Transient Disturbance in a Half-Space under Generalized Magneto-Thermoelasticity with Internal Heat Source

Abstract

The transient waves caused by a line heat source with a uniform velocity inside isotropic homogeneous thermoelastic perfectly conducting half-space permeated into a uniform magnetic field are studied. The formulation is applied under three theories of generalized thermoelasticity: Lord-Shulman theory with one relaxation time, Green-Lindsay 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. The normal mode analysis is used to obtain the expression for the temperature, displacement components and the thermal stresses. 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.

Generalized Magneto-thermoelasticity in a Fiber-Reinforced Anisotropic Half-Space

“…We have found that the time has a significant effect on the field quantities. Figures 7, 8, 9, 10, 11, and 12 show the variation of the temperature, displacement components, u, v, and stress components, σ x x , σ yy , σ xy , and induced magnetic field, h, with time t at 8,9,10,11,12,13, and 14, the solid lines refer to the case with reinforcement (WRE) and the dotted lines refer to the case without reinforcement (NRE), i.e., (α = 0, β = 0, and (μ L − μ T ) = 0). It is easy to see from Figs.…”

“…Singh [6] studied a problem on wave propagation in an anisotropic generalized thermoelastic solid and obtained a cubic equation, which gives the dimensional velocities of various plane waves. Recently, a number of investigations [7][8][9][10][11][12] have been carried out using the aforesaid theories of generalized thermoelasticity under the effect of a magnetic field.…”

Transient thermo‐elastic disturbances in a visco‐elastic semi‐space due to moving internal heat source

“…This results are showing inOthman et al (2009). By comparing the figures of solutions obtained under the three thermoelastic theories, important phenomena are observed: Distribution…”

Effect of rotation on plane waves in generalized thermo-microstretch elastic solid with a relaxation time

“…Othman and Lotfy [27] studied two-dimensional problem of generalized magneto-thermoelasticity under the effect of temperature dependent properties. Othman and Lotfy [28] studied transient disturbance in a half-space under generalized magneto-thermoelasticity with moving internal heat source. Othman and Lotfy [29] studied the plane waves in generalized thermo-microstretch elastic half-space by using a general model of the equations of generalized thermo-microstretch for a homogeneous isotropic elastic half space.…”