Thermoelastic Half-space Research Articles

Stroh analysis of Rayleigh waves in anisotropic thermoelastic medium

ABSTRACTThe present article is concerned with the Stroh analysis of Rayleigh surface wave propagation in anisotropic homogeneous thermoelastic medium. The problem is considered in the context of three-phase-lag model of generalized thermoelasticity. The secular equation is with complex coefficients and the surface wave is damped in time and dispersed. The results are illustrated for the case of an orthotropic homogeneous thermoelastic half space and an explicit bicubic form of the characteristic equation with complex coefficients is obtained. The analysis of these Rayleigh waves for homogeneous orthotropic half space is numerically exemplified.

Effect of Anisotropic Thermal Conductivity on Deformation of a Thermoelastic Half-Space Subjected to Surface Loads

Effect of Anisotropic Thermal Conductivity on Deformation of a Thermoelastic Half-Space Subjected to Surface Loads

Two-Dimensional Deformation in a Thermoelastic Solid with Microtemperatures Subjected to an Internal Heat Source

The purpose of this paper is to study the two dimensional deformation in a generalized thermoelastic medium with microtemperatures having an internal heat source subjected to a mechanical force. The force is acting along the interface of generalized thermoelastic half space and generalized thermoelastic half space with microtemperatures having an internal heat source. The normal mode analysis has been applied to obtain the exact expressions for the considered variables. The effect of internal heat source and microtemperatures on the above components has been depicted graphically.

Effect of heat source and gravity on a fractional order fiber reinforced thermoelastic medium

In this article, the theory of fractional order two temperature generalized thermoelasticity is employed to study the wave propagation in a fiber reinforced anisotropic thermoelastic half space in the presence of moving internal heat source. The whole space is assumed to be under the influence of gravity. The surface of the half-space is subjected to an inclined load. Laplace and Fourier transform techniques are employed to solve the problem. Expressions for different field variables in the physical domain are derived by the application of numerical inversion technique. Physical fields are presented graphically to study the effects of gravity and heat source. Effects of time, reinforcement, fractional parameter and inclination of load have also been reported. Results of some earlier workers have been deduced from the present analysis. 2010MSC: 74A15, 80A20.

Thermal Stresses in Thermoelastic Half-Space Without Energy Dissipation Subjected to Rotation and Magnetic Field

Thermal Stresses in Thermoelastic Half-Space Without Energy Dissipation Subjected to Rotation and Magnetic Field

Eigenvalue approach to coupled thermoelasticity in a rotating isotropic medium

In this paper the linear theory of the thermoelasticity has been employed to study the effect of the rotation in a thermoelastic half-space containing heat source on the boundary of the half-space. It is assumed that the medium under consideration is traction free, homogeneous, isotropic, as well as without energy dissipation. The normal mode analysis has been applied in the basic equations of coupled thermoelasticity and finally the resulting equations are written in the form of a vector- matrix differential equation which is then solved by eigenvalue approach. Numerical results for the displacement components, stresses, and temperature are given and illustrated graphically. Comparison was made with the results obtained in the presence and absence of the rotation. The results indicate that the effect of rotation, non-dimensional thermal wave and time are very pronounced.

Effect of rotation on Rayleigh waves in magneto-thermoelastic transversely isotropic medium with thermal relaxation times

The present article deals with the propagation of Rayleigh surface waves in homogeneous transversely isotropic medium. Effect of rotation on Rayleigh waves in thermoelastic half-space is studied under the purview of the three-phase-lag model in presence of magnetic field. The normal mode analysis is used to obtain the expressions for the displacement components, stresses, and temperature distribution. The frequency equations in the closed form are derived and the path of particles during Rayleigh wave propagation is found elliptical. In order to illustrate the analytical developments, the numerical solution is carried out and the computer-simulated results in respect of Rayleigh wave velocity, attenuation coefficient, and specific loss are presented graphically.

Dynamic problem in 3D thermoelastic half-space with rotation in context of G-N type II and type III

In this paper, comparison between G-N model of type II (without energy dissipation) and G-N model of type III (with energy dissipation) has been shown in a three dimensional thermoelastic half space with rotation subjected to time dependent heat source on the traction free boundary. Eigenvalue methodology has been adopted to solve the equations resulting from the application of the Normal mode analysis to the non-dimensional coupled equations. Variation of the numerically computed values of thermal stresses and temperature with and without rotation has been illustrated graphically.

Application of fractional order theory to a functionally graded perfect conducting thermoelastic half space with variable Lamé’s Modulii

In this work, the model of fractional magneto-thermoelasticity is applied to a one-dimensional thermal shock problem for a functionally graded half-space whose surface is assumed to be traction free and subjected to an arbitrary thermal loading. The Lame’s modulii is taken as functions of the vertical distance from the surface of thermoelastic perfect conducting medium in the presence of a uniform magnetic field. Laplace transform and the perturbation techniques are used to derive the solution in the Laplace transform domain. Numerical inversion of the Laplace transform is carried out to obtain the temperature, displacement, stress and induced magnetic and electric field distributions. Numerical results are represented graphically and discussed.

Thermo-mechanical interactions in a fractional order generalized thermoelastic solid with diffusion

The main objective of the present paper is to analyze the effects of fractional order parameter, diffusion, velocity of moving load and time on wave propagation in a two dimensional generalized thermoelastic half-space. Medium is assumed to be unstrained and unstressed initially and has uniform temperature. The governing equations of the fractional generalization of Lord-Shulman model for an isotropic and homogeneous medium are solved by means of the Laplace–Fourier transforms. By employing a numerical inversion technique, the distributions of different fields like displacement, stresses, temperature, concentration and chemical potential are computed numerically and displayed graphically for copper material. All the physicals fields are found to be significantly affected by the above mentioned parameters. The problem of generalized thermoelasticity with diffusion has been reduced as a special case of our problem.

Rayleigh surface wave propagation in orthotropic thermoelastic solids under three-phase-lag model

ABSTRACTThe present article deals with the propagation of Rayleigh surface waves in a homogeneous, orthotropic thermoelastic half-space in the context of three-phase-lag model of thermoelasticity. The frequency equations in closed form are derived and the amplitude ratios of surface displacements and temperature change during the Rayleigh wave propagation on the surface of half-space have been computed analytically. The path of particles during Rayleigh wave propagation is found elliptical and eccentricity of the ellipse is derived. To illustrate the analytical developments, the numerical solution is performed and the computer-simulated results in respect of phase velocity, attenuation coefficient, and specific loss are presented graphically.

On an influence of thermal stresses and magnetic field in thermoelastic half-space without energy dissipation

ABSTRACTIn this article, a two-dimensional problem for a homogeneous, isotropic, and thermoelastic half-space subjected to magnetic field and time-dependent heat source is investigated. The boundary conditions at the surface have been considered in the context of Green-Naghdi’s second model (GN-II) of thermoelasticity. The normal mode analysis and eigenvalue approach techniques are used to solve the nondimensional coupled equations. The effect of magnetic field, frequency, wave number, and time is analyzed theoretically and computed numerically. Comparison was made with the results obtained in the presence and absence of the magnetic field. Numerical results for the displacement components, mean value of normal stresses, dilatation, and temperature have been represented graphically to show the physical meaning of the external parameters. The results indicate that the effect of magnetic field, frequency, wave number, and time is very pronounced and effective on the phenomena.

Propagation of waves in an initially stressed generalized electromicrostretch thermoelastic medium with temperature-dependent properties under the effect of rotation

ABSTRACTIn the present article, a model of the equations of generalized electromicrostretch thermoelasticity in an initially stressed perfectly conducting elastic medium under the effect of temperature-dependent properties is studied. The entire elastic medium is rotating with a uniform angular velocity. Reflection phenomena of plane waves in electromicrostretch thermoelasticity is investigated under two theories proposed by Lord and Shulman (L–S) and Green and Lindsay (G–L). Amplitude ratios and energy ratios of various reflected waves are presented when an elastic wave is made incident obliquely at the plane boundary of an electromicrostretch thermoelastic solid half-space. It has been verified that there is no dissipation of energy at the boundary surface during reflection. Numerical examples calculate the amplitude ratios to evince the effects of initial stress parameter, rotation, and temperature-dependent properties, and the results obtained are depicted graphically.

On temperature and stresses in a thermoelastic half-space with temperature dependent properties

The paper deals with the axisymmetric problem of the thermoelastic half-space with temperature dependent properties. The thermal coefficients: heat conductivity and coefficient of linear expansion are assumed to be functions of temperature. The mechanical properties: Young modulus and Poisson ratio are taken into account as constants. Two cases of boundary conditions are considered: a normal heat flux acting on a circle with given radius and two variants of the boundary conditions on the outside of the heated region: (1) a thermal insulation, or (2) a constant temperature, taken as reference. The boundary is assumed to be free of mechanical loadings. The linear dependences of thermal properties on temperature is considered as a special case. The obtained exact results are presented in the forms of multiple integrals and the detailed analysis are derived for linear dependences of the thermal properties on temperature.

Effect of Impedance Boundary on Reflection of Plane Waves from free Surface of a Rotating Thermoelastic Solid Half Space

The coupled partial differential equations governing a rotating thermoelastic medium in context of Lord and Shulman theory are solved for plane wave solutions. A cubic velocity equation is obtained, which correspond to the speeds of propagation of three coupled plane waves. A reflection phenomenon is considered in a rotating thermoelastic solid half-space for incidence of a coupled plane wave. The plane surface of the half-space is subjected to impedance boundary conditions, where normal and tangential tractions are proportional to normal and tangential displacement components time frequency, respectively. The expressions for energy ratios of all reflected waves are obtained and computed numerically for a particular material representing the medium. The dependence of energy ratios on rotation parameter, impedance parameters and angle of incidence is shown graphically.

Rotation of Two-Temperature Generalized Thermoelastic Half-Space Subjected to Thermal Shock and Without Energy Dissipation

In this work, a mathematical model for the thermoelastic medium with constant elastic parameters in the context of two-temperature generalized thermoelasticity without energy dissipation has been constructed. The governing equations of the mathematical model will be taken when the medium is quiescent first. Laplace transforms techniques will be used to get the general solution for any set of boundary conditions. The solution will be obtained for a particular model when the medium is subjected to a thermal load by using stat-space approach. The inversion of the Laplace transforms will be calculated numerically and after that we’ll present the results graphically with some comparisons to study the impact of thermal or mechanical load on the speed of progress of mechanical and thermal waves through the medium. Also, to studying the effect of the two-temperature parameter rotation parameter on all the studied field.

Reflection of plane waves in thermoelastic medium with double porosity

Purpose The purpose of this paper is to study the reflection of plane waves in thermoelastic medium with double porosity structure. Design/methodology/approach A two-dimensional model is considered of an isotropic thermoelastic half-space with double porosity. Thermoelasticity with one relaxation time given by Lord and Shulman (1967) has been used to study the problem. It is found that there exists four coupled longitudinal waves, namely, longitudinal wave (P), longitudinal thermal wave (T), longitudinal volume fractional wave corresponding to pores (PVI) and longitudinal volume fractional wave corresponding to fissures (PVII), in addition to an uncoupled transverse wave (SV). Findings The formulae for amplitude ratios of various reflected waves are obtained in closed form. It is found that these amplitude ratios are functions of angle of incidence. Effect of porosity and thermal relaxation time is shown graphically on the amplitude ratios with angle of incidence for a particular model. Originality/value Reflection of plane waves is of great practical importance. There are many organic and inorganic deposits beneath the earth surface. Wave propagation is the simplest and most economical technique to detect these. The model discussed in the present paper can provide useful information for experimental researchers working in the field of geophysics and earthquake engineering, along with seismologist working in the field of mining tremors and drilling into the crust of the earth.

Analytical solution of thermoelastic interaction in a half-space by pulsed laser heating

In this article, we consider the problem of a two-dimensional thermoelastic half-space in the context of generalized thermoelastic theory with one relaxation time. The surface of the half-space is taken to be traction free and thermally insulated. The solution of the considered physical quantity can be broken down in terms of normal modes. The nonhomogeneous basic equations have been written in the form of a vector-matrix differential equation, which is then solved by an eigenvalue approach. The exact analytical solution is adopted for the temperature, the components of displacement and stresses. The results obtained are presented graphically for the effect of laser pulse to display the phenomena physical meaning. The graphical results indicate that the thermal relaxation time has a great effect on the temperature, the components of displacement and the components of stress.

Reflection of Plane Waves in Generalized Thermoelastic Half Space under the Action of Uniform Magnetic Field

Reflection of longitudinal displacement waves in a generalized thermoelastic half space under the action of uniform magnetic field has been investigated. The magnetic field is applied in such a direction that the problem can be considered as a two-dimensional one. The discussion is based on the three theories of generalized thermoelasticity: Lord-Shulman (L-S), Green-Lindsay (G-L), and Green-Naghdi (G-N) with energy dissipation. We compute the possible wave velocities for different models. Amplitude ratios have been presented. The effects of magnetic field on various subjects of interest are discussed and shown graphically.

Axisymmetric analysis of a thermoelastic isotropic half-space under buried sources in displacement and temperature potentials

ABSTRACTAnalytical and numerical investigations have been made to determine the solution of a thermoelastic isotropic half-space under buried mechanical load and heat flux based on Biot’s coupled thermoelasticity. Using a scalar potential function, the coupled governing equations have been uncoupled and a sixth order partial differential equation that governs the potential function is received. Applying the Hankel transform to suppress the radial variable, a sixth order ordinary differential equation with respect to depth is received. Solving that equation and utilizing the boundary and continuity conditions, the potential function is derived and displacements, temperature, and stress components are derived in the transformed domain in two regions. Applying the inverse Hankel transform, responses are derived in the physical domain as line integrals. The line integrals are calculated numerically through Mathematica software. Numerical results are depicted graphically for different cases of vertical load and heat flux. Effects of elastic and thermal properties as well as the depth of buried loads and frequency of excitation are investigated. Numerical evaluation shows that the agreement between the results of this study for surface excitation and the results reported in the literature is excellent.