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This paper aims to investigate the transient disturbances created by an internal line heat source that suddenly starts moving uniformly inside a visco‐elastic half‐space.

Generalised theory of thermo‐elasticity with relaxation time proposed by Lord‐Shulman is applied. The material of the semi‐infinite medium is an isotropic visco‐elastic solid of Kelvin‐Voight type. Fourier and Laplace transform techniques are used.

Applying the Fourier and Laplace transform techniques, expressions for displacement components in the transformed domain are found. These expressions prove the existence of three waves – a modified thermal wave, a visco‐elastic wave of defused nature and a transverse visco‐elastic wave.

Surface displacement components were evaluated on the boundary for only a short time.

The paper provides numerical results that are illustrated graphically to highlight the variations of surface displacement components with distance for different values of time, source depth and velocity of the source.

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.

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.

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.

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

The present paper aims to study the effect of rotation on the general model of the equations of generalized thermo‐microstretch for a homogeneous isotropic elastic half‐space solid whose surface is subjected to a thermal shock is considered. The problem is in the context of the generalized thermoelasticity Lord‐Şhulman's theory with one relaxation time, as well as the classical dynamical coupled theory.

The normal mode analysis is used to obtain the exact expressions.

For the displacement components, force stresses, temperature, couple stresses and microstress distribution.

The variations of the considered variables through the horizontal distance are illustrated graphically. Comparisons are made with the results in the presence and absence of rotation and in the presence and absence of microstretch constants between the two theories.

under the effect of temperature dependent properties is established. The modulus of elasticity is taken as a linear function on reference temperature. The formulation is applied under three theories of the generalized thermoelasticity: Lord‐Shulman and Green‐Naghdi (of type II) without energy dissipation, as well as the coupled theory. The normal mode analysis is used to obtain the expressions for the temperature, displacement components and the thermal stresses distributions. Numerical results are illustrated graphically for each problem considered. A Comparison is made with the results predicted by the three theories in the presence and absence of magnetic field and with the case where the modulus of elasticity is independent of temperature.

A model of the equations of two-dimensional problems in a half space, whose surface in free of micropolar thermoelastic medium possesses cubic symmetry as a result of a mode-I crack is studied. There acts an initial magnetic field parallel to the plane boundary of the half-space. The crack is subjected to prescribed temperature and stress distribution. The formulation in the context of the Lord-Shulman theory includes one relaxation time and Green-Lindsay theory with two relaxation times, as well as the classical dynamical coupled theory. The paper aims to discuss these issues.

The normal mode analysis is used to obtain the exact expressions for the displacement, microrotation, stresses and temperature distribution.

The variations of the considered variables with the horizontal distance are illustrated graphically. Comparisons are made with the results in the presence of magnetic field.

A comparison is also made between the three theories for different depths in 3D plots.

The purpose of this paper is to formulate a model of the equations of a two‐dimensional problem with the deformation of micropolar generalized thermoelastic medium with voids under the influence of various sources in the context of the Lord‐Shulman, Green‐Lindsay theories, as well as the classical dynamical coupled theory.

The normal mode analysis was used to obtain the exact expressions of the displacement components, force stress, coupled stress, change in volume fraction field and temperature distribution. Numerical results were given and illustrated graphically when the volume source was applied.

The presence of voids plays a significant role on all the physical quantities. The value of normal displacement and normal force stress increases while the temperature, tangential force stress and the couple stress increase and then decrease due to the presence of voids. The value of all the physical quantities converges to zero with increase in distance z.

Comparisons are made with the results predicted by the three theories in the presence and the absence of material constants due to voids.

The purpose of this paper is to study the reflection of a plane harmonic wave at the interface of thermo-microstretch elastic half space. The modulus of elasticity is taken as a linear function of reference temperature. The formulation is applied to generalized thermoelasticity theories, the Lord-Shulman and Green-Lindsay theories, as well as the classical dynamical coupled theory. Using potential function, the governing equations reduce to ten-order differential equation.

Coefficient ratios of reflection of different waves with the angle of incidence are obtained using continuous boundary conditions. By numerical calculations, the variation of coefficient ratios of reflection with the angle of incidence is illustrated graphically for magnesium crystal micropolar material under three theories.

The effect of different temperature-dependent constants and frequency on the coefficient ratios of reflection is illustrated graphically in context of Lord-Shulman theory.

The reflection coefficient ratios are given analytically and illustrated graphically. The effects of thermal relaxation times are very small on reflection coefficient ratio. The temperature-dependent constant and wave frequency have a strong effect on the reflection coefficient ratios.

The purpose of this paper is to analyse the transient effects in a functionally graded photo-thermoelastic (TE) medium with gravity and rotation by considering two generalised TE theories: Lord–Shulman (LS) and Green–Lindsay (GL). The governing equations are derived in rectangular Cartesian coordinates for a two dimensional problem.

All the physical properties of the semiconductor are supposed to vary exponentially with distance. The analytical solution is procured by employing normal mode technique on the resulting non-dimensional coupled field equations with appropriate boundary conditions.

For the mechanically loaded thermally insulated surface, normal displacement, stress components, temperature distribution and carrier density are calculated numerically with the help of MATLAB software for a silicon semiconductor and displayed graphically. Some particular cases of interest have also been deduced from the present results.

The effects of rotation and non-homogeneity on the different physical fields are investigated on the basis of analytical and numerical results. Comparisons are made with the results predicted by GL theory in the presence and absence of gravity for different values of time. Comparisons are also made between the three theories in the presence of rotation, gravity and in-homogeneity. Such problems are very important in many dynamical systems.

The purpose of this paper is to study the effect of gravity on the general model of the equations of generalized magneto‐thermo‐microstretch for a homogeneous isotropic elastic half‐space solid whose surface is subjected to a mode‐I crack. The problem is in the context of the Green and Naghdi theory of both types (II and III).

The normal mode analysis is used to obtain the expressions for the displacement components, the force stresses, the temperature, the couple stress and the microstress distribution.

The variations in variables against distance components are given graphically in 2D and 3D.

The linear theory of elasticity is of paramount importance in the stress analysis of steel, which is the commonest engineering structural material. To a lesser extent, the linear elasticity describes the mechanical behavior of the other common solid materials, e.g. concrete, wood and coal. However, the theory does not apply to the behavior of many of the newly synthetic materials of the elastomer and polymer type, e.g. polymethyl‐methacrylate (Perspex), polyethylene and polyvinyl chloride.

Comparisons are made with the results in the presence and absence of gravity and initially applied magnetic field with two cases: the first for the generalized micropolar thermoelasticity elastic medium (without stretch constants) between both types (II, III); and the second for the generalized magneto‐thermoelastic medium with stretch (without micropolar constants) between both types (II, III).

The present investigation is concerned with the two-dimensional deformations in an inhomogeneous fiber-reinforced thermoelastic medium under the influence of gravity in the context of Green–Lindsay theory.

Material properties are supposed to be graded in x-direction, and normal mode technique is adopted to obtain the exact expressions for the temperature field, displacement components and stresses.

Numerical computations have been carried out with the help of MATLAB software, and the results are depicted graphically to observe the disturbances induced in the considered medium. Comparisons made within the theory of the physical quantities are shown in figures to highlight the effects of fiber reinforcement, inhomogeneity parameter, gravity and time.

In the present work, we have investigated the effects of fiber reinforcement, inhomogeneity parameter, gravity and time in an inhomogeneous, fiber-reinforced thermoelastic medium under the influence of gravity. Although various investigations do exist to observe the disturbances in a thermoelastic medium under the effects of different parameters, the work in its present form i.e. thermally induced vibrations in an inhomogeneous fiber-reinforced thermoelastic material with gravity has not been studied till now. The present work is useful and valuable for analysis of problems involving thermal shock, gravity parameter, fiber reinforcement, inhomogeneous and elastic deformation.