Acta Mechanica Solida Sinica

, Volume 23, Issue 3, pp 200–212 | Cite as

Electro-Magneto-Thermoelastic Plane Waves in Micropolar Solid Involving Two Temperatures

Article

Abstract

The model of equations of micropolar generalized magneto-thermoelasticity is introduced within the context of the theory of two temperatures generalized thermoelasticity and we consider a problem of an isotropic homogeneous micropolar medium taking into account the heat effects and allowing the magnetic field effects. A plane wave analysis is employed to obtain the exact formulas of the two temperatures (conductive and mechanical), displacement components, micro-rotation components, stresses, couple stresses, induced electric current, electric field and magnetic field. Arbitrary application is chosen to enable us to get the complete solution. The considered variables are presented graphically and discussions are made for the results.

Key words

elasticity electromagnetic plane waves micropolar material two temperatures theory heat transfer 

Nomenclature

λ, μ

Lame’s constants

α, β, ε, v

Micropolar elastic constants

j

Micro-inertia

ρ

Density

ui

Components of displacement

wi

Components of rotation

σij

Components of stress

μij

Components of couple stress

e

Dilatation

ϕ

Conductive temperature

θ

Mechanical temperature

To

Reference temperature

cE

Specific heat at constant strain

αT

Coefficient of linear thermal expansion

γ

= (3λ +2μ)α T

k

Thermal conductivity

qi

Component of heat flux

a*

Two temperature parameter

τo

Relaxation time

D

Electric displacement vector

E

Induced electric field vector

J

Current density vector

B

Magnetic induction vector

H

Magnetic intensity vector

h

Induced magnetic field vector

Ho

Initial uniform magnetic field

ρe

Charge density

εo

Dielectric constant

μo

Magnetic permeability

δij

Kronecker delta function

eijk

Permutation symbol

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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2010

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of EducationAlexandria UniversityAlexandriaEgypt
  2. 2.Department of Mathematics, Faculty of ScienceAlexandria UniversityAlexandriaEgypt

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