This problem deals with the thermo-visco-elastic interaction due to step input of temperature on the stress free boundaries of a homogeneous visco-elastic isotropic spherical shell in the context of generalized theories of thermo-elasticity. Using the Laplace transformation the fundamental equations have been expressed in the form of vector-matrix differential equation which is then solved by eigen value approach. The inverse of the transformed solution is carried out by applying a method of Bellman et al. [R. Bellman, R.E. Kolaba, J.A. Lockette, Numerical Inversion of the Laplace Transform, American Elsevier Publishing Company, New York, 1966]. The stresses are computed numerically and presented graphically in a number of figures for copper material. A comparison of the results for different theories (TEWED (GN-III), three-phase-lag method) is presented. When the body is elastic and the outer radius of the shell tends to infinity, the corresponding results agree with the result of existing literature. © 2008 Elsevier Inc. All rights reserved.

A KAR

M KANORIA

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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 Mathematical Modelling

The present problem deals with the thermo-elastic interaction of a gold nano-beam resonator induced by ramp-type heating under the two temperature theory of generalized thermoelasticity. The governing equations are constructed in the context of two-temperature three-phase-lag model (2T3P) and two-temperature Lord-Shulman (2TLS) model of generalized thermoelasticity. Using the Laplace transform, the fundamental equations have been expressed in the form of a vector-matrix differential equation which is then solved by Eigen value approach and Mathematica software package has been used as a tool. The inversion of Laplace transforms are computed numerically using the method of Fourier series expansion technique. Numerical results for lateral vibration, temperature, displacement, stress, and the strain energy are presented graphically for Lord-Shulman model and also for threephase lag model. A numerical instance of gold nano-beam in femtoseconds scale has been calculated to present the effect of the ramping time parameter on the entire studied field. The effect of two-temperature parameter is also discussed on the physical fields. © 2017 Growing Science Ltd. All rights reserved.

Engineering Solid Mechanics

Modeling and analysis of vibration of a gold nano-beam under two-temperature theory

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.

Three dimensional viscoelastic medium under thermal shock

This paper is concerned with the determination of the thermoelastic stress, strain and conductive temperature in a piezoelastic half-space body in which the boundary is stress free and subjected to thermal loading in the context of the fractional order two-temperature generalized thermoelasticity theory (2TT). The two-temperature three-phase-lag (2T3P) model, two-temperature Green-Naghdi model III (2TGNIII) and two-temperature Lord-Shulman (2TLS) model of thermoelasticity are combined into a unified formulation introducing unified parameters. The basic equations have been written in the form of a vector-matrix differential equation in the Laplace transform domain that is then solved by the state-space approach. The numerical inversion of the transform is carried out by a method based on Fourier series expansion techniques. The numerical estimates of the quantities of physical interest are obtained and depicted graphically. The effect of the fractional order parameter, two-temperature and electric field on the solutions has been studied and comparisons among different thermoelastic models are made. © The Author(s) 2013.

Mathematics and Mechanics of Solids

One-dimensional problem of a fractional order two-temperature generalized thermo-piezoelasticity

This paper is concerned with the determination of thermoelastic stresses, strain and conductive temperature in a spherically symmetric spherical shell. The two-temperature three-phase-lag thermoelastic model (2T3P) and two-temperature Green–Naghdi model III (2TGNIII) are combined into a unified formulation. There is no temperature at the outer boundary, and thermal load is applied at the inner boundary. The basic equations have been 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 numerical inversion of the transform is carried out using Fourier series expansion techniques. Because of the short duration of the second sound effects, small time approximations of the solutions are studied. The physical quantities have been computed numerically and presented graphically in a number of figures. A complete and comprehensive analysis of the results has been presented for the 2T3P and the 2TGNIII models. These results have also been compared with those of the one-temperature three-phase-lag thermoelastic model (1T3P) and one-temperature Green–Naghdi model III (1TGNIII). © 2014, Springer-Verlag Wien.

Acta Mechanica

Thermoelastic response in a symmetric spherical shell

This paper deals with the problem of thermoelastic interactions in a functionally graded isotropic unbounded medium due to the presence of periodically varying heat sources in the context of the three-phase-lag thermoelastic models, GN ii (TEWOED) and GN iii (TEWED). The governing equations of three-phase-lag thermoelastic model (3P), generalized thermoelasticity without energy dissipation (GN ii) and with energy dissipation (GN iii) for a functionally graded material (i.e., a material with spatially varying material properties) are established. The governing equations are expressed in a Laplace-Fourier double transform domain and solved in that domain. Then the inversion of the Fourier transform is carried out 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 transform is done numerically using a method based on Fourier series expansion technique. The numerical estimates of the thermal displacement, temperature and thermal stress are obtained for a hypothetical material. The solution to the analogous problem for homogeneous isotropic material is obtained by taking a suitable non-homogeneity parameter. Finally, the results obtained are presented graphically to show the effect of non-homogeneity on thermal displacement, temperature and thermal stress. A comparison of the results for different theories (three-phase-lag model, GN ii and GN iii) is presented and the effect of non-homogeneity is also shown. In absence of non-homogeneity the results corresponding to the 3P model, GN ii and GN iii model agree with the results of the existing literature. © The Author(s) 2012.

Generalized thermoelastic interaction in a functionally graded isotropic unbounded medium due to varying heat source 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	Data powered by TypesetApplied Mathematical Modelling
Publisher	Data powered by TypesetELSEVIER SCIENCE INC
ISSN	0307-904X