Spherically symmetric thermo-visco-elastic waves in a visco-elastic medium with a spherical cavity

Banerjee, Santwana; Roychoudhuri, S. K.

doi:10.1016/0898-1221(95)00070-f

Cited by 19 publications

(16 citation statements)

References 5 publications

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“…Several experimental studies [5][6][7] indicate that the thermal relaxation time effects can be of relevance in the cases involving a rapidly propagating crack tip, a localized moving heat source with high intensity, shock wave propagation, laser processing technique etc. Subsequently, several investigations [8][9][10][11][12][13][14][15] based on these generalized theories were carried out.…”

Section: Introductionmentioning

confidence: 99%

A study of generalized thermoelastic interactions in an unbounded medium with a spherical cavity

Mukhopadhyay

Kumar

2008

Computers & Mathematics with Applications

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a b s t r a c tThe aim of the present paper is to study the thermoelastic interactions in an unbounded elastic medium with a spherical cavity in the context of four different theories of thermoelasticity, namely: the classical coupled dynamical thermoelasticity, the extended thermoelasticity, the temperature-rate-dependent thermoelasticity and the thermoelasticity without energy dissipation in a unified way. The cavity surface is assumed to be stress free and is subjected to a smooth and time-dependent-heating effect. The solutions for displacement, temperature and stresses are obtained with the help of the Laplace transform procedure. Firstly the short-time approximated solutions for four different theories have been obtained analytically. Then following the numerical method proposed by Bellman et al. [R. Bellmen, R.E. Kolaba, J.A. Lockette, Numerical Inversion of the Laplace Transform, American Elsevier Pub. Co., New York, 1966] for the inversion of Laplace transforms, the numerical values of the physical quantities are also computed for the copper material and results are displayed in graphical forms to compare the results obtained for the theory of thermoelasticity without energy dissipation with the results of other thermoelasticity theories.

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Section: Introductionmentioning

confidence: 99%

A study of generalized thermoelastic interactions in an unbounded medium with a spherical cavity

Mukhopadhyay

Kumar

2008

Computers & Mathematics with Applications

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“…Several experimental studies [6][7][8] indicate that the thermal relaxation time effects can be of relevance in the cases involving a rapidly propagating crack tip, a localized moving heat source with high intensity, shock wave propagation, laser processing technique etc. Subsequently, several investigations [9][10][11][12] based on these generalized theories were carried out.…”

Section: Introductionmentioning

confidence: 99%

A Problem on Thermoelastic Interactions in an Infinite Medium with a Cylindrical Hole in Generalized Thermoelasticity III

Mukhopadhyay

Kumar

2008

Journal of Thermal Stresses

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The aim of the present article is to study the thermoelastic interactions in an infinite elastic medium with a cylindrical hole in the context of generalized thermoelasticity III, recently developed by Green and Nagdhi [1]. The boundary of the hole is assumed to be stress free and is subjected to a ramp type heating. In order to make a comparison between this thermoelastic model with other thermoelastic models, the problem is formulated on the basis of three different theories of thermoelasticity, namely: the extended thermoelasticity proposed by Lord and Shulman [2], the thermoelasticity without energy dissipation (Green and Nagdhi [3]) and thermoelasticity with energy dissipation (thermoelasticity type III [1]) in a unified way. The solutions for displacement, temperature and stresses are obtained with the help of Laplace transform procedure. Firstly the short time approximated solutions for three different theories have been obtained analytically. Then following a numerical method for the inversion of Laplace transforms, the numerical values of the physical quantities are also computed for the copper material and results are displayed in graphical forms to compare the results obtained from different models of generalized thermoelasticity.

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“…Kar and Kanoria (2007) investigated the distribution of stresses due to a step input of the temperature at the boundary of a spherical hole in a homogeneous isotropic unbounded body in the context of generalized theories of thermoelasticity. Furthermore, Banerjee and Roychoudhuri (1995) studied the spherically symmetric thermo-viscoelastic wave propagation in an infinite isotropic viscoelastic solid (Kelvin-Voight type) with a spherical cavity. Ezzat et al (2001Ezzat et al ( , 2002a applied the state space approach to a one-dimensional problem of the generalized thermo-viscoelasticity.…”

mentioning

confidence: 99%

Relaxation Effects of a Saturated Porous Media Using the Two-Dimensional Generalized Thermoelastic Theory

Liu

Ding

et al. 2010

Transp Porous Med

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A model of the equations of a generalized thermoelasticity (GT) with relaxation times for a saturated porous medium is given in this article. The formulation can be applied to the GT theories: Lord-Shulman theory, Green-Lindsay theory, and Coupled theory for the porous medium. A two-dimensional thermoelastic problem that is subjected to a time-dependent thermal/mechanical source is investigated with the model of the generalized porous thermoelasticity. By using the Laplace transform and the Fourier transform technique, solutions for the displacement, temperature, pore pressure, and stresses are obtained with a semi-analytical approach in the transform domain. Numerical results are also performed for portraying the nature of variations of the field variables. In addition, comparisons are presented with the corresponding four theories.

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Spherically symmetric thermo-visco-elastic waves in a visco-elastic medium with a spherical cavity

Cited by 19 publications

References 5 publications

A study of generalized thermoelastic interactions in an unbounded medium with a spherical cavity

A study of generalized thermoelastic interactions in an unbounded medium with a spherical cavity

A Problem on Thermoelastic Interactions in an Infinite Medium with a Cylindrical Hole in Generalized Thermoelasticity III

Relaxation Effects of a Saturated Porous Media Using the Two-Dimensional Generalized Thermoelastic Theory

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