Effect of fractional parameter on plane waves of generalized magneto-thermoelastic diffusion with reference temperature-dependent elastic medium
01 Apr 2013-Computers & Mathematics With Applications (Pergamon Press, Inc.)-Vol. 65, Iss: 7, pp 1103-1118
TL;DR: The present paper is concerned with the investigation of disturbances in a homogeneous, isotropic reference temperature-dependent elastic medium with fractional order generalized thermoelastic diffusion and analytical expressions for displacement components, stresses, temperature field, concentration and chemical potential are obtained.
Abstract: The present paper is concerned with the investigation of disturbances in a homogeneous, isotropic reference temperature-dependent elastic medium with fractional order generalized thermoelastic diffusion. The formulation is applied to the generalized thermoelasticity based on the fractional time derivatives under the effect of diffusion. The analytical expressions for displacement components, stresses, temperature field, concentration and chemical potential are obtained in the physical domain by using the normal mode analysis technique. These expressions are calculated numerically for a copper-like material and depicted graphically. Effect of fractional parameter and presence of diffusion is analyzed theoretically and numerically. Comparisons are made with the results predicted by the fractional and without fractional order in the presence and absence of diffusion.
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02 Oct 2019
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TL;DR: This work is devoted to the investigation of a two-dimensional porous material under weak, strong and normal conductivity, using the eigenvalues method, and the derived technique is assessed with numerical results that are obtained from the porous mediums using simplified symmetric geometry.
Abstract: This work is devoted to the investigation of a two-dimensional porous material under weak, strong and normal conductivity, using the eigenvalues method. By using Laplace–Fourier transformations with the eigenvalues technique, the variables are analytically obtained. The derived technique is assessed with numerical results that are obtained from the porous mediums using simplified symmetric geometry. The results, including the displacements, temperature, stresses and the change in the volume fraction field, are offered graphically. Comparisons are made among the outcomes obtained under weak, normal and strong conductivity.
61 citations
TL;DR: In this article, the fractional order Green-Lindsay model of generalized thermoelasticity with voids (FGLV) subjected to instantaneous heat sources in a plane area has been established using the Riemann-Liouville fractional integral operator and applied to solve a problem of determining the distribution of temperature, the volume fraction field, the deformation and the stress field in an infinite elastic medium.
57 citations
TL;DR: In this paper, a fractional order Lord & Shulman model of generalized thermoelasticity with voids subjected to a continuous heat sources in a plane area has been established using the Caputo fractional derivative and applied to solve a problem of determining the distributions of the temperature field, the change in volume fraction field, and the deformation and the stress field in an infinite elastic medium.
Abstract: In the present work, a fractional order Lord & Shulman model of generalized thermoelasticity with voids subjected to a continuous heat sources in a plane area has been established using the Caputo fractional derivative and applied to solve a problem of determining the distributions of the temperature field, the change in volume fraction field, the deformation and the stress field in an infinite elastic medium. The Laplace transform together with an eigenvalue approach technique is applied to find a closed form solution in the Laplace transform domain. The numerical inversions of the physical variables in the space-time domain are carried out by using the Zakian algorithm for the inversion of Laplace transform. Numerical results are shown graphically and the results obtained are analyzed .
40 citations
TL;DR: In this article, the constitutive relations and the governing equations for nonlocal thermoelastic solid in the presence of diffusion are derived for the free vibration of a thermo-elastic diffusive cloud.
Abstract: In this article, the constitutive relations and the governing equations are derived for nonlocal thermoelastic solid in the presence of diffusion. The free vibration of a thermoelastic diffusive cy...
39 citations
Cites background from "Effect of fractional parameter on p..."
...[29] investigated the analysis of plane wave in generalized magneto-thermoelasticity with temperature-dependent medium in the presence of diffusion....
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TL;DR: In this paper, a linear dissipative mechanism whose Q is almost frequency independent over large frequency ranges has been investigated by introducing fractional derivatives in the stressstrain relation, and a rigorous proof of the formulae to be used in obtaining the analytic expression of Q is given.
Abstract: Summary Laboratory experiments and field observations indicate that the Q of many non-ferromagnetic inorganic solids is almost frequency independent in the range 10-2-107 cis, although no single substance has been investigated over the entire frequency spectrum. One of the purposes of this investigation is to find the analytic expression for a linear dissipative mechanism whose Q is almost frequency independent over large frequency ranges. This will be obtained by introducing fractional derivatives in the stressstrain relation. Since the aim of this research is also to contribute to elucidating the dissipating mechanism in the Earth free modes, we shall treat the dissipation in the free, purely torsional, modes of a shell. The dissipation in a plane wave will also be treated. The theory is checked with the new values determined for the Q of spheroidal free modes of the Earth in the range between 10 and 5 min integrated with the Q of Rayleigh waves in the range between 5 and 0.6 min. Another check of the theory is made with the experimental values of the Q of the longitudinal waves in an aluminium rod in the range between lo-’ and 10-3s. In both checks the theory represents the observed phenomena very satisfactorily. The time derivative which enters the stress-strain relation in both cases is of order 0.15. The present paper is a generalized version of another (Caputo 1966b) in which an elementary definition of some differential operators was used. In this paper we give also a rigorous proof of the formulae to be used in obtaining the analytic expression of Q; moreover, we present two checks of the theory with experimental data. The present paper is a generalized version of another (Caputo 1966b) in which an elementary definition of some differential operators was used. In this paper we give also a rigorous proof of the formulae to be used in obtaining the analytic expression of Q; moreover, we present two checks of the theory with experimental data. In a homogeneous isotropic elastic field the elastic properties of the substance are specified by a description of the strains and stresses in a limited portion of the field since the strains and stresses are linearly related by two parameters which describe the elastic properties of the field. If the elastic field is not homogeneous nor isotropic the properties of the field are specified in a similar manner by a larger number of parameters which also depend on the position.
3,372 citations
TL;DR: The model of dissipation based on memory introduced by Caputo is generalized and checked with experimental dissipation curves of various materials.
Abstract: The model of dissipation based on memory introduced by Caputo is generalized and checked with experimental dissipation curves of various materials
725 citations
TL;DR: A quasi-static uncoupled theory of thermoelasticity based on the heat conduction equation with a time-fractional derivative of order α is proposed in this article.
Abstract: A quasi-static uncoupled theory of thermoelasticity based on the heat conduction equation with a time-fractional derivative of order α is proposed. Because the heat conduction equation in the case 1≤α≤2 interpolates the parabolic equation (α = 1) and the wave equation (α = 2), the proposed theory interpolates a classical thermoelasticity and a thermoelasticity without energy dissipation introduced by Green and Naghdi. The Caputo fractional derivative is used. The stresses corresponding to the fundamental solutions of a Cauchy problem for the fractional heat conduction equation are found in one-dimensional and two-dimensional cases.
482 citations