The problem of two-dimensional magnetic micropolar generalized thermoelastic medium in the presence of the combined effect of Hall currents subjected to ramp-type heating is investigated. The medium is permeated by a strong transverse magnetic field imposed perpendicularly on the displacement plane, the induced electric field being neglected. Ohm’s law is modified by including two terms, one for the cross product of the current density and the initial magnetic field and the other for the cross product of the velocity and the initial magnetic field. The Laplace and exponential Fourier transform techniques are employed to transform the governing partial differential equations to ODE, which are solved exactly. Comparisons with the previously published work are conducted and the results are found to be in good agreement. The distributions of the temperature, displacement, stress, microrotation, and current density are obtained. The numerical values of these functions are represented graphically
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References
A. C. Eringen and E.S. Suhubi, „Non-linear theory of micro-elastic solids. I,” Int. J. Eng. Sci., No. 2, 189–203 (1964).
E. S. Suhubi and A. C. Eringen, “Nonlinear theory of micro-elastic solids. II,” Int. J. Eng. Sci., No. 2, 389–404 (1964).
A. C. Eringen, “A unified theory of thermo-mechanical materials,” Int. J. Eng. Sci., No. 4, 179–202 (1966).
A. C. Eringen, Linear Theory of Micropolar Elasticity, ONR Technical Report No. 29, School of Aeronautics, Aeronautics and Engineering Science, Purdue University (1965).
A. C. Eringen, “Linear theory of micropolar elasticity,” J. Mech., 15, 909–923 (1966).
M. A. Biot, “Thermoelasticity and irreversible thermodynamics,” J. Appl. Phys., 27, 240–253 (1956).
H. Lord and Y. Shulman, “A generalized dynamical theory of thermoelasticity,” J. Mech. Phys. Solids, 15, 299 (1967).
A. E. Green and K. A. Lindsay, “Thermoelasticity,” J. Elasticity, No. 2, 1–7 (1972).
A. E. Green and N. Laws, “On the entropy production inequality,” Arch. Ration. Mech. Anal., 45, 45–47 (1972).
M. A. Ezzat and H. M. Youssef, “Generalized magneto-thermoelasticity in a perfectly conducting medium,” Int. J. Solids Struct., 42, 6319–6334 (2005).
L. Knopoff, “The interaction between elastic wave motion and a magnetic field in electrical conductors,” J. Geophys. Res., 60, 441–456 (1955).
P. Chadwick, Ninth Int. Congr. Appl. Mech., 7, 143 (1957).
S. Kaliski and J. Petykiewicz, “Equation of motion coupled with the field of temperature in a magnetic field involving mechanical and electrical relaxation for anisotropic bodies,” Proc. Vibr. Probl., 4, 1–12 (1959).
G. Paria, “On magneto-thermoelastic plane waves,” Proc. Cambr. Phil. Soc., 56, 527–531 (1962).
A. Wilson, Proc. Cambr. Phil. Soc., 59, 483–488 (1963).
G. Paria, “Magneto-elasticity and magneto-thermoelasticity,” Adv. Appl. Mech., 10, 73–112 (1967).
A. Nayfeh and S. Namat-Nasser, “Electromagneto-thermoelastic plane waves in solids with relaxation,” J. Appl. Mech., E, 39, 108–113 (1972).
S. Choudhuri, “Electro-magneto-thermoelastic plane waves in rotating media with thermal relaxation,” Int. J. Eng. Sci., 22, 519–530 (1984).
H. Sherief and M. Ezzat, “A thermal sock problem in magneto-thermoelasticity with thermal relaxation,” Int. J. Solids Struct., 33, 4449–4459 (1996).
R. Kumar, “Effect of rotation in magneto-micropolar thermoelastic medium due to mechanical and thermal sources,” Chaos, Solitons & Fractals, 41, No. 4, 1619–1633 (2009).
R. Kumar, and M. Singh, “Effect of rotation and imperfection on reflection and transmission of plane waves in anisotropic generalized thermoelastic media,” J. Sound Vibr., 324, Nos. 3–5, 773–797 (2009).
R. Kumar and P. Ailawalia, “Moving load response in micropolar thermoelastic medium without energy dissipation possessing cubic symmetry,” Int. J. Solids Struct., 44, 4068–4078 (2007).
M. Aouadi, “Temperature dependence of an elastic modulus in generalized linear micropolar thermoelasticity,” ZAMP, 1057–1074 (2006).
G. Honig and U. Hirdes, “A method for the numerical inversion of Laplace transform,” J. Comp. Appl. Math., 10, 113–132 (1984).
A. C. Eringen, “Plane wave in nonlocal micropolar elasticity,” Int. J. Eng. Sci., 22, 1113–1121 (1984).
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Published in Prikladnaya Mekhanika, Vol. 50, No. 1, pp. 130–144, January–February 2014.
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Zakaria, M. Effect of Hall Current on Generalized Magneto-Thermoelasticity Micropolar Solid Subjected to Ramp-Type Heating. Int Appl Mech 50, 92–104 (2014). https://doi.org/10.1007/s10778-014-0615-0
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DOI: https://doi.org/10.1007/s10778-014-0615-0