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.

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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

Thermoelastic wave propagation in a transversely isotropic thick plate under Green–Naghdi theory due to gravitational field

Journal of Thermal Stresses

The aim of the present contribution is concerned with the interactions of thermoelastic displacements, temperatures and stresses for the three-phase-lag and Green-Naghdi heat equations in a functionally graded transversely isotropic plate subjected to a spatially varying heat source. The upper surface of the plate is stress free with prescribed surface temperature while the lower surface of the plate rests on a rigid foundation and is thermally insulated. The governing equations for displacement and temperature fields are obtained in the Laplace-Fourier transform domain by applying Laplace and Fourier transform techniques. The inversion of double transform has been done numerically. The numerical inversion of Laplace transform is done by using a method based on the Fourier Series expansion technique. The solution to the analogous problem for isotropic material is obtained by taking suitable nonhomogeneity parameters. A comparative study between isotropic material and transversely isotropic material is also shown. In absence of nonhomogeneity, the results corresponding to Green-Naghdi II, Green-Naghdi III and 3P lag models agree with the results of the existing literature. © The Author(s) 2015.

Mathematics and Mechanics of Solids

Propagation of thermal waves in a functionally graded thick plate

The aim of the present contribution is the determination of the thermoelastic temperatures, stress, displacement, and strain in an infinite isotropic elastic body with a spherical cavity in the context of the mechanism of the two-temperature generalized thermoelasticity theory (2TT). The two-temperature Lord–Shulman (2TLS) model and two-temperature dual-phase-lag (2TDP) model of thermoelasticity are combined into a unified formulation with unified parameters. The medium is assumed to be initially quiescent. The basic equations are written in the form of a vector matrix differential equation in the Laplace transform domain, which is then solved by the state-space approach. The expressions for the conductive temperature and elongation are obtained at small times. The numerical inversion of the transformed solutions is carried out by using the Fourier-series expansion technique. A comparative study is performed for the thermoelastic stresses, conductive temperature, thermodynamic temperature, displacement, and elongation computed by using the Lord–Shulman and dual-phase-lag models. © 2016, Pleiades Publishing, Ltd.

Journal of Applied Mechanics and Technical Physics

Generalized thermoelastic problem of an infinite body with a spherical cavity under dual-phase-lags

This article deals with the thermoelastic interaction in a three-dimensional homogeneous and isotropic viscoelastic medium under the Dual-phase-lag model of generalized thermoelasticity. The resulting non-dimensional coupled equations are applied to a specific problem of a halfspace whose surface is traction-free and is subjected to a time-dependent thermal shock. The analytical expressions for the displacement components, stress, temperature and strain are obtained in the physical domain by employing normal mode analysis. These expressions are also calculated for a copper-like material and have been depicted graphically. Discussions have been made to highlight the effect of viscosity on the studied field. The phenomenon of a finite speed of propagation is observed for each field. Also, if the effect of viscosity is neglected, the results agree with the existing literature. © 2016 Growing Science Ltd. All rights reserved.

Fulltext

Engineering Solid Mechanics

Three dimensional viscoelastic medium under thermal shock

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

In this article, a new mathematical model of magneto-thermoelasticity has been constructed to investigate the transient phenomena in the context of a new consideration of heat conduction with fractional order, where the anisotropic fibre-reinforced medium is rotating with an uniform angular velocity. The governing equations for Green-Naghdi theory have been formulated and solved analytically employing the normal mode analysis. Numerical results for the temperature, displacement and stresses are obtained and have been depicted graphically. According to the numerical results and corresponding graphical representations, conclusions about this new theory have been constructed. Finally, some comparisons have been shown to estimate the effect of magnetic field, reinforcement and the presence of non-local fractional parameter on all the studied fields.

Journal	Data powered by TypesetJournal of Thermal Stresses
Publisher	Data powered by TypesetTaylor and Francis Ltd.
ISSN	0149-5739