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Journal ArticleDOI

Effect of rotation in magneto-micropolar thermoelastic medium due to mechanical and thermal sources

30 Aug 2009-Chaos Solitons & Fractals (Pergamon)-Vol. 41, Iss: 4, pp 1619-1633
TL;DR: In this paper, a two dimensional problem in electromagnetic micropolar generalized thermoelastic medium, in the presence of a transverse magnetic field subjected to mechanical force or thermal source (concentrated or uniformly distributed), is investigated.
Abstract: In this work, a two dimensional problem in electromagnetic micropolar generalized thermoelastic medium, in the presence of a transverse magnetic field subjected to mechanical force or thermal source (concentrated or uniformly distributed), is investigated. The entire elastic medium is rotating with a uniform angular velocity. Laplace and Fourier transform techniques are used to solve the problem and the Descartes’ method along with irreducible case of Cardan’s method is used to obtain the roots of eight degree equation. The transformed components of normal strain, normal stress, tangential couple stress, temperature distribution, induced electric field and magnetic field are obtained. The integral transforms have been inverted by using a numerical technique. Magnetic effects and effect of rotation have been depicted graphically on the resulting quantities. Particular cases of interest are also deduced from the present investigation.
Citations
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Journal ArticleDOI
TL;DR: In this article, a homogeneous transversely isotropic thermo-elastic rotating medium with two temperature and magnetic effect due to thermomechanical sources is investigated, where Laplace and Fourier transform technique is applied to solve the problem.

39 citations

Journal ArticleDOI
TL;DR: In this paper, the moving heat source response in a homogeneous, isotropic, micropolar semi-infinite medium in the presence of a finite rotation about its axis has been considered.
Abstract: The present paper deals with the moving heat source response in a homogeneous, isotropic, micropolar semi-infinite medium in the presence of a finite rotation about its axis. In this context, two-temperature generalized thermoelasticity theory has been considered. In order to obtain the physical aspects of displacement, microrotation, stress distribution and temperature changes, a complex quartic equation has been solved by employing Descartes’ algorithm with the help of an irreducible Cardan’s method. To illustrate the analytical developments, the numerical solutions have been carried out for aluminum–epoxy composite, and the variations in displacement, microrotation, stress distribution and temperature changes have been shown graphically. This work may find applications in geophysics.

20 citations

Journal ArticleDOI
TL;DR: In this paper, the disturbances in a homogeneous transversely isotropic thermoelastic rotating medium with two temperature, in the presence of the combined effects of Hall currents and magnetic field due to normal force of ramp type, were investigated.
Abstract: This investigation is concerned with the disturbances in a homogeneous transversely isotropic thermoelastic rotating medium with two temperature, in the presence of the combined effects of Hall currents and magnetic field due to normal force of ramp type. The formulation is applied to the thermoelasticity theories developed by Green-Naghdi Theories of Type-II and Type-III. Laplace and Fourier transform technique is applied to solve the problem. The analytical expressions of displacements, stress components, temperature change and current density components are obtained in the transformed domain. Numerical inversion technique has been applied to obtain the results in the physical domain. Numerically simulated results are depicted graphically to show the effects of Hall current and anisotropy on the resulting quantities. Some special cases are also deduced from the present investigation.

17 citations

Journal ArticleDOI
TL;DR: In this paper, the authors investigated the disturbances in a homogeneous transversely isotropic thermoelastic rotating medium with two temperatures, in the presence of the combined effects of Hall currents and magnetic field.
Abstract: The present article is concerned with the investigation of disturbances in a homogeneous transversely isotropic thermoelastic rotating medium with two temperatures, in the presence of the combined effects of Hall currents and magnetic field. The formulation is applied to the thermoelasticity theories developed by Green-Naghdi theories of type-II and type-III. Laplace and Fourier transform techniques are applied to solve the problem. The analytical expressions of displacements, stress components, temperature change, and current density components are obtained in the transformed domain. A numerical inversion technique has been applied to obtain the results in the physical domain. Numerical simulated results are depicted graphically to show the effect of Hall current and two temperatures on resulting quantities. Some special cases are also deduced from the present investigation.

17 citations


Cites background from "Effect of rotation in magneto-micro..."

  • ...[29] R. Kumar and Rupender, Effect of rotation in magneto-micropolar thermoelastic medium due to mechanical and thermal sources, Chaos, Solitons Fractals, vol. 41, pp. 1619–1633, 2009....

    [...]

  • ...Several authors (Das and Kanoria [27], Kumar and Kansal [28], Kumar and Rupender [29], Atwa and Jahangir [30], Mahmoud [31]) have considered various problems in generalized thermoelasticity to study the effect of rotation....

    [...]

Journal ArticleDOI
31 Aug 2012
TL;DR: In this paper, a two dimensional problem in magnetic micropolar generalized thermoelastic medium, in the presence of a transverse magnetic field -taking into consideration the effect of Hall current- subjected to ramp-type heating, is investigated.
Abstract: In this work, a two dimensional problem in magnetic micropolar generalized thermoelastic medium, in the presence of a transverse magnetic field -taking into consideration the effect of Hall current- subjected to ramp-type heating, is investigated. The entire elastic medium is rotating with a uniform angular velocity. Laplace-Fourier transform technique is used to solve the problem. The transformed components of normal strain, normal stress, tangential couple stress, temperature distribution, and the current density components are obtained. The integral transforms have been inverted by using a numerical technique. Hall current effects and effect of rotation have been depicted graphically on the resulting quantities.

16 citations

References
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Journal ArticleDOI
TL;DR: In this article, a generalized dynamical theory of thermoelasticity is formulated using a form of the heat transport equation which includes the time needed for acceleration of heat flow.
Abstract: In this work a generalized dynamical theory of thermoelasticity is formulated using a form of the heat transport equation which includes the time needed for acceleration of the heat flow. The theory takes into account the coupling effect between temperature and strain rate, but the resulting coupled equations are both hyperbolic. Thus, the paradox of an infinite velocity of propagation, inherent in the existing coupled theory of thermoelasticity, is eliminated. A solution is obtained using the generalized theory which compares favourably with a known solution obtained using the conventional coupled theory.

3,266 citations

Book
01 Jan 1986
TL;DR: In this article, the authors present a self-contained account of the recent theory of micropolar elasticity, which is fully deterministic as against the background of the recently popular indeteiministic couple stress theory.
Abstract: In this article we present a self-contained account of the recent theory of micropolar elasticity. Micropolar elastic materials, roughly speaking, are the classical elastic materials with extra independent degrees of freedom for the local rotations. These materials respond to spin inertia and body and surface couples, and as a consequence they exhibit certain new static and dynamic effects, e.g., new types of waves and couple stressesThe theory is fully deterministic as against the background of the recently popular indeteiministic couple stress theory (cf. Art 23). The mechanics of certain classes of materials with fiberous and elongated grains (e.g , dumbbell types ' 0rains) represents a potential field of application of the theory. The geometry of deformation and its measures are introduced on a more effects general background of materials exhibiting granular and microstructure^Cmicromorphic materials). Various types of microstralns and microrotations are discussed. Compatibility conditions for the micropolar strains are derived The kinematics of strains, microstralns and rotations are presented Basic, laws of motion, conservation of mass, conservation of microlnertia, balance of momentum, balance of moment of momentum, conservation of energy are postulated and their local forms are obtained. The thermodynamics of micropolasolids Is formulated and the consequences of the entropy inequality are discussed. Constitutive equations are found for the linear theory of micropolar elasticity. The basic field equations and initial and boundary conditions are given. The indeterminate couple stress theory is shown to result as a special case of the theory when the motion is constrained. Several static and dynamic problems are solved to reveal seme ot the new physical phenomera exhibited by

328 citations

Journal ArticleDOI
TL;DR: In this paper, the transverse plane wave dispersion in linear, non-local micropolar elastic solids is derived by equating the frequency of the Transverse Acoustical (TA) branch at the end of the Brillouin zone.

278 citations

Journal ArticleDOI
TL;DR: In this article, the variational iteration method is applied to solve the Cauchy problem arising in one dimensional nonlinear thermoelasticity, and the numerical results of this method are compared with the exact solution of an artificial model to show the efficiency of the method.
Abstract: This paper applies the variational iteration method to solve the Cauchy problem arising in one dimensional nonlinear thermoelasticity. The advantage of this method is to overcome the difficulty of calculation of Adomian’s polynomials in the Adomian’s decomposition method. The numerical results of this method are compared with the exact solution of an artificial model to show the efficiency of the method. The approximate solutions show that the variational iteration method is a powerful mathematical tool for solving nonlinear problems.

153 citations