Fractional order generalized thermoelastic half-space subjected to ramp-type heating

Youssef, Hamdy M.; Al-Lehaibi, Eman A. N.

doi:10.1016/j.mechrescom.2010.06.003

Cited by 64 publications

(15 citation statements)

References 14 publications

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“…The uniqueness of the solution has also been proved in the same work. Youssef & Al-Lehaibi [7] have studied a problem on an elastic half space using this theory. Sherief et al [8] and Ezzat & Fayik [9] have also constructed some model in generalized thermoelasticity by using fractional time-derivatives.…”

Section: Introductionmentioning

confidence: 99%

The Effect of Hydrostatic Initial Stress on the Plane Waves in a Fiber-Reinforced Magneto-Thermoelastic Medium with Fractional Derivative Heat Transfer

2016

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An effect of three factors -the order of fractional derivative, the hydrostatic initial stress, and parameter of magnetic field -on the plane waves in the half-space made of fiber-reinforced material, that is described by the theory of generalized magnetothermoelasticity, is studied. The problem is solved numerically using the normal mode analysis. The results correspond to the Lord-Shulman model and the model, that uses the fractional derivatives and are presented in the form of graphs. The findings show pronounced effect of mentioned three factors. The results are compared with the case, when the initial stress and magnetic field are absent.

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Section: Introductionmentioning

confidence: 99%

The Effect of Hydrostatic Initial Stress on the Plane Waves in a Fiber-Reinforced Magneto-Thermoelastic Medium with Fractional Derivative Heat Transfer

2016

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“…Abbas [26] used eigenvalue approach in three-dimensional generalized thermoelastic interactions with temperature-dependent material properties. Youssef and Al-Lehaibi [27] studied the fractional order generalized thermoelastic half-space subjected to ramp-type heating.…”

Section: Introductionmentioning

confidence: 99%

Eigenvalue approach on fractional order theory of thermoelastic diffusion problem for an infinite elastic medium with a spherical cavity

Abbas

2015

Applied Mathematical Modelling

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Please cite this article as: I.A. Abbas, Eigenvalue approach on fractional order theory of thermoelastic diffusion problem for an infinite elastic medium with a spherical cavity, Appl. Math. Modelling (2015), doi: http://dx. Abstract:In this work, we study a problem in a fractional order theory of thermoelastic diffusion in an infinite medium with a spherical cavity at an elevated temperature field arising out of a ramptype heating and loading bounding surface of the cavity. The chemical potential is assumed a known function of time on the bounding cavity. The form of vector-matrix differential equation in the Laplace transform domain, the basic equations have been written, which is then solved by an eigenvalue technique. The analytical solution in the Laplace domain is obtained for the displacement, the temperature, the concentration, the stress components and chemical potential.Numerical results represented graphically.

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“…Recently, Youssef [11] considered a new formula of heat conduction in the context of the fractional integral operator definition. In [11,12], the 1D problem is presented in the context of the fractional order of generalized thermoelasticity and the effects of the fractional order parameter are discussed on all of the studied fields. Povstenko [13] used the theory of thermal stresses based on the heat conduction equation with Caputo's time-fractional derivative to investigate thermal stresses in an infinite body with a circular cylindrical hole.…”

Section: Introductionmentioning

confidence: 99%

Fractional Order Thermoelasticity Theory for a Half-Space Subjected to an Axisymmetric Heat Distribution

Mashat

Zenkour

Abouelregal

2015

Mechanics of Advanced Materials and Structures

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The present work is concerned with a traction-free thermoelastic half-space subjected to a known axisymmetric temperature distribution. The thermoelastic interactions inside the medium are investigated by employing the fractional order theory of thermoelasticity. The problem is solved by using Laplace's and Hankel's transforms. The inverse transforms are computed numerically. The variations of temperature, displacements, and stresses inside the half-space are investigated. The field variables for a particular material are graphically presented. Comparisons are made within the theory in the presence and absence of fractional order parameter.

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Fractional order generalized thermoelastic half-space subjected to ramp-type heating

Cited by 64 publications

References 14 publications

The Effect of Hydrostatic Initial Stress on the Plane Waves in a Fiber-Reinforced Magneto-Thermoelastic Medium with Fractional Derivative Heat Transfer

The Effect of Hydrostatic Initial Stress on the Plane Waves in a Fiber-Reinforced Magneto-Thermoelastic Medium with Fractional Derivative Heat Transfer

Eigenvalue approach on fractional order theory of thermoelastic diffusion problem for an infinite elastic medium with a spherical cavity

Fractional Order Thermoelasticity Theory for a Half-Space Subjected to an Axisymmetric Heat Distribution

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