  
Approximate Solutions ◽  
Wave Profile ◽  
Flexural Wave ◽  
Flexural Waves ◽  
Analytical Extension ◽  
Scattering Of Elastic Waves ◽  
Classical Models ◽  
The Time Domain

We study the scattering of elastic waves by platonic clusters in the time domain, both for plane wave excitations and for a specified initial wave profile. We show that we can use an analytical extension of our problem to calculate scattering frequencies of the solution. These allow us to calculate approximate solutions that give the flexural wave profile accurately in and around the cluster for large times. We also discuss the early-time behaviour of flexural waves in terms of the classical models of Sommerfeld and Brillouin.

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