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Journal ArticleDOI

On wave propagation in a random micropolar thermoelastic medium, second moments, and associated Green’s tensor

11 Sep 2015-Waves in Random and Complex Media (Taylor & Francis)-Vol. 25, Iss: 4, pp 506-535
TL;DR: In this article, wave propagation in a random weakly thermal micropolar elastic medium has been studied, where the smooth perturbation technique has been employed and the classical thermoelasticity has been used.
Abstract: The couple stress theory developed by Eringen comprises granular materials as also composite fibrous materials. As such, micropolar materials present an inclusive model of composite materials. This article endeavors to study aspects of wave propagation in a random weakly thermal micropolar elastic medium. The smooth perturbation technique has been employed. The classical thermoelasticity has been used. Six different types of waves have been observed to propagate in the random interacting medium. Dispersion equations have been derived. The effects due to random variations of micropolar elastic and thermal parameters have been observed. Change of phase speed occurs on account of randomness. Attenuation coefficients for high-frequency waves have been computed. Second moment properties have been discussed with application to wave propagation in the random micropolar elastic medium. 36 + 1 components of the associated Green’s tensor have been computed. Integrals involving correlation functions have been transf...
Citations
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Journal ArticleDOI
TL;DR: In this article, the nonlinear generalized thermoelasticity of a functionally graded material (FGM) layer was investigated and the elasticity modulus, thermal conductivity, thermal e...
Abstract: Current investigation deals with the nonlinear generalized thermoelasticity of a functionally graded material (FGM) layer. It is assumed that the elasticity modulus, thermal conductivity, thermal e...

11 citations

Journal ArticleDOI
TL;DR: In this paper, the fundamental solution for a steady point heat source acting on the surface of a semi-infinite transversely isotropic micropolar thermoelastic material is constructed by six newly introduced harmonic functions.
Abstract: Purpose The purpose of this paper is to study the fundamental solution in transversely isotropic micropolar thermoelastic media. With this objective, the two-dimensional general solution in transversely isotropic thermoelastic media is derived. Design/methodology/approach On the basis of the general solution, the fundamental solution for a steady point heat source on the surface of a semi-infinite transversely isotropic micropolar thermoelastic material is constructed by six newly introduced harmonic functions. Findings The components of displacement, stress, temperature distribution and couple stress are expressed in terms of elementary functions. From the present investigation, a special case of interest is also deduced and compared with the previous results obtained. Practical implications Fundamental solutions can be used to construct many analytical solutions of practical problems when boundary conditions are imposed. They are essential in the boundary element method as well as the study of cracks, defects and inclusions. Originality/value Fundamental solutions for a steady point heat source acting on the surface of a micropolar thermoelastic material is obtained by seven newly introduced harmonic functions. From the present investigation, some special cases of interest are also deduced.

6 citations

Journal ArticleDOI
TL;DR: Elastic wave propagation has been explored in an infinite granular thermoelastic medium rotating with constant speed using the method of smooth perturbation to find the solution of governing equations in the relevant media.
Abstract: Elastic wave propagation has been explored in an infinite granular thermoelastic medium rotating with constant speed. The elastic and thermal parameters of the granular medium are taken to be randomly fluctuated so that the medium represents the randomly fluctuating inhomogeneous medium. The method of smooth perturbation has been used, which requires the inversion of a deterministic differential operator to find the solution of governing equations in the relevant media. The analysis is based on the dynamics of granular medium as propounded by N. Oshima. All field parameters are functions of space vector and time. A general dispersion equation for waves propagating in the rotating random granular generalized thermal elastic medium has been obtained. The compression and shear wave propagations have been studied. It has been pointed out that in the case of compression waves, the mean and auto-correlation function of the thermo-mechanical coupling parameter greatly influence the mean wave propagation. For shear waves, however, randomness has no effect on wave propagation. Effects of non-random granular elastic medium, randomness and rotation of the frame of reference are discernible from analyses of dispersion equations. The study may find applications in soil mechanics, seismology and oil-prospecting. Computational results have been shown.

5 citations

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 or methods from "On wave propagation in a random mic..."

  • ...The components of Green’s tensor corresponding to L0 < V0 >¼ dð~x, ~x 0Þdij were computed earlier by Mitra and Bhattacharyya [13] in the form: Glj ¼ G0 G1 0 G2 G3 0 0 0 G4 0 @ 1 A (14) where G4 rð Þ ¼ 14pr e ibrI3, b ¼ b1 þ ib2, sayð Þ, and b1 ¼ xg0 2 0 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1þ t20x2 q þ t0x 1 2 , b2 ¼ xg0 2 0 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1þ t20x2 q t0x 1 2 : (15) Now, L0 < V ~xð Þ > ¼ q0- 2~A k0 þ l0ð Þ ~k:~A ~k ðl0 þ j0Þk2~A þ ij0ð~k ~BÞ ij0 ~k ~A a0 þ b0ð Þ~k ~k:~B c0k2~B 2j0~B þ q0jx2~B ixg0 1 ixt0ð ÞC 0k2C 0 BB@ 1 CCA ei~k:~x : (16) Now by virtue of (10) and (11), we get < L1 >< V ~xð Þ > ¼ i m2 ixm3ð ÞC~k 0 xh0m2ð1 ixt0dlkÞð~k:~AÞ 0 B@ 1 CAei~k:~x : (17) < L2 >< V ~xð Þ > ¼ 0: (18) < L1 > L 1 0 < L1 >< V ~xð Þ > ¼ ei~k:~x ð xh0m2 1 ixt0dlkð Þ m2 ixm3ð Þ ~k:~A r!...

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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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  • ...Mitra and Bhattacharyya [13] perhaps for the first time endeavored to study wave propagation phenomenon in the micropolar thermoelastic medium, second moments and associated Green’s tensor in the random domain....

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  • ...were computed earlier by Mitra and Bhattacharyya [13] in the form:...

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Journal ArticleDOI
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...

4 citations


Cites background or methods from "On wave propagation in a random mic..."

  • ...[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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References
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BookDOI
01 Jan 1999

1,585 citations

ReportDOI
01 Sep 1965
TL;DR: In this article, a special class of micro-elastic materials called Micropolar Solids are presented for couple stress and distributed body couples, and the couple stress theory is shown to emanate as a spacial case of the present theory.
Abstract: : Equations of motion, constitutive equations and boundary conditions are presented for a special class of micro-elastic materials called Micropolar Solids. These solids respond to micro-rotational motions and spin inertia and can support couple stress and distributed body couples. The couple stress theory is shown to emanate as a spacial case of the present theory when the motion is constrained so that micro- and macro-rotations coincide. Several energy and uniqueness theorems are given.

929 citations


"On wave propagation in a random mic..." refers background or methods in this paper

  • ...[25] Eringen AC....

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  • ...[2] Eringen AC....

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  • ...References [1] Eringen AC....

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  • ...The equations of motion, constitutive equations, and boundary conditions for the micropolar elastic field have been derived by Eringen [1,2]....

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  • ...[4] Eringen AC....

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Book ChapterDOI
01 Jun 1967
TL;DR: In this paper, the complete theory of 3M continua, with and without E-M interactions, was given, and balance laws, jump conditions and nonlinear constitutive equations were obtained, so that the theory is complete and closed.
Abstract: In the four previous chapters we have given the complete theory of 3M continua, with and without E-M interactions. Balance laws, jump conditions, and nonlinear constitutive equations were obtained, so that the theory is complete and closed. Beginning with Chapter 5 we explore applications of these theories. By means of mathematical solutions and experimental observations, we try to exhibit new physical phenomena predicted by microcontinuum theories. The aim here is not to be exhaustive with the discussion of all problems for this is neither possible nor desirable, as there is a very large volume of literature in the field. It is not desirable since a large number of solutions tend to hide the main purpose, namely, the new physical phenomena that are not in the domain of predictions of classical field theories.

584 citations

Book
13 Dec 2009
TL;DR: In this paper, the authors present a model of linear hyperbolic thermoelasticity with finite wave speeds and a central equation of the problem of initial-boundary value problems.
Abstract: Preface Introduction 1. Fundamentals of linear thermoelasticity with finite wave speeds 2. Formulations of initial-boundary value problems 3. Existence and uniqueness theorems 4. Domain of influence theorems 5. Convolutional variational principles 6. Central equation of thermoelasticity with finite wave speeds 7. Exact aperiodic-in-time solutions of Green-Lindsay theory 8. Kirchhoff type formulas and integral equations in Green- Lindsay theory 9. Thermoelastic polynomials 10. Moving discontinuity surfaces 11. Time-periodic solutions 12. Physical aspects and applications of hyperbolic thermoelasticity 13. Nonlinear hyperbolic rigid heat conductor of the Coleman type References Index

376 citations


"On wave propagation in a random mic..." refers background in this paper

  • ...The classical thermoelasticity instead of generalized thermoelasticity [9] has been chosen as the first simplest model in the random micropolar thermal domain of research....

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