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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
01 May 1996
TL;DR: In this paper, the problem of Rayleigh wave in a micropolar generalized thermoelastic half-space with stretch was investigated. And the frequency and wave velocity equations for symmetric and anti-symmetric vibrations were obtained for the first problem and frequency equation has also been derived for the second problem.
Abstract: In the present investigation, we discuss two different problems namely (i) Rayleigh-Lamb problem in micropolar generalized thermoelastic layer with stretch and (ii) Rayleigh wave in a micropolar generalized thermoelastic half-space with stretch. The frequency and wave velocity equations for symmetric and anti-symmetric vibrations are obtained for the first problem. The frequency equation has also been derived for the second problem. The special cases of the above said problems of micropolar generalized thermoelasticity with stretch for Green-Lindsay and Lord-Shulman theory have been discussed in detail. Results of these analysis reduce to those without thermal and stretch effects

29 citations


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

  • ...[8] B. Singh and R. Kumar, “Reflection and Refraction of plane waves at an interface between micropolar elastic solid and viscoelastic solid,” Int....

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  • ...[11] R. Kumar and B. Singh, “Wave propagation in a micropolar generalized thermoelastic body with stretch,” Proc....

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  • ...[12] R. Kumar and B. Singh, “Reflection of plane waves from the flat boundary of amicropolar generalized thermoelastic half-space with stretch,” Indian J. pure appl....

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  • ...Kumar and Singh [11] studied the problem of wave propagation in a micropolar generalized thermoelastic body with stretch....

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  • ...Singh and Kumar [8] studied reflection and refraction problems in micropolar medium....

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Journal ArticleDOI

29 citations


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

  • ...and refraction in micropolar elastic, micropolar thermoelastic and micro-stretch media ([6], [7])....

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Journal ArticleDOI
TL;DR: In this article, a general formalism of the analysis of mean (or coherent) elastic waves for an arbitrary shape of the scatterers and the solutions of some specific problems in the case of spherical scatterrs are presented.
Abstract: The problem of propagation of plane harmonic waves in an infinite elastic solid containing a random configuration ofN identical scatterers of finite size is considered. The paper presents the general formalism of the analysis of mean (or coherent) elastic waves for an arbitrary shape of the scatterers and the solutions of some specific problems in the case of spherical scatterers. The equations expressing the average total field in terms of the probability density function and scattering properties of individual scatterers are presented. These equations concern an arbitrary shape of the scatterers and include the effects of single and multiple scattering. In the case of dilute and uniform distribution of spherical scatterers the more detailed analysis of average total field leads to the determination of the equivalent homogeneous medium in which the mean wave propagates. For the limit of the low frequences the effective parameters of the medium are given and they turn out to be the same as those obtained within effective modulus theory in static case.

26 citations


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

  • ...Sobczyk [28] studied elastic wave propagation in a discrete random medium....

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Journal ArticleDOI
TL;DR: In this paper, the effect of wave propagation in an interacting random infinite magneto-thermo- visco-elastic medium has been studied formulating a generalised theory of thermoelasticity that combines both the generalised theories developed by Lord and Shulman (2) as well as by Green and Lindsay (3).
Abstract: The problem of wave propagation in an interacting random infinite magneto-thermo- visco-elastic medium has been studied formulating a generalised theory of thermoelasticity recently proposed by Noda, Furuk-Awa and Ashida (1) that combines both the generalised theories developed by Lord and Shulman (2) as well as by Green and Lindsay (3). The perturbation technique relevant to stochastic differential equations has been employed to obtain the relation connecting displacement amplitudes of waves propagating in the interacting media. The appropriate Green's tensor essential for the discussion has been obtained in the course of analysis. A more general coupled dispersion relation for longitudinal and transverse waves has been deduced to determine the effect of visco- elasticity, relaxation times, and rotation on the phase velocity of the coupled waves. The equations have been analysed for a particular form of thermo-mechanical coupling and autocorrelation function to show that the effect (of the order of e 2 only) of the thermal field is to attenuate the longitudinal type waves and to alter the phase-speed depending upon the values of the visco-elastic parameters, relaxation times, and rotation. Cases of low and high frequencies have also been studied, and numer- ical calculations have been done to determine the effect of visco-elastic parameters, relaxation times, rotation, and thermoelastic coupling on the phase velocity and attenuation coefficient of the waves. (~) 1998 Elsevier Science Ltd. All rights reserved.

25 citations


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

  • ...The generalized thermal field equation is written in the form ([17], [45]):...

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