The generalized thermo-elasticity theory, i.e., Green and Naghdi (G-N) III theory, with energy dissipation (TEWED) is employed in the study of time-harmonic plane wave propagation in an unbounded, perfectly electrically conducting elastic medium subject to primary uniform magnetic field. A more general dispersion equation with complex coefficients is obtained for coupled magneto-thermo-elastic wave solved in complex domain by using the Leguerre's method. It reveals that the coupled magneto-thermoelastic wave corresponds to modified dilatational and thermal wave propagation with finite speeds modified by finite thermal wave speeds, thermo-elastic coupling, thermal diffusivity, and the external magnetic field. Numerical results for a copper-like material are presented. © 2009 Shanghai University and Springer-Verlag GmbH.

P DAS

M KANORIA

University of Calcutta (informally known as Calcutta University or CU) is a collegiate public state university located in Kolkata, West Bengal, India.&nbsp;Within India it is recognized as a &quot;Five-Star University&quot; and accredited &quot;A&quot; Grade by National Assessment and Accreditation Council.

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The University of Calcutta has secured the Fifth position among the Universities of India in the prestigious &quot;Indian University Ranking 2019&quot; list, released by the NIRF of the Ministry of Human Resource Development, Government of India.

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It was established on 24 January 1857, and was one of the first institutions in Asia to be established as a multidisciplinary and Western-style university. Its alumni and faculty include several heads of state, heads of government, social reformers, prominent artists, only academy award winner and Dirac medal winner in India, many Fellows of the Royal Society and five Nobel laureates as of 2019 which is highest in South Asia.

University Of Calcutta

Applied Mathematics and Mechanics (English Edition)

The aim of this article is to study the gravitational response in an infinite, homogeneous, transversely isotropic thick plate. The upper surface of the plate is free from traction, and the surface temperature distribution is imposed on it. The lower surface of the plate is kept on a rigid base and is thermally insulated. The heat conduction equations in the presence of heat source are of hyperbolic types among them (i) without energy dissipation (GN-II model) and (ii) with energy dissipation (GN-III model). The Laplace–Fourier double-transform technique has been developed to solve the nondimensional coupled field equations. The physical quantities are obtained in the space–time domain using a numerical inversion method. Numerical calculations are performed for a thick plate made of magnesium (Mg) metal and have been depicted graphically to estimate the effect of gravity. The results for the isotropic material (Cu) and that of the transversely isotropic material (Mg) have been compared for both the models. © 2017 Taylor & Francis.

Journal of Thermal Stresses

Thermoelastic wave propagation in a transversely isotropic thick plate under Greenâ€“Naghdi theory due to gravitational field

This paper deals with the problem of magneto-thermoelastic interactions in a functionally graded isotropic, unbounded, rotating medium due to a periodically varying heat source in the context of the linear theory of generalized thermoelasticity without energy dissipation and with energy dissipation. The governing equations of generalized thermoelasticity (GN model) for a functionally graded material under the influence of a magnetic field are established. The Laplace–Fourier double transform technique has been used to get the solution. The inversion of Fourier transform is done by using residual calculus, where the poles of the integrand are obtained numerically in the complex domain by using Laguerre’s method, and the inversion of the Laplace transformation is done numerically using a method based on Fourier series expansion technique. The numerical estimates for displacements, temperature and stress are obtained for a hypothetical material. The solution to the analogous problem is obtained by taking a suitable non-homogeneous parameter. Finally, the results obtained are presented graphically to show the effect of rotation, non-homogeneity, damping coefficient and magnetic field on displacements, temperature and stress. © 2015, Springer-Verlag Wien.

Acta Mechanica

Magneto-thermoelastic response in a functionally graded rotating medium due to a periodically varying heat source

This article deals with the problem of finite thermoelastic wave propagation in an unbounded rotating medium due to a periodically varying heat source under the influence of a magnetic field. The governing equations for generalized thermoelasticity with energy dissipation (GNIII) and without energy dissipation (GNII) have been solved by using the Laplace-Fourier double transform technique. The inversion of the Fourier transform has been done by using residual calculus, and the inversion of the Laplace transformation is carried out using Fourier series expansion technique. The physical quantities have been computed numerically and presented graphically to compare the results for different theories (GNII and GNIII) and to show the effects of rotation, magnetic field, and the damping coefficient on the physical quantities. © 2014 Copyright Taylor & Francis Group, LLC.

Study of finite thermal waves in a magnetothermoelastic rotating medium

This article deals with a problem of magneto-thermoelastic interactions in a transversely isotropic hollow cylinder due to thermal shock in the context of three-phase-lag theory of generalized thermoelasticity. The governing equations of generalized thermoelasticity of the above model under the influence of a magnetic field are established. The Laplace transform method has been used to transform the equation into the space domain, where the Galerkin finite element technique has been employed to solve the resulting equations in the transformed domain. The inversion of the Laplace transformation is done by applying a method of Bellman et al. The stresses and temperature distributions have been computed numerically and presented graphically in a numbers of figures. A comparison of the results for different theories (GN-III and 3P models) are presented and the effect of magnetic field is discussed. The results for an isotropic material (Cu) have been deduced numerically and presented graphically to compare with those of transversely isotropic material (Mg). © 2013 Copyright Taylor and Francis Group, LLC.

Analysis of magneto-thermoelastic response in a transversely isotropic hollow cylinder under thermal shock with three-phase-lag effect

This paper dealswith the problem of magneto-thermo-elastic interactions in an unbounded, perfectly conducting elastic medium due to the presence of periodically varying heat sources in the context of linear theory of generalized thermo-elasticity with energy dissipation (TEWED or GN-III model), without energy dissipation (TEWOED or GN-II model) and three-phase-lag model (3P model). The governing equations of generalized thermo-elasticity of the above models under the influence of a magnetic field are established. The Laplace-Fourier double transform technique has been used to get the solution. The inversion of the Fourier transform has been done by using residual calculus, where poles of the integrand are obtained numerically in a complex domain by using Laguerre's method, and the inversion of the Laplace transformation is done numerically using a method based on Fourier series expansion technique. Displacement, temperature, stress and strain distributions have been computed numerically and presented graphically in numbers of figures. A comparison of the results for different theories (GN-II, GN-III and 3P model) and the effect of magnetic field and damping coefficient on the physical quantities has been discussed. © 2011 Springer-Verlag.

Magneto-thermo-elastic response in a perfectly conducting medium with three-phase-lag effect

The distribution of stresses due to step input of temperature on the boundaries of a homogeneous transversely isotropic circular disc is investigated by applying Laplace transform technique in the context of generalized theories of thermo-elasticity. The inverse of the transformed solution is carried out by applying a method of Bellman et al. The stresses are computed numerically and presented graphically in a number of figures. A comparison of the results for different theories (CTE, CCTE, TRDTE(GL), TEWED(GN)) and the effect of anisotropy on the stresses are also presented. When the material is isotropic and outer radius of the disc tends to infinity, the corresponding result agrees with that of existing literature. © 2007 Elsevier Masson SAS. All rights reserved.

European Journal of Mechanics, A/Solids

Thermoelastic interaction with energy dissipation in a transversely isotropic thin circular disc

The distribution of stresses due to step input of temperature at the boundary of a spherical hole in a homogeneous isotropic unbounded body is investigated by applying Laplace transform technique in the context of generalized theories of thermo-elasticity. The inverse of the transformed solution is carried out by applying a method of Bellman et al. The stresses are computed numerically and presented graphically in a number of figures for aluminum-epoxy composite material. The comparison among the theories i.e. classical thermo-elasticity (CTE), classical coupled thermo-elasticity (CCTE), temperature-rate-dependent thermo-elasticity (TRDTE(GL)) and thermo-elasticity with energy dissipation (TEWED(GN)) theory is presented graphically. © 2006 Elsevier Ltd. All rights reserved.

Journal	Applied Mathematics and Mechanics (English Edition)
Publisher	SHANGHAI UNIV
ISSN	0253-4827