Effect of inertial coefficients in the propagation of plane waves in micropolar porous materials

2017 ◽  
Vol 06 (01) ◽  
pp. 1750007 ◽  
Author(s):  
R. Lianngenga
Keyword(s):  
Free Surface ◽  
Porous Materials ◽  
Plane Waves ◽  
Body Waves ◽  
Plane Body ◽  
Reflected Waves ◽  
Phase Velocities ◽  
Energy Ratios

The problem of phase velocities and attenuations of plane body waves and its reflection from a stress-free surface has been investigated in the micropolar porous materials. The amplitude and energy ratios of reflected waves are obtained analytically. The effect of inertial coefficients in the propagation of plane body waves is computed numerically for a particular model.

Reflection of Plane Waves in a Rotating Temperature-Dependent Thermoelastic Solid with Diffusion

2012 ◽  
Vol 28 (4) ◽  
pp. 599-606
Author(s):  
B. Singh ◽  
L. Singh ◽  
S. Deswal
Keyword(s):  
Half Space ◽  
Plane Waves ◽  
Reflection Coefficients ◽  
Angle Of Incidence ◽  
Governing Equations ◽  
Temperature Dependent ◽  
Reflected Waves ◽  
Energy Ratios ◽  
Rotation Parameters ◽  
Thermoelastic Solid

ABSTRACTThe governing equations of a model of rotating generalized thermoelastic diffusion in an isotropic medium with temperature-dependent mechanical properties are formulated in context of Lord-Shulman theory of generalized thermoelasticity. The modulus of elasticity is taken as a linear function of reference temperature. The solution of the governing equations indicates the existence of four coupled plane waves in x-z plane. The reflection of plane waves from the free surface of a rotating temperature-dependent thermoelastic solid half-space with diffusion is considered. The required boundary conditions are satisfied by the appropriate potentials for incident and reflected waves in the half-space to obtain a system of four non-homogeneous equations in the reflection coefficients. The expressions for energy ratios of the reflected waves are also obtained. The reflection coefficients and energy ratios are found to depend upon the angle of incidence, reference temperature, thermodiffusion and rotation parameters. Aluminum material is modeled as the half-space to compute the absolute values of the reflection coefficients and the energy ratios. Effects of temperature dependence and rotation parameters on the reflection coefficients and energy ratios are shown graphically for a certain range of the angle of incidence of the incident plane wave.

Wave propagation in an initially stressed rotating thermo-diffusive medium with two-temperature and micro-concentrations

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Devender Sheoran ◽  
Ramesh Kumar ◽  
Sunil Kumar ◽  
Kapil Kumar Kalkal
Keyword(s):  
Plane Waves ◽  
Generalized Thermoelasticity ◽  
Angle Of Incidence ◽  
Amplitude Ratios ◽  
Conservation Of Energy ◽  
Content Type ◽  
Reflected Waves ◽  
Diffusive Medium ◽  
Energy Ratios ◽  
Two Temperature

Purpose The purpose of this paper is to study the reflection of plane waves in an initially stressed rotating thermoelastic diffusive medium with micro-concentrations and two-temperature. Design/methodology/approach A two-dimensional model of generalized thermoelasticity is considered. The governing equations are transformed into the non-dimensional forms using the dimensionless variables. Then, potential functions are introduced for the decoupling of the waves. Further, appropriate boundary conditions are assumed to completely solve the problem. Finally, numerical computations are performed using MATLAB. Findings The problem is solved analytically and it is found that there exist five coupled waves in addition to an independent micro-concentration wave in the considered medium. The amplitude ratios and energy ratios of these reflected waves have also been computed numerically for a specific material. Originality/value The modulus values of amplitude ratios are presented graphically to exhibit the effects of angular velocity, initial stress, two-temperature, diffusion and micro-concentration parameters. The expressions of energy ratios obtained in explicit form are also depicted graphically as functions of angle of incidence. The law of conservation of energy at the free surface during reflection phenomenon is also verified.

The effect of boundaries on wave propagation in a liquid-filled porous solid: III. Reflection of plane waves at a free plane boundary (general case)

1962 ◽  
Vol 52 (3) ◽  
pp. 595-625 ◽  
Author(s):  
H. Deresiewicz ◽  
J. T. Rice
Keyword(s):  
Electromagnetic Waves ◽  
Plane Waves ◽  
Body Waves ◽  
Porous Solid ◽  
Plane Boundary ◽  
Field Equations ◽  
Attenuation Coefficients ◽  
Reflected Waves ◽  
Three Body ◽  
Analytical Expressions

abstract A general solution is derived of Biot's field equations governing small motions of a porous solid saturated with a viscous liquid. The solution is then employed to study some of the phenomena attendant upon the reflection from a plane, traction-free boundary of each of the three body waves predicted by the equations. The problem, though more complex, bears some similarity to that of electromagnetic waves in a conducting medium, in that some of the reflected waves are inhomogeneous, planes of constant amplitude not coinciding with planes of constant phase. Analytical expressions are displayed for the phase velocities, attenuation coefficients, angles of reflection and the amplitude ratios, and explicit formulas are given for the limiting cases of low and high frequencies, representing first-order corrections for porosity of the solid and viscosity of the liquid, respectively. The paper concludes with a presentation of results of numerical calculations pertinent to a kerosene-saturated sandstone.

scholarly journals DISCRETE TIME SOLUTION OF PLANE P‐SV WAVES IN A PLANE LAYERED MEDIUM

Geophysics ◽  
1970 ◽  
Vol 35 (2) ◽  
pp. 197-219 ◽  
Author(s):  
Clint W. Frasier
Keyword(s):  
Free Surface ◽  
Discrete Time ◽  
Acoustic Waves ◽  
Plane Waves ◽  
Normal Incidence ◽  
Small Time ◽  
Body Waves ◽  
Response Matrix ◽  
Constant Matrix ◽  
P And Sv Waves

For plane waves at normal incidence to a layered elastic medium, both the forward and inverse discrete time problems have been previously solved. In this paper the forward problem of calculating the waves in a medium of plane, homogeneous, isotropic layers is extended to P and SV body waves at nonnormal incidence, where the horizontal phase velocity of each wave is greater than the shear and compressional velocities of each layer. Vertical traveltimes for P and SV waves through each layer are rounded off to unequal integer multiples of a small time increment Δτ. This gives a 4×4 layer matrix analogous to the 2×2 layer matrix for normal incidence obtained by previous authors. Reflection and transmission responses recorded at the free surface of a layered half space are derived as matrix series in integer powers of the Fourier transform variable [Formula: see text]. These responses are generated recursively by polynomial division and include all multiply reflected P and SV waves with mode conversions. It is shown that the reflection response matrix generated by a source at the free surface equals the product of a constant matrix and the positive time part of the autocorrelation matrix of the transmission response matrix due to a deep source. This is an extension to nonnormal incidence of a theorem proved by Claerbout for acoustic waves at normal incidence.

Q values and wave inhomogeneity parameters of reflected inhomogeneous P and S waves at the free surface of an effective Biot solid

2020 ◽  
Vol 222 (2) ◽  
pp. 919-939 ◽  
Author(s):  
Xu Liu ◽  
Stewart Greenhalgh ◽  
Bing Zhou ◽  
Zhengyong Ren ◽  
Huijian Li
Keyword(s):  
Free Surface ◽  
Incidence Angle ◽  
Complex Form ◽  
Dissipation Factor ◽  
Seismic Wave Propagation ◽  
Energy Balance Equation ◽  
P Wave ◽  
Biot Theory ◽  
Reflected Waves ◽  
Phase Velocities

SUMMARY In this study, new methods are developed to estimate the dissipation factors, inhomogeneity parameters and phase velocities of the reflected waves at the free surface of a poro-viscoelastic solid in which the seismic wave propagation is described by effective Biot theory. The Christoffel equations of an effective Biot medium are solved for a general harmonic plane wave and the three complex velocities obtained corresponding to the shear wave (SV), fast-P wave and slow-P wave, together with their polarizations. Based on the complex form of the energy balance equation in an effective Biot material, expressions are derived for the energy ratios at the free surface. Moreover, the equations for the inhomogeneity parameters are derived as functions of the complex slowness or the unit polarization vectors. Based on the implicit and the explicit dissipation factor expressions, two methods are developed to obtain the dissipation factors, the inhomogeneity parameters and the phase velocities of mode-converted waves. These methods are illustrated by numerical examples which show that the dissipation factors, inhomogeneity parameters and phase velocities of reflected waves can strongly depend on the incidence angle (also reflected angle), the incident wave inhomogeneity parameter and the wave frequency. Ignoring these dependencies and using dissipation factors only valid for homogeneous waves can cause discrepancies in computed phase velocities and dissipation factors for interface generated (reflected/transmitted) inhomogeneous waves.

SURFACE AMPLITUDES OF REFLECTED BODY WAVES

Geophysics ◽  
1957 ◽  
Vol 22 (4) ◽  
pp. 842-847 ◽  
Author(s):  
L. Knopoff ◽  
R. W. Fredricks ◽  
A. F. Gangi ◽  
L. D. Porter
Keyword(s):  
Free Surface ◽  
Body Waves ◽  
Plane Body

The components of the surface motions of a plane free surface are computed for the incidence of plane body waves.

Reflection and transmission of elastic waves in a system of corrugated layers

1967 ◽  
Vol 57 (3) ◽  
pp. 393-419
Author(s):  
A. Levy ◽  
H. Deresiewicz
Keyword(s):  
Incident Wave ◽  
Elastic Waves ◽  
Scattered Field ◽  
Single Layer ◽  
Body Waves ◽  
Numerical Computations ◽  
Plane Body ◽  
Reflection And Transmission ◽  
Plane Parallel

abstract The scattered field generated by normally incident body waves in a system of layers having small, but otherwise arbitrary, periodic deviations from plane parallel boundaries is shown to consist of superposed plane body and surfacetype waves. Results of numerical computations for two like half-spaces separated by a sinusoidally corrugated single layer, and by two layers, reveal the variation of the amplitude of the field with ratios of velocities, densities, impedances, and with those of depth of layers and wavelength of the boundary corrugations to the wavelength of the incident wave.

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