Transient disturbance in a half‐space under generalized magneto‐thermoelasticity with a stable internal heat source under three theories

Abstract

Purpose

The purpose of this paper is to study the transient waves caused by a line heat source with a stable internal heat source inside isotropic homogenous thermoelastic perfectly conducting half‐space permeate into a uniform magnetic field. The formulation is applied under three theories of generalized thermoelasticity Lord‐Shulman (L‐S) theory with one relaxation time, Green‐Lindsay (G‐L) theory with two relaxation times, as well as the classical dynamical coupled theory. The problem is reduced to the solution of three differential equations by introducing the elastic and thermoelastic potentials.

Design/methodology/approach

The normal mode analysis is used to obtain the expressions. Numerical results are given and illustrated graphically. Comparisons are made with the results predicted by the three theories in the presence and absence of magnetic field and the internal heat source.

Findings

The results are graphically described for the medium of copper. We can conclude that the magnetic field has a great effect on the displacement components and this effect produces the same trend under the three theories. The results show that the relaxation times have salient effect to the distribution of displacement at small values of time.

Originality/value

The present theoretical results may provide interesting information for experimental scientists /researchers/seismologist working on this subject.

Citation

Lotfy, K. (2011), "Transient disturbance in a half‐space under generalized magneto‐thermoelasticity with a stable internal heat source under three theories", Multidiscipline Modeling in Materials and Structures, Vol. 7 No. 1, pp. 73-90. https://doi.org/10.1108/15736101111141458