Thermal stresses in an infinite circular cylinder

Abd-Alla, A. M.; Yahya, G. A.; Farhan, A. M.

doi:10.1007/s12206-012-0424-5

Cited by 6 publications

(6 citation statements)

References 15 publications

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“…Abd-Alla et al [1] investigated propagation of Rayleigh waves in generalized magnetothermoelastic orthotropic material under initial stress and gravity field. Thermal stresses in an infinite circular cylinder have been investigated by Abd-Alla et al [2]. Abd-Alla and Mahmoud [3] studied the magnetothermoelastic problem in rotational nonhomogeneous orthotropic hollow cylinder under the hyperbolic heat conduction model.…”

Section: Introductionmentioning

confidence: 99%

Effects of Rotation and Gravity Field on Surface Waves in Fibre-Reinforced Thermoelastic Media under Four Theories

Abd-Alla

Abo‐Dahab

Al-Mullise

2013

Journal of Applied Mathematics

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Estimation is done to investigate the gravitational and rotational parameters effects on surface waves in fibre-reinforced thermoelastic media. The theory of generalized surface waves has been firstly developed and then it has been employed to investigate particular cases of waves, namely, Stoneley waves, Rayleigh waves, and Love waves. The analytical expressions for surface waves velocity and attenuation coefficient are obtained in the physical domain by using the harmonic vibrations and four thermoelastic theories. The wave velocity equations have been obtained in different cases. The numerical results are given for equation of coupled thermoelastic theory (C-T), Lord-Shulman theory (L-S), Green-Lindsay theory (G-L), and the linearized (G-N) theory of type II. Comparison was made with the results obtained in the presence and absence of gravity, rotation, and parameters for fibre-reinforced of the material media. The results obtained are displayed by graphs to clear the phenomena physical meaning. The results indicate that the effect of gravity, rotation, relaxation times, and parameters of fibre-reinforced of the material medium is very pronounced.

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Section: Introductionmentioning

confidence: 99%

Effects of Rotation and Gravity Field on Surface Waves in Fibre-Reinforced Thermoelastic Media under Four Theories

Abd-Alla

Abo‐Dahab

Al-Mullise

2013

Journal of Applied Mathematics

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“…M. Abd-Alla [1] has considered an infinite circular cylinder and determined the thermal stresses by using the Fourier transform method. The thermal stresses in a transversely isotropic medium with a penny-shaped crack has been studied by Y. M. Tasi [19] .…”

Section: Introductionmentioning

confidence: 99%

Hollow Cylinder with Thermoelastic Modelling by Reduced Differential Transform

Pimpare¹,

Sutar²

2022

JIMS

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The term thermal stresses are related to mechanics of materials. The thermal stress is formed due to any changes in temperature of a material. The large change in temperature concludes to higher the thermal stresses. Also, there is an effect of thermal expansion coefficient on thermal stresses. The thermal expansion coefficient is different for different materials. In the present paper, the design of a mathematical model concerning the thermal stresses in hollow cylinder subject to the heat conduction with initial and boundary conditions have developed. The basic aim of this work is related to calculations of thermal stresses and thermoelastic displacement in the hollow cylinder by using the reduced differential transform method. The analytical solution is satisfied with the aim of special cases for the copper material properties. The numerical results are illustrated graphically by using mathematical software SCILAB.

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“…Hetnarski and Ignaczak [3] presented a survey article of representative theories in the range of generalized thermoelasticity. The counterparts of our problem in the contexts of the thermoelasticity theories have been considered by using analytical and numerical methods [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Free vibration of a thermoelastic hollow cylinder with one relaxation time

Abbas

Hobiny

2015

Can. J. Phys.

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The aim of this paper is to study the free vibration problem of a thermoelastic hollow cylinder in the context of the Lord and Shulman theory with one relaxation time. The eigenvalue approach is used to get the analytical solutions. The dispersion relations for the existence of various types of possible modes of vibrations are obtained. The validation of the roots for the dispersion relation is presented. The numerical results of frequency shift, natural frequency, and thermoelastic damping of vibrations have been presented graphically. PACS No.: 62.20.Dc. Résumé : Nous étudions ici les vibrations libres d'un cylindre creux fait d'un matériau thermoélastique, en utilisant la théorie de Lord et Shulman avec un seul temps de relaxation. Nous utilisons une approche aux valeurs propres afin de trouver des solutions analytiques et obtenons les relations de dispersion pour les différents modes possibles de vibration. Nous validons les racines de ces relations de dispersion. Nous présentons graphiquement le déplacement en fréquence, la fréquence naturelle et l'amortissement thermoélastique des vibrations. [Traduit par la Rédaction]

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Thermal stresses in an infinite circular cylinder

Cited by 6 publications

References 15 publications

Effects of Rotation and Gravity Field on Surface Waves in Fibre-Reinforced Thermoelastic Media under Four Theories

Effects of Rotation and Gravity Field on Surface Waves in Fibre-Reinforced Thermoelastic Media under Four Theories

Hollow Cylinder with Thermoelastic Modelling by Reduced Differential Transform

Free vibration of a thermoelastic hollow cylinder with one relaxation time

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