Generalized magneto-thermoelasticity in a conducting medium with variable material properties. (English) Zbl 1087.74029
Summary: We constructed the equations of magneto generalized-thermoelasticity with one relaxation time and electrical conductivity; the thermal conductivity and the modulus of elasticity are taken to be variable. A general one-dimensional problem of a conducting medium has been solved taking into account a constant magnetic field that acts normal to the bounding plane. Laplace and Fourier transforms are used. The resulting formulation is applied to a thermal shock half-space problem that has a constant displacement on the boundary. The inverse Fourier transforms are obtained analytically while the inverse Laplace transforms are obtained numerically. The temperature, displacement and stress distributions are represented graphically.
MSC:
74F15 | Electromagnetic effects in solid mechanics |
74F05 | Thermal effects in solid mechanics |
80A20 | Heat and mass transfer, heat flow (MSC2010) |
References:
[1] | Knopoff, L., The interaction between elastic wave motion and a magnetic field in electrical conductors, J. Geophys. Res., 60, 441-456 (1955) |
[2] | Chadwick, P., Ninth Int. Congr. Appl. Mech., 7, 143 (1957) |
[3] | Kaliski, S.; Petykiewicz, J., Equation of motion coupled with the field of temperature in a magnetic field involving mechanical and electrical relaxation for anistropic bodies, Proc. Vibr. Probl., 4, 1 (1959) |
[4] | Biot, M., Thermoelasticity and irreversible thermo-dynamics, J. Appl. Phys., 27, 240-253 (1956) · Zbl 0071.41204 |
[5] | Lord, H.; Shulman, Y., A generalized dynamical theory of thermoelasticity, J. Mech. Phys. Solid, 15, 299-309 (1967) · Zbl 0156.22702 |
[6] | Nayfeh, A.; Nemat-Nasser, S., Electromagneto-thermoelastic plane waves in solids with thermal relaxation, J. Appl. Mech. Ser. E, 39, 108-113 (1972) · Zbl 0232.73112 |
[7] | Choudhuri, S., Electro-magneto-thermo-elastic waves in rotating media with thermal relaxation, Int. J. Eng. Sci., 22, 519-530 (1984) · Zbl 0543.73132 |
[8] | Sherief, H., Problem in electromagneto thermoelasticity for an infinitely long solid conducting circular cylinder with thermal relaxation, Int. J. Eng. Sci., 32, 1137-1149 (1994) · Zbl 0899.73447 |
[9] | Sherief, H.; Ezzat, M., A thermal-shock problem in magneto-thermoelasticity with thermal relaxation, Int. J. Solids Struct., 33, 4449-4459 (1996) · Zbl 0919.73292 |
[10] | Sherief, H.; Ezzat, M., A problem in generalized magneto-thermoelasticity for an infinitely long annular cylinder, J. Eng. Math., 34, 387-402 (1998) · Zbl 0933.74023 |
[11] | Ezzat, M., Generation of generalized magneto-thermoelastic waves by thermal shock in a perfectly conducting half-space, J. Thermal Stresses, 20, 617-633 (1997) |
[12] | Ezzat, M.; Othman, M.; El-Karamany, A., Electromagneto-thermoelastic plane waves with thermal relaxation in a medium of perfect conductivity, J. Thermal Stresses, 24, 411-432 (2001) |
[13] | Ezzat, M.; Othman, M., State space approach to generalized magneto-thermoelasticity with thermal relaxation in a medium of perfect conductivity, J. Thermal Stresses, 25, 409-429 (2002) |
[14] | Sherief, H.; Youssef, H., Short time solution for a problem in magneto-thermoelasticity with thermal relaxation, J. Thermal Stresses, 27, 1-23 (2004) |
[15] | Ezzat, M.a.; Othman, M. I.; El-Karamany, The dependence of the modulus of elasticity on the reference temperature in generalized thermoelasticity, J. Thermal Stresses, 24, 1159-1176 (2001) |
[16] | Kittel, C., Introduction to Solid State Physics (1976), John Wiley and Sons: John Wiley and Sons New York |
[17] | Churchill, R. V., Operational Mathematics (1972), McGraw-Hill Book Company: McGraw-Hill Book Company New York · Zbl 0071.32505 |
[18] | Honig, G.; Hirdes, U., A method for the numerical inversion of the laplace transform, J. Comput. Appl. Math., 10, 113-132 (1984) · Zbl 0535.65090 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.