Reflection/transmission laws for slowness vectors in viscoelastic anisotropic media

Červený, Vlastislav

doi:10.1007/s11200-007-0022-7

Cited by 16 publications

(7 citation statements)

References 18 publications

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“…The perturbation formula for the slowness vector presented in this paper may also find applications in the solution of the problem of reflection and transmission of homogeneous and inhomogeneous plane waves at a plane interface separating two homogeneous, viscoelastic, isotropic or anisotropic media. More specifically, the perturbation formula may be used in the determination of slowness vectors of individual reflected and transmitted waves from the slowness vector of the incident wave, see Červený (2007). As a whole, the problem of reflection and transmission of plane waves at a plane interface between two homogeneous, viscoelastic, isotropic or anisotropic media is, however, far from being solved.…”

Section: Discussionmentioning

confidence: 99%

Weakly inhomogeneous plane waves in anisotropic, weakly dissipative media

Červený¹,

Pšenčı́k

2008

Geophysical Journal International

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S U M M A R YWeakly inhomogeneous time-harmonic plane waves propagating in homogeneous anisotropic, weakly dissipative media are studied using the perturbation method. Only dissipation mechanisms, which can be described within the framework of linear viscoelasticity, are considered. As a reference (non-perturbed) case, plane waves with a real-valued slowness vector propagating in perfectly elastic anisotropic media are used. Simple approximate expressions for the complex-valued slowness and polarization vectors of weakly inhomogeneous plane waves propagating in anisotropic, weakly dissipative media are derived. Special attention is devoted to the imaginary part of the slowness vector, known as the attenuation vector, which is responsible for the amplitude attenuation of a plane wave. The derived approximate expression for the attenuation vector depends on the material (intrinsic) dissipation parameters as well as on the inhomogeneity of the plane wave. Its scalar product with the energy-velocity vector yields, however, the intrinsic attenuation factor, which does not depend on the inhomogeneity of the wave, and which thus represents a very suitable measure of the material dissipation. The derived expression for the intrinsic attenuation factor is valid for media of unrestricted anisotropy and weak dissipation and for homogeneous as well as weakly inhomogeneous plane waves. The intrinsic attenuation factor is inversely proportional to the scalar quantity, which, in isotropic viscoelastic media, corresponds to the well-known quality factor Q. Its generalization to anisotropic weakly viscoelastic media is directionally dependent. Numerical examples are presented, in which the accuracy of the approximate formulae based on the perturbation method is studied. The results indicate that the presented perturbation results are sufficiently accurate to be used in practical applications. Strong directivity of the intrinsic attenuation factor shows its great potential in solving inverse problems.

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Section: Discussionmentioning

confidence: 99%

Weakly inhomogeneous plane waves in anisotropic, weakly dissipative media

Červený¹,

Pšenčı́k

2008

Geophysical Journal International

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“…For D = 0, the plane wave is homogeneous, and for D ̸ = 0 it is inhomogeneous. In order to determine the incident wave belong to θ 0 and D, we use the mixed specification of slowness vector p = σn + iDm(see [11,14])…”

Section: Incident Wavementioning

confidence: 99%

“…In order to study the reflection and transmission of waves, slowness vector p is expressed in terms of a known real-valued unit vector n (the unit vector of x 3 axis) and a complex-valued vector p 0 as follows [11,12,14]. Note that plane Σ S coincides to x 3 = 0 one.…”

Section: Reflected and Transmitted Wavesmentioning

confidence: 99%

The propagation of inhomogeneous waves in an orthotropic viscoelastic medium

Xuan

2023

Preprint

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The present paper deals with the propagation of inhomogeneous waves in an orthotropic viscoelastic medium. For chosen directions of propagation and a real finite inhomogeneity parameter, a complex slowness vector is specified to define the propagation of inhomogeneous incident wave. Then the reflection , transmission of plane waves at a plane interface between two orthotropic viscoelastic halfspaces are discussed. In this incidence, horizontal slowness determines the slowness vectors for all reflected, transmitted waves. For each reflected, transmitted wave, the corresponding slowness vector is resolved to define its phase direction, phase velocity and attenuation angle. Appropriate boundary conditions on this wave-field determine the amplitude ratios for reflected, transmitted waves relative to the incident wave. The numerical examples are provided to show the effect of the inhomogeneity of incident wave on the propagation characteristic as well as the reflection and transmission coefficients of the reflected, transmitted waves.

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“…The polarization vectors u R α ∈ R 3 of the reflected contributions are evaluated in direction of the corresponding slowness vectors. Červený [65] defines the reflected slowness vector as a function of incoming slowness vector and thus the reflected contributions are governed by the corresponding slowness vectors i.e., s R α (m − y). Also, the direction of reflected slowness vectors governs the scattering coefficients.…”

Section: Simulation Of Wave Propagationmentioning

confidence: 99%

Simulation of Ultrasonic Backscattering in Polycrystalline Microstructures

Dobrovolskij

Schladitz

2022

Acoustics

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Ultrasonic testing of polycrystalline media relies heavily on simulation of the expected signals in order to detect and correctly interpret deviations due to defects. Many effects disturb ultrasonic waves propagating in polycrystalline media. One of them is scattering due to the granular microstructure of the polycrystal. The thus arising so-called microstructural noise changes with grain size distribution and testing frequency. Here, a method for simulating this noise is introduced. We geometrically model the granular microstructure to determine its influence on the backscattered ultrasonic signal. To this end, we utilize Laguerre tessellations generated by random sphere packings dividing space into convex polytopes—the cells. The cells represent grains in a real polycrystal. Cells are characterized by their volume and act as single scatterers. We compute scattering coefficients cellwise by the Born approximation. We then combine the Generalized Point Source Superposition technique with the backscattered contributions resulting from the cell structure to compute the backscattered ultrasonic signal. Applying this new methodology, we compute the backscattered signals in a pulse-echo experiment for a coarse grain cubic crystallized Inconel-617 and a fine grain hexagonal crystallized titanium. Fitting random Laguerre tessellations to the observed grain structure allows for simulating within multiple realizations of the proposed model and thus to study the variation of the backscattered signal due to microstructural variation.

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Reflection/transmission laws for slowness vectors in viscoelastic anisotropic media

Cited by 16 publications

References 18 publications

Weakly inhomogeneous plane waves in anisotropic, weakly dissipative media

Weakly inhomogeneous plane waves in anisotropic, weakly dissipative media

The propagation of inhomogeneous waves in an orthotropic viscoelastic medium

Simulation of Ultrasonic Backscattering in Polycrystalline Microstructures

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