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Fractional order generalized thermoelastic half-space subjected to ramp-type heating. (English) Zbl 1272.74143

From the summary: In this work, we will construct a mathematical model of an elastic material with constant parameters fills the half-space and the governing equations will be taken into the context of the fractional order generalized thermoelasticity theory. The medium is assumed initially quiescent and Laplace transforms and state-space techniques will be used to obtain the general solution for any set of boundary conditions. The general solution obtained is applied to a specific problem of a medium subjected to ramp-type heating and traction free. The inverse of the Laplace transforms are computed numerically using a method based on Fourier expansion techniques. Some comparisons have been shown in figures to estimate the effects of the fractional order parameter on all the studied felids.

MSC:

74F05 Thermal effects in solid mechanics
80A20 Heat and mass transfer, heat flow (MSC2010)
26A33 Fractional derivatives and integrals
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[1] Abd-Alla, A. N.; Maugin, G. A.: Nonlinear equations for thermoelastic magnetizable conductors, Int. J. Eng. sci. 28, 589 (1990) · Zbl 0715.73025 · doi:10.1016/0020-7225(90)90088-Z
[2] Anisimov, S. I.; Kapeliovich, B. L.; Perelman, T. L.: Electron emission from metal surfaces exposed to ultra-short llaser pulses, Sov. phys. JETP 39, 375 (1974)
[3] Bahar, L. Y.; Hetnarski, R. B.: State space approach to thermoelasticity, J. therm. Stresses 1, 135 (1978)
[4] Bargmann, H.: Recent developments in the field of thermally induced waves and vibrations, Nrecl. eng. Des. 27, 372 (1974)
[5] Boley, B. A.: D.p.h.hasselmanr.a.hellerthermal stresses, Thermal stresses, 1-11 (1980)
[6] Chandrasekaraiah, D. S.; Murthy, H. N.: Thermoelasticity of infinite elastic material with spherical cavity, J. therm. Stresses 16, 55 (1993)
[7] Chandrasekhariah, D. S.: Thermoelasticity with second sound: a review, Appl. mech. Rev. 39, 355 (1986) · Zbl 0588.73006 · doi:10.1115/1.3143705
[8] Erbay, S.; Suhubi, E. S.: Longitudinal wave propagation in a generalized thermo-elastic cylinder, J. therm. Stresses 9, 279 (1986)
[9] Eringen, A. C.; Maugin, G. A.: Electrodynamics of continua, vol. 2, (1989)
[10] Furukawa, T.; Noda, N.; Ashida, F.: Generalized thermoelasticity for an infinite bode with cylindrical hole, JSME int. J. 31, 26 (1990)
[11] Green, A. E.; Lindsay, K. A.: Thermoelasticity, J. elasticity 2, 1 (1972) · Zbl 0775.73063 · doi:10.1007/BF00045689
[12] Hanig, G.; Hirdes, U.: A method for the numerical inversion of Laplace transform, J. comp. Appl. math. 10, 113 (1984) · Zbl 0535.65090 · doi:10.1016/0377-0427(84)90075-X
[13] Lord, H.; Shulman, Y.: A generalized dynamical theory of thermo-elasticity, J. mech. Phys. solids 15, 299 (1967) · Zbl 0156.22702 · doi:10.1016/0022-5096(67)90024-5
[14] Maugin, G. A.: Continuum mechanics of electromagnetic solids, (1988) · Zbl 0652.73002
[15] Misra, J. C.; Kar, S. B.; Samanta, S. C.: The effects of mechanical and thermal relaxations in a heated viscoelastic medium containing a cylindrical hole were studied, Trans. CSME 11, 151 (1987)
[16] Naotak, N.; Hetnarski, R.; Tanigawa, Y.: Thermal stresses, (2003)
[17] Povstenko, Y. Z.: Fractional heat conduction equation and associated thermal stress, J. therm. Stresses 28, 83 (2005)
[18] Qiu, T. Q.; Tien, C. L.: Heat transfer mechanism during short-pulse laser heating of metals, ASME J. Heat transfer 115, 835 (1993)
[19] Tzou, D. Y.: Macro-to-microscale heat transfer: the lagging behavior, (1997)
[20] Warren, W. E.; Chen, P. J.: Wave propagation in the two-temperature theory of thermoelasticity, Acta mech. 16, 21 (1973) · Zbl 0251.73011 · doi:10.1007/BF01177123
[21] Youssef, H. M.: Two-dimensional generalized thermoelasticity problem for a half-space subjected to ramp-type heating, Eur. J. Mech. A: solids 25, 745 (2006) · Zbl 1099.74018 · doi:10.1016/j.euromechsol.2005.11.005
[22] Youssef, H. M.: Theory fractional order generalized thermoelasticity, J. heat transfer (ASME) 132, No. 6 (2010) · Zbl 1425.74148
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