Abstract
The interaction between magnetic field and thermal field in an elastic half-space, homogeneous and isotropic under two temperature and initial stress are investigated using a normal mode method in the framework of the Lord–Şhulman theory, with thermal shock and rotation. The medium rotates with a uniform angular velocity, and it is considered to be permeated by a uniform magnetic field and hydrostatic initial stress. The general solution we obtain is finally applied to a specific problem. The variations in temperature, the dynamical temperature, the stress and the strain distributions through the horizontal distance are calculated by an appropriate numerical example and graphically illustrated.
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03 November 2020
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Abbreviations
- \(\delta _{{ij}}\) :
-
Kronecker delta function
- \(\alpha _{t}\) :
-
Coefficient of linear thermal expansion
- T :
-
Absolute temperature
- \(T_0\) :
-
Reference temperature chosen so that \(\left| {\frac{T-T_0 }{T_0 }} \right| <1\)
- \(\phi =\phi _0 -{T}\) :
-
Conductive temperature
- \(\eta \) :
-
Hydrostatic initial stress
- \(\lambda , \mu \) :
-
Lame’s constants
- \(\mu _0\) :
-
Magnetic permeability
- \(\theta ={T}-{T}_0\) :
-
Thermodynamical temperature
- \(\rho \) :
-
Density of the medium
- \(\sigma _{{ij}}\) :
-
Components of the stress tensor
- \(\tau _0\) :
-
Thermal relaxation time
- a :
-
Two-temperature parameter
- \({C}_{{E}}\) :
-
Specific heat at constant strain
- e :
-
Cubical dilatation
- \({e}_{{ij}}\) :
-
Components of the strain tensor
- \({F}_{i}\) :
-
Lorentz force
- K :
-
Thermal conductivity
- P :
-
Initial pressure
- \({u}_{i}\) :
-
Components of the displacement vector
- \(F_{i}\) :
-
Lorentz body force
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Abo-Dahab, S.M. A two-temperature generalized magneto-thermoelastic formulation for a rotating medium with thermal shock under hydrostatic initial stress. Continuum Mech. Thermodyn. 32, 883–900 (2020). https://doi.org/10.1007/s00161-019-00765-3
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DOI: https://doi.org/10.1007/s00161-019-00765-3