Dilatational waves at a microstretch solid/fluid interface

2016 ◽  
Vol 23 (20) ◽  
pp. 3448-3467 ◽  
Author(s):  
Dilbag Singh ◽  
Neela Rani ◽  
Sushil Kumar Tomar
Keyword(s):  
Half Space ◽  
Aluminum Matrix ◽  
Elastic Solid ◽  
Specific Model ◽  
Reflection And Transmission Coefficients ◽  
Angle Of Incidence ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Special Cases ◽  
Microstretch Fluid

The present work is concerned with the study of reflection and transmission phenomena of dilatational waves at a plane interface between a microstretch elastic solid half-space and a microstretch liquid half-space. Eringen's theory of micro-continuum materials has been employed for addressing the mathematical analysis. Reflection and transmission coefficients, corresponding to various reflected and transmitted waves, have been obtained when a plane dilatational wave strikes obliquely at the interface after propagating through the solid half-space. It is found that the reflection and transmission coefficients are functions of the angle of incidence, the frequency of the incident wave and the elastic properties of the half-spaces. Numerical calculations have been carried out for a specific model by taking an aluminum matrix with randomly distributed epoxy spheres as the microstretch solid medium, while the microstretch fluid is taken arbitrarily with suitably chosen elastic parameters. The computed results obtained have been depicted graphically. The results of earlier studies have been deduced from the present formulation as special cases.

scholarly journals Reflection and transmission of elastic waves at viscous liquid/micropolar elastic solid interface

2001 ◽  
Vol 26 (11) ◽  
pp. 685-694 ◽  
Author(s):  
Rajneesh Kumar ◽  
Sushil K. Tomar
Keyword(s):  
Viscous Liquid ◽  
Half Space ◽  
Incident Wave ◽  
Elastic Waves ◽  
Elastic Solid ◽  
Specific Model ◽  
Angle Of Incidence ◽  
Amplitude Ratios ◽  
Reflection And Transmission ◽  
Special Case

Amplitude ratios of various reflected and transmitted elastic waves from a plane interface separating a viscous liquid half-space and a micropolar elastic solid half-space, are obtained in two cases (i) when longitudinal wave propagating through the solid half-space is made incident at the interface and (ii) when “coupled-wave” propagating through the solid half-space is made incident at the interface. These amplitude ratios have been computed numerically for a specific model and results obtained are presented graphically. It is found that these amplitude ratios depend on the angle of incidence of the incident wave and the effect of viscosity of the liquid on amplitude ratios is noticed. The problem studied by Tomar and Kumar (1995) has been reduced as a special case of our problem.

THE SEISMIC WAVE ENERGY REFLECTED FROM VARIOUS TYPES OF STRATIFIED HORIZONS

Geophysics ◽  
1940 ◽  
Vol 5 (2) ◽  
pp. 149-155 ◽  
Author(s):  
M. Muskat ◽  
M. W. Meres
Keyword(s):  
Seismic Wave ◽  
Wave Energy ◽  
Incident Energy ◽  
Preceding Paper ◽  
Reflection And Transmission Coefficients ◽  
Angle Of Incidence ◽  
Reflection And Transmission ◽  
Transmission Coefficients

Two applications are made of the reflection and transmission coefficients reported in the preceding paper. These concern the effect of the angle of incidence upon the fraction of incident energy returning to the surface, and the effect of velocity stratification upon the energy return.

On the scattering of water waves by a submerged slender barrier

1998 ◽  
Vol 40 (2) ◽  
pp. 171-189
Author(s):  
P. K. Kundu ◽  
N. K. Saha
Keyword(s):  
Finite Length ◽  
Water Waves ◽  
Vertical Plate ◽  
Perturbation Technique ◽  
Reflection And Transmission Coefficients ◽  
Reflection And Transmission ◽  
First Order ◽  
Transmission Coefficients ◽  
Special Cases ◽  
Analytical Expressions

AbstractAn approximate analysis, based on the standard perturbation technique, is described in this paper to find the corrections, up to first order to the reflection and transmission coefficients for the scattering of water waves by a submerged slender barrier, of finite length, in deep water. Analytical expressions for these corrections for a submerged nearly vertical plate as well as for a submerged vertically symmetric slender barrier of finite length are also deduced, as special cases, and identified with the known results. It is verified, analytically, that there is no first order correction to the transmitted wave at any frequency for a submerged nearly vertical plate. Computations for the reflection and transmission coefficients up to O(ε), where ε is a small dimensionless quantity, are also performed and presented in the form of both graphs and tables.

Propagation of Elastic Waves at Micropolar Viscoelastic Solid/Fluid-Saturated Incompressible Porous Solid Interface

2018 ◽  
Vol 15 (08) ◽  
pp. 1850076 ◽  
Author(s):  
M. S. Barak ◽  
Vinod Kaliraman
Keyword(s):  
Half Space ◽  
Incident Wave ◽  
Plane Surface ◽  
Elastic Solid ◽  
Specific Model ◽  
Porous Solid ◽  
Angle Of Incidence ◽  
Amplitude Ratios ◽  
Viscoelastic Solid ◽  
Micropolar Viscoelastic Solid

The present paper concerned with the reflection and transmission of plane wave from a plane surface separating a micropolar viscoelastic solid (MVES) half-space and a fluid-saturated (FS) incompressible porous solid half-space is studied. A longitudinal wave ([Formula: see text]-wave) or transverse wave (SV-wave) impinges obliquely at the interface. Amplitude ratios for various reflected and transmitted waves have been obtained with the help of boundary conditions at the interface. Then, these amplitude ratios have been computed numerically for a specific model and results thus obtained are shown graphically with the angle of incidence of the incident wave. It is found that these amplitude ratios depend on the angle of incidence of the incident wave as well as on the properties of media. From the present investigation, a special case, when FS porous half-space reduces to empty porous solid and MVES half-space reduces to micropolar elastic solid, has also been deduced and discussed with the help of graphs.

scholarly journals Modelling Reflection and Transmission of Acoustic Waves at a Semiconductor: Fluid Interface

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
A. Sharma ◽  
J. N. Sharma ◽  
Y. D. Sharma
Keyword(s):  
Acoustic Waves ◽  
Grazing Incidence ◽  
Reflection And Transmission Coefficients ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Saw Devices ◽  
Special Cases ◽  
Gauss Elimination ◽  
Programming Software ◽  
Matlab Programming

The paper concentrates on the study of reflection and transmission characteristics of acoustic waves at the interface of a semiconductor half-space underlying an inviscid liquid. The reflection and transmission coefficients varying with the incident angles are examined. Calculated results are verified by considering the quasilongitudinal () and quasitransverse () waves. The special cases of normal and grazing incidence are also derived and discussed. Finally, the numerical computations of reflection and transmission coefficients are carried out with the help of Gauss elimination method by using MATLAB programming software for silicon (Si) and germanium (Ge) semiconductors. The computer simulated-results have been plotted graphically for Si and presented in tabular form in case of Ge semiconductors. The study may be useful in semiconductors, geology, and seismology in addition to surface acoustic wave (SAW) devices.

The viscoelastic reflection/transmission problem: Two special cases

1983 ◽  
Vol 73 (6A) ◽  
pp. 1673-1683
Author(s):  
E. S. Krebes
Keyword(s):  
Incident Wave ◽  
Incidence Angle ◽  
Reflection And Transmission Coefficients ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
First Case ◽  
Special Cases ◽  
Mathematical Formulas ◽  
Linear Viscoelastic ◽  
Ray Bending

Abstract In the general problem of plane wave reflection and transmission at a boundary separating two linear viscoelastic media, the mathematical formulas for the reflection and transmission coefficients, the transmission angle, the attenuation vector, etc., are not easily interpretable because they cannot easily be expressed in terms of the basic input parameters (Q, incidence angle, etc.). To gain further insight, we study two special cases in which mathematical simplifications occur. No low-loss approximations are involved. In the first case, the incident wave is homogeneous, and the Q values of the two layers are equal, and we find, among other things, that the reflection and transmission coefficients are the same as the ones for perfect elasticity (they do not involve complex velocities, etc., and are independent of Q). In the second special case, the degree of inhomogeneity of the incident wave approaches its upper limit, and we find that the reflection and transmission coefficients approach constant (complex) values independent of the incidence angle, and that there is almost no ray-bending (refraction) upon transmission of the incident wave through the boundary.

An Application of Elastodynamic Reciprocity to Reflection by an Obstacle in a Waveguide

2000 ◽  
Vol 16 (2) ◽  
pp. 97-101
Author(s):  
J.D. Achenbach
Keyword(s):  
Transverse Wave ◽  
Elastic Layer ◽  
Wave Motion ◽  
Elastic Solid ◽  
Orthogonality Condition ◽  
Reflection And Transmission Coefficients ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Planar Array ◽  
Wave Modes

ABSTRACTThe reciprocal identity which connects two elastodynamic states, denoted by A and B, is used in this paper to obtain two results for an elastic layer. The first is an orthogonality condition for wave modes. For that case the states A and B are wave modes propagating in the same direction. The second result concerns reflection and transmission of wave motion by an obstacle in the layer. Now state A is defined by a superposition of incident wave modes and its reflection and transmission by the obstacle. Expressions for the reflection and transmission coefficients are obtained by selecting counter propagating wave modes for state B. It is also shown that the reflection by an obstacle in a layer can be extended to obtain the reflection and transmission coefficients for a planar array of obstacles in an unbounded elastic solid. For clarity all results are presented for horizontally polarized transverse wave motion.

Effect of local fluid flow on the reflection and transmission of elastic waves at an interface between an elastic solid and a double-porosity medium

Geophysics ◽  
2020 ◽  
Vol 85 (4) ◽  
pp. T237-T256
Author(s):  
Enjiang Wang ◽  
Jing Ba ◽  
José M. Carcione ◽  
Yang Liu ◽  
Hongchao Dong
Keyword(s):  
Fluid Flow ◽  
Elastic Waves ◽  
Vertical Direction ◽  
Elastic Solid ◽  
Double Porosity ◽  
Reflection And Transmission Coefficients ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Slowness Vector ◽  
Local Fluid Flow

We have studied the reflection and transmission of elastic waves incident on an interface separating an elastic solid and a double-porosity medium described by the Biot-Rayleigh model that considers the effect of local fluid flow (LFF). The P1- and SV-wave incidence generates two reflected elastic waves in the elastic solid and four transmitted inhomogeneous waves in the double-porosity medium, represented by Helmholtz potential functions. The reflection and transmission coefficients are derived in closed form based on the boundary conditions at the interface. Energy ratios are then derived, and energy conservation at the interface is verified. The contribution of fluid flow to the three transmitted longitudinal waves in the double-porosity medium is expressed as a function of frequency, the transmission coefficient, and the corresponding slowness vector. Numerical examples indicate that LFF predicts significant compressional-wave velocity dispersion in the seismic band, and frequency-dependent reflection and transmission coefficients. For the case in which the incidence angle is larger than the critical angle, the transmitted P1-wave shows a nonzero energy flux in the vertical direction, whereas it does not if LFF is absent.

Propagation of SH-Waves Through Non Planer Interface between Visco-Elastic and Fibre-Reinforced Solid Half-Spaces

2017 ◽  
Vol 33 (4) ◽  
pp. 545-557
Author(s):  
B. Prasad ◽  
P. C. Pal ◽  
S. Kundu
Keyword(s):  
Closed Form ◽  
Half Space ◽  
Seismic Waves ◽  
Order Approximation ◽  
Elastic Half Space ◽  
Angle Of Incidence ◽  
Sh Waves ◽  
Transmission Coefficients ◽  
Reflection And Refraction ◽  
Special Cases

AbstractIn the propagation of seismic waves through layered media, the boundaries play crucial role. The boundaries separating the different layers of the earth are irregular in nature and not perfectly plane. It is, therefore, necessary to take into account the corrugation of the boundaries while dealing with the problem of reflection and refraction of seismic waves. The present study explores the reflection and refraction phenomena of SH-waves at a corrugated interface between visco-elastic half-space and fibre-reinforced half-space. Method of approximation given by Rayleigh is adopted and the expressions for reflection and transmission coefficients are obtained in closed form for the first and second order approximation of the corrugation. The closed form formulae of these coefficients are presented for a corrugated interface of periodic shape (cosine law interface). It is found that these coefficients depend upon the amplitude of corrugation of the boundary, angle of incidence and frequency of the incident wave. Numerical computations for a particular type of corrugated interface are performed and a number of graphs are plotted. Some special cases are derived.

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