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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 article, the amplitude ratios of reflected and refracted waves depend on the angle of emergence and frequency of the incident wave, and the amplitude ratio for different values of frequency ratio ( ω 2 /ω 2 0 ).

25 citations


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

  • ...[6] R. Kumar, “Wave propagation in micropolar viscoelastic generalized thermoelastic solid,” Int....

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  • ...[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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  • ...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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  • ...[7] R. Kumar, and S. Deswal, “Surface wave propagation in a micropolar thermoelastic medium without energy dissipation,” J. Sound&Vibrations, vol. 256, no. 1, pp. 173–178, 2002....

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Journal ArticleDOI
TL;DR: In this paper, the analysis of the dynamics of structural systems with randomly varying parameters is presented, and the analysis is based on the theory of random integral equations, including error estimation, which is applied to the problems of harmonic vibration of a beam with random varying density and a uniform beam resting on a randomly inhomogeneous Winkler foundation.

20 citations

Journal ArticleDOI
TL;DR: In this paper, a set of correlation equations which are useful in the quantitative determination of the covariance properties of the waves is presented, which are used in the analysis of a scalar wave propagating in a random medium.
Abstract: Extensive studies have been made on the mean or effective properties of waves propagating in a random medium. We present in this paper a set of correlation equations which are useful in the quantitative determination of the covariance properties of the waves. As an example, the problem of a scalar wave propagating in a random medium is considered.

17 citations


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

  • ...[34] K. K. Chen, and T. T. Soong, “Covariance properties of waves propagating in a random medium,” J. Acoustical....

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  • ...A detailed discussion on properties and applications of random differential equations can be found, among others, in the treatise of Soong [35]....

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  • ...Chen and Soong [34] derived a set of correlation equations which are useful in the quantitative evaluation of the covariance properties of waves propagating in a random medium....

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  • ...[35] T. T. Soong, RandomDifferential Eqnarrays in Science and Engineering....

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Journal ArticleDOI

16 citations


Additional excerpts

  • ...Karal and Keller [38], Keller and Karal [39]), Chow [40], Chen and Tien [41] and many others adopted the method in studying elastic, electromagnetic, thermal and other waves....

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  • ...Karal and Keller [38], Keller and Karal [39]), Chow [40], Chen and Tien [41] and many others adopted the method in studying elastic, electromagnetic, thermal and other waves....

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  • ...[41] Y. M. Chen, and C. L. Tien, “Penetration of temperature waves in a random medium,” J. Maths., and Physics, vol. XLVI, no. 2, June 1967....

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Journal ArticleDOI
TL;DR: In this article, a theoretical analysis of the wave field radiated by a point source in a weakly inhomogeneous one-dimensional random medium is presented, based on a perturbation technique and includes all single and double scattering terms, as well as some scattering terms of higher order.
Abstract: A theoretical analysis of the wave field radiated by a point source in a weakly inhomogeneous one‐dimensional random medium is presented. The analysis is based on a perturbation technique and includes all single‐ and double‐scattering terms, as well as some scattering terms of higher order. Approximate expressions, valid when the absorption of the medium is small, are obtained for the mean intensity (i.e., the mean square of the modulus of the complex wave amplitude) and the mean energy flux of the wave as a function of propagation range. These expressions show that, as a consequence of backscattering by the random inhomogeneities of the medium, the mean intensity and mean energy flux decrease more rapidly with range than would be the case in the absence of randomness. This more rapid rate of decrease with range can be interpreted as an excess attenuation of the wave as a result of the randomness of the medium. It is also found that the mean radiated power is altered slightly by the randomness of the medium. The excess‐attenuation results are found to be consistent with observations.

12 citations


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

  • ...Wenzel [29] made a theoretical study on radiation and attenuation of waves in a random medium....

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