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Journal ArticleDOI

On waves in a random micropolar conducting magneto-thermo-viscoelastic medium

TL;DR: In this article, the effects of random inhomogeneity on wave propagation in the interacting micropolar conducting magneto-generalized thermo-viscoelastic medium were studied.
Abstract: Effects of random inhomogeneity on wave propagation in the interacting micropolar conducting magneto-generalized thermo-viscoelastic medium are studied. The couple stress theory relevant to...
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Journal ArticleDOI
01 Dec 1985

38 citations

Journal ArticleDOI
J. L. Davis1
TL;DR: In this paper, a mathematical analysis of wave propagation in a one-dimensional bounded viscoelastic medium under prescribed boundary conditions is made, and closed form expressions for wave velocity as a function of ratio of relaxation frequency to frequency of applied periodic displacement are obtained for the steady state part of the solution.
Abstract: A mathematical analysis is made of the problem of wave propagation in a one-dimensional bounded viscoelastic medium under prescribed boundary conditions. Closed form expressions are obtained for viscoelastic waves for the case of a relaxation function involving a single relaxation time. An expression for the phase velocity as a function of ratio of relaxation frequency to frequency of applied periodic displacement is obtained for the steady state part of the solution. The generalization to a relaxation function involving a finite number of relaxation times is discussed, and a method is sketched out for solving the more general integropartial differential equation of motion. Comments are made on the molecular interpretation of viscoelastic models.

9 citations

Journal ArticleDOI
TL;DR: In this paper, the effects of rotation, ramp parameter and magnetic field in a micropolar generalized thermo-viscoelastic medium were studied in a three-phase lag theory of thermoelasticity.
Abstract: This paper is devoted to three-phase-lag theory of thermo-elasticity to study the effects of rotation, ramp parameter and magnetic field in a micropolar generalized thermo-viscoelastic medium. By e...

7 citations


Cites background from "On waves in a random micropolar con..."

  • ...Bhattacharyya [21] investigated the effect of magnetic field on the wave propagation in a random micropolar conducting thermoviscoelasticmedium....

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Journal ArticleDOI
TL;DR: In this paper, the problem of wave propagation in a rotating random micropolar generalized thermoelastic medium was examined. The entire frame of reference was assumed to be rotating with a uniform angula.
Abstract: This article examines the problem of wave propagation in a rotating random micropolar generalized thermoelastic medium. The entire frame of reference is assumed to be rotating with a uniform angula...

4 citations


Cites background from "On waves in a random micropolar con..."

  • ...All these studies, CONTACT R. K. Bhattacharyya rabindrakb@yahoo.com Department of Applied Mathematics, University of Calcutta, 92....

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  • ...[15] R. K. Bhattacharyya, “On waves in a random micropolar conducting magneto-thermo-viscoelastic medium,” Int....

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  • ...It has been shown that the mean field quantity, < V >, a seven-vector, representing the displacement vector, the micro-rotation vector, and temperature, satisfies an integro-differential equation involving the associated Green’s tensor which was computed by Mitra and Bhattacharyya [13]....

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  • ...Later, Bhattacharyya [25] used the same method to study wave propagation in the random magnetothermo-viscoelastic medium....

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  • ...[13] M. Mitra and R. K. Bhattacharyya, “On wave propagation in a random micropolar thermoelastic medium, second moments and associated Green’s tensor,” Waves Random Complex Media, vol. 25, no. 4, pp. 506–535, 2015....

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References
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Journal ArticleDOI
TL;DR: In this paper, the energy flux in both the forward and backward directions was derived from the spectral equations, and the analysis was restricted to fluctuations that satisfy the conditions τμ is the characteristic time of the fluctuations, k 0 is the mean radiation wavenumber, L z is the correlation length of the random fluctuations in the mean propagation direction and L FS is a mean scattering length.
Abstract: In Ref. [1] (Appendix A) we derived equations governing the frequency and spatial spectrum of radiation propagating in three-dimensional time-dependent random media with randomly varying sound speed c ( x , t). From the spectral equations we determine equations for the energy flux in both the forward and backward directions. We consider media that are spatially homogeneous and isotropic and stationary in time. In order to allow an independence assumption the analysis is restricted to fluctuations that satisfy the conditions τμ ≫ L z /c 0 and τμ ≪ L FS/c 0 where τμ is the characteristic time of the fluctuations, k 0 is the mean radiation wavenumber, L z is the characteristic correlation length of the random fluctuations in the mean propagation direction and L FS is a mean scattering length. We consider various values of γ = (k 0 L z )2/2. When γ ≪ 1 we find the usual radiation transfer equations. When γ ≫ 1, but back-scattering can be neglected, we find the forward-scattering equations. We also consider γ ...

5 citations


"On waves in a random micropolar con..." refers background in this paper

  • ...[27] M. J. Beran, S. Frankenthal, V. Deshmukh, and A. M. Whitman, “Propagation of radiation in time-dependent three-dimensional random media,” Waves in random & complex media, vol. 18, no. 3, pp. 435–460, 2008....

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  • ...Beran, Frankenthal, Deshmukh and Whitman [27] studied propagation of radiation in time-dependent three-dimensional random media....

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Journal ArticleDOI
TL;DR: In this paper, the probability density distributions of the power reflection coefficient, and of the various fluxes of the components of an erstwhile plane wave that propagates in a one-dimensionalally stratified slab of a time-independent scattering medium are calculated.
Abstract: We calculate the probability density distributions of the power reflection coefficient, and of the various fluxes of the components of an erstwhile plane wave that propagates in a one-dimensionally stratified slab of a time-independent scattering medium. We determine the second- and fourth-order statistics of the power-fluxes, discuss the relevance of this problem to the localization phenomenon, examine the distribution of the emerging power-flux and the limitations on the assumption that it possesses a lognormal distribution, and finally discuss and rationalize the differences between the above and the corresponding characteristics of the radiation propagating in a time-dependent variant of this problem.

4 citations


"On waves in a random micropolar con..." refers background in this paper

  • ...[27] M. J. Beran, S. Frankenthal, V. Deshmukh, and A. M. Whitman, “Propagation of radiation in time-dependent three-dimensional random media,” Waves in random & complex media, vol. 18, no. 3, pp. 435–460, 2008....

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  • ...Beran, Frankenthal, Deshmukh and Whitman [27] studied propagation of radiation in time-dependent three-dimensional random media....

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  • ...[26] M. J. Beran, and J. J. McCoy, “Mean field variations in a statistical sample of heterogeneous linearly elastic solids,” Int....

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  • ...[31] S. Frankenthal, and M. J. Beran, “Propagation in onedimensionally stratified time-independent scattering media,” Waves in Random & Complex Media, vol. 17, no. 2, pp. 189–212, 2007....

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  • ...Beran and McCoy ([25], [26]) proposed the technique of iterative perturbation in studying mean field variations in the dielectric and other media....

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Journal ArticleDOI
TL;DR: In this article, the smooth perturbation technique is employed to investigate the problem of reflection of waves incident on the plane boundary of a semi-infinite elastic medium with randomly varying inhomogeneities.
Abstract: In this paper the smooth perturbation technique is employed to investigate the problem of reflection of waves incident on the plane boundary of a semi-infinite elastic medium with randomly varying inhomogeneities. Amplitude ratios have been obtained for various types of incident and reflected waves. It has been shown that an incidentSH orSV type of wave gives rise to reflectedSH, P andSV waves, the main components beingSH andP, SV in the respective cases. The reflected amplitudes have been calculated depending upon the randomness of the medium to the square of the small quantity ɛ, where ɛ measures the deviation of the medium from homogeneity. An incidentP-type wave produces mainly aP component and also a weakSH component to the order of ɛ2. The reflected amplitudes obtainable for elastic media are also altered by terms of the same order. The direction of the reflected wave is influenced by randomness in some cases.

4 citations

Book ChapterDOI
01 Jan 2003
TL;DR: In this paper, the components of the Green tensor for interacting conducting magnetic and elastic fields in an infinite homogeneous medium are expressed in the form of Fourier integrals by the use of the Fourier transforms.
Abstract: The interaction of conducting magnetic and elastic or viscoelastic and thermal or thermoelastic fields in an infinite random medium has been under study for some time. Knopoff [1] and Wilson [2] undertook the study of the effect of the presence of magnetic fields in elastic wave propagation. However, the evaluation and application of Green’s functions are essential to the study of wave propagation in interacting magnetic and viscoelastic or elastic fields in random media following J.B. Keller’s perturbation procedure. This is illustrated by the study of wave propagation in random elastic medium by Karal and Keller [3], in random thermoelastic media by Chow [4]. Van Kampen [5] has shwon that the study of the exact solution of wave propagation in a medium with randon refractive index depends on the knowledge of the relevant Green’s function. A knowledge of Green’s function is also essential for the one body scattering problem and the problem of multiple scattering by randomly distributed scatterers (Frisch [6]). In this paper, the components of the Green’s tensor for interacting conducting magnetic and elastic fields in an infinite homogeneous medium is expressed in the form of Fourier integrals by the use of Fourier transforms. It has been possible to evaluate the appropriate integrals approximately for the case of a conducting medium. Two sets of Green’s functions, depending upon high and low frequencies have been presented.

3 citations


"On waves in a random micropolar con..." refers methods in this paper

  • ...[16] R. K. Bhattacharyya, “On wave propagation in a random magneto-thermo-viscoelastic medium,” Ind. J. Pure Appl....

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  • ...The present paper perhaps is the second attempt in micropolar literature at computing effects of random variation of parameters in a well-defined interacting medium, the first one being the paper by Mitra and Bhattacharyya [14]....

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  • ...Earlier, Bhattacharyya in two © Taylor & Francis Group, LLC successive papers ([15], [16]) examined problems of wave propagation in a random magneto-thermo-viscoelastic medium and wave propagation in a random magnetothermo-viscoelastic medium respectively....

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  • ...Kumar and coworkers studied various problems of wave propagation, reflection CONTACT R.K. Bhattacharyya rabindrakb@yahoo.com Biswakosh Lane, Kolkata , India. and refraction in micropolar elastic, micropolar thermoelastic and micro-stretch media ([6], [7])....

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  • ...Bhattacharyya ([16], [42]) and Bera [17] pursued the method in the study of wave propagation phenomena in coupled media....

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