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Magneto-thermo-elastic waves in an infinite perfectly conducting elastic solid with energy dissipation

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Abstract

The generalized thermo-elasticity theory, i.e., Green and Naghdi (G-N) III theory, with energy dissipation (TEWED) is employed in the study of time-harmonic plane wave propagation in an unbounded, perfectly electrically conducting elastic medium subject to primary uniform magnetic field. A more general dispersion equation with complex coefficients is obtained for coupled magneto-thermo-elastic wave solved in complex domain by using the Leguerre’s method. It reveals that the coupled magneto-thermoelastic wave corresponds to modified dilatational and thermal wave propagation with finite speeds modified by finite thermal wave speeds, thermo-elastic coupling, thermal diffusivity, and the external magnetic field. Numerical results for a copper-like material are presented.

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Abbreviations

u :

displacement vector

λ, µ:

Lamé constants

ρ :

constant mass density of the medium

γ :

thermal modulus

α t :

coefficient of linear thermal expansion

T 0 :

uniform reference temperature

T :

small temperature increase above the reference temperature T 0

J :

electric current density vector

B :

magnetic induction vector

c υ :

specific heat of the medium at constant strain

K*:

a material constant characteristic for the G-N theory

H :

total magnetic field vector at any time

E :

electric field vector

µe :

magnetic permeability of the medium

σ :

electric conductivity of the medium

c T :

non-dimensional finite thermal wave speed of G-N theory of thermo-elasticity II

ε T :

thermo-elastic coupling constant

K :

thermal conductivity

κ :

thermal diffusivity

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Authors and Affiliations

  1. Netaji Subhash Engineering College, Technocity, Police Para, Panchpota, Garia, Kolkata, 700152, India

    Payel Das

  2. Department of Applied Mathematics, University of Calcutta, 92 A.P.C Road, Kolkata, 700009, West Bengal, India

    Mridula Kanoria

Authors
  1. Payel Das
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  2. Mridula Kanoria
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Corresponding author

Correspondence to Mridula Kanoria.

Additional information

(Communicated by Xing-ming GUO)

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Das, P., Kanoria, M. Magneto-thermo-elastic waves in an infinite perfectly conducting elastic solid with energy dissipation. Appl. Math. Mech.-Engl. Ed. 30, 221–228 (2009). https://doi.org/10.1007/s10483-009-0209-6

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  • DOI: https://doi.org/10.1007/s10483-009-0209-6

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