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.

The effect of boundaries on wave propagation in a liquid-filled porous solid

1960 ◽  
Vol 50 (4) ◽  
pp. 599-607
Author(s):  
H. Deresiewicz
Keyword(s):  
Wave Propagation ◽  
Free Boundary ◽  
General Solution ◽  
Elastic Waves ◽  
Body Waves ◽  
Porous Solid ◽  
Field Equations ◽  
Reflected Waves ◽  
Three Body ◽  
Propagation Of Elastic Waves

ABSTRACT A general solution is deduced of the differential equations which describe the propagation of elastic waves in a nondissipative liquid-filled porous solid. The solution is then used to examine some of the phenomena which arise when each of the three body waves predicted by the field equations is, in turn, incident on a plane traction-free boundary. It is found, for example, that an obliquely incident wave of each type in general gives rise to reflected waves of all three types.

Ray-synthetic seismograms for SH waves in anelastic media

1980 ◽  
Vol 70 (1) ◽  
pp. 29-46
Author(s):  
E. S. Krebes ◽  
F. Hron
Keyword(s):  
Plane Waves ◽  
Synthetic Seismograms ◽  
Body Waves ◽  
Plane Boundary ◽  
Theory Approach ◽  
Reflection And Transmission ◽  
Sh Waves ◽  
Transmission Coefficients ◽  
Mathematical Properties ◽  
Crustal Model

abstract The linear theory of viscoelasticity is used to study the effects of anelasticity on SH body waves propagating through a layered medium. The mathematical properties of SH waves in a viscoelastic medium are outlined. Reflection and transmission coefficients for SH plane waves impinging upon a plane boundary separating two anelastic media are calculated and compared with the coefficients for the perfectly elastic case. Synthetic seismograms for teleseismic SH body waves are computed for a plane-layered crustal model in both the elastic and anelastic cases, using a ray theory approach.

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.

Effects of rotation, voids and diffusion on characteristics of plane waves in a thermoelastic material

2019 ◽  
Vol 16 (1) ◽  
pp. 73-92
Author(s):  
Baljeet Singh ◽  
Himanshu Singla
Keyword(s):  
Plane Waves ◽  
Rotation Frequency ◽  
Two Dimensions ◽  
Amplitude Ratios ◽  
Field Equations ◽  
Content Type ◽  
Reflected Waves ◽  
Thermoelastic Material ◽  
Effects Of Rotation ◽  
And Diffusion

Purpose The purpose of this paper is to study the effects of rotation, voids and diffusion on characteristics of plane waves in a thermoelastic material. Design/methodology/approach Lord and Shulman generalization of linear thermoelasticity is used to study the plane waves in a rotating thermoelastic material with voids and diffusion. The thermoelastic solid is rotating with a uniform angular velocity. The problem is specialized in two dimensions to study wave propagation. The plane harmonic solutions of governing field equations in a plane are obtained. Findings A velocity equation is obtained which indicates the propagation of five coupled plane waves in the medium. Reflection of an incident plane wave from stress-free surface of a half-space is also considered to obtain the amplitude ratios of various reflected waves. A numerical example is considered to illustrate graphically the effects of rotation, frequency, void and diffusion parameters on speeds and amplitude ratios of plane waves. Originality/value The present problem covers the combined effects of rotation, voids and diffusion on characteristics of plane waves in linear thermoelastic material in the context of Lord and Shulman (1967) and Aouadi (2010) theories, which are not studied in literature yet.

Gravitational waves in general relativity III. Exact plane waves

1959 ◽  
Vol 251 (1267) ◽  
pp. 519-533 ◽  
Keyword(s):  
Plane Wave ◽  
Gravitational Waves ◽  
Electromagnetic Waves ◽  
Plane Waves ◽  
Flat Space ◽  
Field Equations ◽  
Test Particles ◽  
Wave Space ◽  
General Plane ◽  
Plane Gravitational Waves

Plane gravitational waves are here defined to be non-flat solutions of Einstein’s empty spacetime field equations which admit as much symmetry as do plane electromagnetic waves, namely, a 5-parameter group of motions. A general plane-wave metric is written down and the properties of plane wave space-times are studied in detail. In particular, their characterization as 4 plane ’ is justified further by the construction of 4 sandwich waves ’ bounded on both sides by (null) hyperplanes in flat space-time. It is shown that the passing of a sandwich wave produces a relative acceleration in free test particles, and inferred from this that such waves transport energy.

scholarly journals Effect of mechanical relaxation time in elastic materials with voids

2019 ◽  
Vol 19 (2) ◽  
pp. 51-58
Author(s):  
R. Lianngenga ◽  
L. Thangmawia
Keyword(s):  
Relaxation Time ◽  
Phase Speed ◽  
Plane Boundary ◽  
Mechanical Relaxation ◽  
Elastic Materials ◽  
Attenuation Coefficients ◽  
Reflected Waves ◽  
Materials With Voids ◽  
Incident Waves ◽  
Elastic Materials With Voids

The effect of mechanical relaxation time in the elastic wave propagation in elastic materials with voids is investigated. The phase speed and the attenuation coefficients are obtained and observed the effect of mechanical relaxation time. The phenomenon of reflection of elastic waves due to the incident waves from a plane boundary of elastic materials with voids is studied. The amplitude and energy ratios of the reflected waves are obtained. Numerically these ratios, phase speeds and the corresponding attenuation coefficients are computed for a particular model and the effect of mechanical relaxation time is discussed.

Electromagnetic waves

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Plane Wave ◽  
Electromagnetic Waves ◽  
Maxwell Equations ◽  
Plane Waves ◽  
Geometrical Optics ◽  
Particle Detection ◽  
Spatial Coordinates ◽  
A Charge

This chapter examines solutions to the Maxwell equations in a vacuum: monochromatic plane waves and their polarizations, plane waves, and the motion of a charge in the field of a wave (which is the principle upon which particle detection is based). A plane wave is a solution of the vacuum Maxwell equations which depends on only one of the Cartesian spatial coordinates. The monochromatic plane waves form a basis (in the sense of distributions, because they are not square-integrable) in which any solution of the vacuum Maxwell equations can be expanded. The chapter concludes by giving the conditions for the geometrical optics limit. It also establishes the connection between electromagnetic waves and the kinematic description of light discussed in Book 1.

scholarly journals Electromagnetic Waves Through Disordered Systems: Comparison of Intensity, Transmission and Conductance

2001 ◽  
Vol 694 ◽  
Author(s):  
Fredy R Zypman ◽  
Gabriel Cwilich
Keyword(s):  
Probability Distribution ◽  
Disordered Systems ◽  
Electromagnetic Waves ◽  
Delta Function ◽  
Rayleigh Distribution ◽  
Dirac Delta Function ◽  
Universal Form ◽  
Dirac Delta ◽  
Diffusive Regime ◽  
Analytical Expressions

AbstractWe obtain the statistics of the intensity, transmission and conductance for scalar electromagnetic waves propagating through a disordered collection of scatterers. Our results show that the probability distribution for these quantities x, follow a universal form, YU(x) = xne−xμ. This family of functions includes the Rayleigh distribution (when α=0, μ=1) and the Dirac delta function (α →+ ∞), which are the expressions for intensity and transmission in the diffusive regime neglecting correlations. Finally, we find simple analytical expressions for the nth moment of the distributions and for to the ratio of the moments of the intensity and transmission, which generalizes the n! result valid in the previous case.

Sign in / Sign up

Export Citation Format

Share Document