Propagation of inhomogeneous plane waves in anisotropic viscoelastic media

2008 ◽  
Vol 200 (3-4) ◽  
pp. 145-154 ◽  
Author(s):  
M. D. Sharma
Keyword(s):  
Plane Waves ◽  
Viscoelastic Media ◽  
Inhomogeneous Plane ◽  
Inhomogeneous Plane Waves

Boundary attenuation angles for inhomogeneous plane waves in anisotropic dissipative media

Geophysics ◽  
2011 ◽  
Vol 76 (3) ◽  
pp. WA51-WA62 ◽  
Author(s):  
Vlastislav Červený ◽  
Ivan Pšenčík
Keyword(s):  
A Priori ◽  
Plane Waves ◽  
Wave Mode ◽  
Viscoelastic Media ◽  
Inhomogeneous Waves ◽  
Slowness Vector ◽  
Inhomogeneous Plane ◽  
Unbounded Media ◽  
Dissipative Media ◽  
Inhomogeneous Plane Waves

We study behavior of attenuation (inhomogeneity) angles [Formula: see text], i.e., angles between real and imaginary parts of the slowness vectors of inhomogeneous plane waves propagating in isotropic or anisotropic, perfectly elastic or viscoelastic, unbounded media. The angle [Formula: see text] never exceeds the boundary attenuation angle [Formula: see text]. In isotropic viscoelastic media [Formula: see text]; in anisotropic viscoelastic media [Formula: see text] may be greater than, equal to, or less than [Formula: see text]. Plane waves with [Formula: see text] do not exist. Because [Formula: see text] in anisotropic viscoelastic media is usually not known a priori, the commonly used specification of an inhomogeneous plane wave by the attenuation angle [Formula: see text] may lead to serious problems. If [Formula: see text] is chosen close to [Formula: see text] or even larger, indeterminate, unstable or even nonphysical results are obtained. We study properties of [Formula: see text] and show that the approach based on the mixed specification of the slowness vector fully avoids the problems mentioned above. The approach allows exact determination of [Formula: see text] and removes instabilities known from the use of the specification of the slowness vector by [Formula: see text]. For [Formula: see text], the approach yields zero phase velocity, i.e., the corresponding wave is a nonpropagating wave mode. The use of the mixed specification leads to the explanation of the deviation of [Formula: see text] from [Formula: see text] as a consequence of different orientations of energy-flux and propagation vectors in anisotropic media. The approach is universal; it may be used for isotropic or anisotropic, perfectly elastic or viscoelastic media, and for homogeneous and inhomogeneous waves, including strongly inhomogeneous waves, like evanescent waves.

scholarly journals New capabilities of Chetaev´s model

2016 ◽  
Vol 2 (2) ◽  
pp. 104-114
Author(s):  
Михаил Савин ◽  
Mihail Savin ◽  
Юрий Израильский ◽  
Yuriy Izrailsky
Keyword(s):  
Experimental Data ◽  
Plane Waves ◽  
Reflection Coefficients ◽  
Geomagnetic Pulsations ◽  
Energy Fluxes ◽  
Field Recordings ◽  
Inhomogeneous Plane ◽  
Inhomogeneous Plane Wave ◽  
S Model ◽  
Inhomogeneous Plane Waves

This paper considers anomalies in the magnetotelluric field in the Pc3 range of geomagnetic pulsations. We report experimental data on Pc3 field recordings which show negative (from Earth’s surface to air) energy fluxes Sz<0 and reflection coefficients |Q|>1. Using the model of inhomogeneous plane wave (Chetaev’s model), we try to analytically interpret anomalies of energy fluxes. We present two three-layer models with both electric and magnetic modes satisfying the condition |Qh|>1. Here we discuss a possibility of explaining observable effects by the resonance interaction between inhomogeneous plane waves and layered media.

scholarly journals Energy flux and dissipation of inhomogeneous plane waves in hereditary viscoelasticity

2019 ◽  
Vol 475 (2231) ◽  
pp. 20190478
Author(s):  
N. H. Scott
Keyword(s):  
Energy Density ◽  
Energy Flux ◽  
Plane Waves ◽  
Time Averaging ◽  
Complex Frequency ◽  
Hereditary Viscoelasticity ◽  
Inhomogeneous Plane ◽  
Dissipative Material ◽  
Comparable Magnitude ◽  
Inhomogeneous Plane Waves

Inhomogeneous small-amplitude plane waves of (complex) frequency ω are propagated through a linear dissipative material which displays hereditary viscoelasticity. The energy density, energy flux and dissipation are quadratic in the small quantities, namely, the displacement gradient, velocity and velocity gradient, each harmonic with frequency ω , and so give rise to attenuated constant terms as well as to inhomogeneous plane waves of frequency 2 ω . The quadratic terms are usually removed by time averaging but we retain them here as they are of comparable magnitude with the time-averaged quantities of frequency ω . A new relationship is derived in hereditary viscoelasticity that connects the amplitudes of the terms of the energy density, energy flux and dissipation that have frequency 2 ω . It is shown that the complex group velocity is related to the amplitudes of the terms with frequency 2 ω rather than to the attenuated constant terms as it is for homogeneous waves in conservative materials.

Transient representation of the Sommerfeld‐Weyl integral with application to the point source response from a planar acoustic interface

Geophysics ◽  
1984 ◽  
Vol 49 (9) ◽  
pp. 1495-1505 ◽  
Author(s):  
Martin Tygel ◽  
Peter Hubral
Keyword(s):  
Point Source ◽  
Plane Waves ◽  
Transient Waves ◽  
Layer Boundary ◽  
Spherical Source ◽  
Time Harmonic ◽  
Starting Point ◽  
Inhomogeneous Plane ◽  
Acoustic Interface ◽  
Inhomogeneous Plane Waves

Point source responses from a planar acoustic and/or elastic layer boundary (as well as from a stack of planar parallel layers) are generally obtained by using as a starting point the Sommerfeld‐Weyl integral, which can be viewed as decomposing a time‐harmonic spherical source into time‐harmonic homogeneous and inhomogeneous plane waves. This paper gives a powerful extension of this integral by providing a direct decomposition of an arbitrary transient spherical source into homogeneous and inhomogeneous transient plane waves. To demonstrate with an example the usefulness of this new point source integral representation, a transient solution is formulated for the reflected/transmitted response from a planar acoustic reflector. The result is obtained in the form of a relatively simple integral and essentially corresponds to the solution obtained by Bortfeld (1962). It, however, is arrived at in a physically more transparent way by strictly superimposing the reflected/transmitted transient waves leaving the interface in response to the incident transient homogeneous and inhomogeneous plane waves coming from the center of the point source.

Inhomogeneous plane waves in layered materials including fluid, solid and porous layers

Wave Motion ◽  
1991 ◽  
Vol 13 (4) ◽  
pp. 329-336 ◽  
Author(s):  
Walter Lauriks ◽  
Jean F. Allard ◽  
Claude Depollier ◽  
André Cops
Keyword(s):  
Plane Waves ◽  
Layered Materials ◽  
Porous Layers ◽  
Inhomogeneous Plane ◽  
Inhomogeneous Plane Waves

Static and propagating exponential solutions of Maxwell’s equations for crystals

1992 ◽  
Vol 438 (1904) ◽  
pp. 485-510
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Plane Waves ◽  
Electric Permittivity ◽  
Complex Vector ◽  
Time Harmonic ◽  
Inhomogeneous Plane ◽  
Isotropic Media ◽  
Special Case ◽  
Inhomogeneous Plane Waves

Solutions of Maxwell’s equations are considered for anisotropic media for which the electric permittivity κ and magnetic permeability µ are assumed to be arbitrary real positive definite symmetric second order tensors. The propagation of time-harmonic electromagnetic inhomogeneous plane waves or ‘propagating exponential solutions’ in such media has been presented previously. These solutions were systematically obtained by prescribing an ellipse - the directional ellipse associated with a bivector (complex vector) C - and finding the corresponding slowness bivectors. Here, it is shown that for some prescribed directional ellipses, not only propagating exponential solutions (PES), but also static exponential solutions (SES), may be obtained. There are a variety of possibilities. For example, for one choice of directional ellipse it is found that two SES and one PES are possible, whereas, for some other choices, only one SES or only one PES is possible. By a systematic use of bivectors and their associated ellipses, all the possible SES and PES are classified. To complete the classification it is necessary to examine special elliptical sections of the ellipsoids associated with the tensors κ , µ , κ -1 , µ -1 . In particular, sections by planes orthogonal to special directions called ‘generalized optic axes’ and ‘generalized ray axes’ play a major role. These axes reduce to the standard optic axes and ray axes in the special case of magnetically isotropic media.

Energy flux for trains of inhomogeneous plane waves

1980 ◽  
Vol 370 (1742) ◽  
pp. 417-429 ◽  
Keyword(s):  
Energy Flux ◽  
Energy Equation ◽  
Plane Waves ◽  
Frequency Dispersion ◽  
Conservation Of Energy ◽  
Inhomogeneous Plane ◽  
Wave Trains ◽  
The Mean ◽  
Point Form ◽  
Inhomogeneous Plane Waves

The propagation of inhomogeneous plane waves in linear conservative systems is considered. It is assumed that the secular equation governing the propagation of a plane wave of slowness S has the form Q ( S ) = 0 where Q is independent of frequency. Dispersion enters via the boundary condi­tions. By using the point form of the conservation of energy equation results are obtained which relate the mean energy flux vector R ˜ with the mean energy density Ẽ for any number of wave trains. In particular for a single train of inhomogeneous plane waves it is shown that R ˜ . S + = Ẽ . The results are relevant in electromagnetism, elasticity and fluid dynamics.

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