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Fractional Order Generalized Thermoelastic Infinite Medium with Cylindrical Cavity Subjected to Harmonically Varying Heat
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Abstract
In this work, a mathematical model of an elastic material with cylindrical cavity will be constructed. The governing equations will be taken into the context of the fractional order generalized thermoelasticity theory (Youssef 2010). Laplace transform and direct approach will be used to obtain the solution when the boundary of the cavity is exposed to harmonically heat with constant angular frequency of thermal vibration. The inverse of Laplace transforms will be computed numerically using a method based on Fourier expansion techniques. Some comparisons have been shown in figures to present the effect of the fractional order parameter and the angular frequency of thermal vibration on all the studied felids.
KeywordsThermoelasticityGeneralized ThermoelasticityFractional OrderCylindrical CavityHarmonically Heat
- R. Kimmich, “Strange Kinetics, Porous Media, and NMR,” Chemical Physics, Vol. 284, 2002, pp. 243-285. doi:10.1016/S0301-0104(02)00552-9
- I. Podlubny, “Fractional Differential Equations,” Academic Press, New York, 1999.
- F. Mainardi and R. Gorenflo, “On Mittag-Lettler-Type Function in Fractional Evolution Processes,” Journal of Computational and Applied Ma-thematics, Vol. 118, No. 1-2, 2000, pp. 283-299. doi:10.1016/S0377-0427 (00)00294-6
- Y. Z. Povs-tenko, “Fractional Heat Conductive and Associated Thermal Stress,” Journal of Thermal Stress, Vol. 28, 2005, pp. 83-102. doi:10.1080/014957390523741
- Y. Fujita, “Integrodifferential Equation Which Interpolates the Heat Equation and Wave Equation (I),” Osaka Journal of Mathematics, Vol. 27, 1990, pp. 309-321.
- Y. Fujita, “Integrodifferential Equation Which Interpolates the Heat Equation and Wave Equation (II),” Osaka Journal of Mathematics, Vol. 27, 1990, pp. 797-804.
- Y. N. Rabotnov, “Creep of Structure Elements,” Naka, Moscow, 1966.
- Y. A. Rossikhin and M. V. Shitikova, “Applications of Fractional Calculus to Dynamic Problems of Linear and Non Linear Hereditary Mechanics of Solids,” Applied Mechanics Reviews, Vol. 50, No.1, 1997, pp. 15-67. doi:10.1115/1.3101682
- H. W. Lord and Y.Shulman, “A Generalized Dynamical Theory of Thermoelasticity,” Journal of the Mechanics and Physics of Solids, Vol. 15, No.5, 1967, pp. 299-309. doi:10.1016/0022-5096(67)90024-5
- S. Kaliski, “Wave Equations of Thermoelasticity,” Bulletin of the Polish Academy of Sciences Technology, Vol. 13, 1965, pp. 253-260.
- H. M. Youssef, “Fractional Order Ge-neralized Thermoelasticity,” Journal of Heat Transfer, Vol. 132 No. 6, 2010. doi:10.1115/1.4000705
- H. M. Youssef, “Generalized Thermoelastic Infinite Medium with Cylindrical Cavity Subjected to Moving Heat Source,” Mechanics Research Communications, Vol. 36, No. 4, 2009, pp. 487-496. doi:10.1016/j.mechrescom. 2008.12.004
- G. Hanig and U. Hirdes, “A Method for the Numerical Inversion of Laplace Transform,” Journal of Computational and Applied Mathematics, Vol. 10, No. 1, 1984, pp. 113-132. doi:10.1016/0377-0427(84)90075-X