Generalized Theory of Thermoviscoelasticity and a Half-Space Problem

Sherief, Hany H.; Allam, M. N. M.; Elhagary, M. A.

doi:10.1007/s10765-011-1017-8

Cited by 61 publications

(12 citation statements)

References 18 publications

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“…Sherief and Ezzat [5] found the solution of a half-space in the form of a series of functions. This theory was extended to deal with micropolar media [6], viscoelastic media [7], and poroelastic media [8]. It was also used to solve a problem with stochastic boundary conditions [9].…”

Section: Introductionmentioning

confidence: 99%

A two-dimensional generalized thermoelastic diffusion problem for a half-space

El-Sayed

2016

Mathematics and Mechanics of Solids

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In this work, we consider the two-dimensional problem of a thermoelastic half-space with a permeating substance in contact with the bounding plane in the context of the theory of generalized thermoelastic diffusion with one relaxation time. The bounding surface of the half-space is taken to be traction free and subjected to a time-dependent thermal shock. Laplace and Fourier transform techniques are used. The solution in the transformed domain is obtained by a direct approach. Numerical inversion techniques are used to obtain the inverse double transforms. Numerical results are represented graphically and discussed.

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Section: Introductionmentioning

confidence: 99%

A two-dimensional generalized thermoelastic diffusion problem for a half-space

El-Sayed

2016

Mathematics and Mechanics of Solids

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“…This theory was improved to deal with various materials. [22][23][24] Heat sources are very important in industry. They are used in many fabrication processes.…”

Section: Introductionmentioning

confidence: 99%

Effect of a 2D axisymmetric cylindrical heat source on a thermoelastic thick plate

Sherief

Zaky

El‐Maghraby

2021

Math Methods in App Sciences

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In this study, we consider a 2D problem of a plate with finite thickness and infinite extent. The upper surface of the plate is traction free and subjected to an axisymmetric heating. The lower surface is thermally insulated and laid on a rigid foundation. A constant heat source in the form of a cylinder lies inside the plate. This problem is in the context of the generalized thermoelasticity theory with one relaxation time. Laplace and Hankel transforms are used to solve the problem. The transforms are numerically inverted. All related functions are shown graphically.

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“…The equations of this theory predict finite speeds of propagation for waves (see [2][3][4][5][6][7]). This theory was expanded to different materials in [8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Study of wave propagation in a half-space in the fractional-order theory of thermoelasticity using the new Caputo definition

Sherief

2018

Mathematics and Mechanics of Solids

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Using fractional derivatives in the sense of new Caputo, we study a problem in the fractional-order theory of thermoelasticity. The problem concerns an elastic half-space. Asymptotic expansions are used. The approximate solution obtained is valid for small times, but the conducted study of wave propagation is exact for all times. We found that there are two waves emanating in the system. One wave, which is mainly mechanical, is traveling with a finite speed. The other wave, which is mainly thermal, was found to have infinite speed. The Laplace transform technique is used. Graphical results are presented and discussed for the relevant functions.

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Generalized Theory of Thermoviscoelasticity and a Half-Space Problem

Cited by 61 publications

References 18 publications

A two-dimensional generalized thermoelastic diffusion problem for a half-space

A two-dimensional generalized thermoelastic diffusion problem for a half-space

Effect of a 2D axisymmetric cylindrical heat source on a thermoelastic thick plate

Study of wave propagation in a half-space in the fractional-order theory of thermoelasticity using the new Caputo definition

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