Green Lindsay Theory Research Articles

Disturbance in Thermo-Microstretch Elastic Medium With Internal Heat Source

The present investigation is aimed at studying the deformation in thermo-microstretch elastic medium occuping the region y ⩾ 0 with a stable internal heat source. A nonviscous fluid layer of height h is overlying the thermoelastic medium and a mechanical source of constant magnitude is applied along the fluid/solid interface. The normal mode analysis is used to obtain the exact expressions for displacement components, force stress, and temperature distribution. The numerical results are given and presented graphically for the Green–Lindsay theory of thermoelasticity. 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 microstretch and microrotation parameters.

Analysis of a contact problem in thermoviscoelasticity under the Green–Lindsay model

In this article, we consider a one-dimensional contact problem in generalized thermoviscoelasticity based on the Green–Lindsay theory. We prove that the energy associated to the system decays exponentially to zero and we analyze a finite element approximation. It is shown that if the continuous solution is sufficiently smooth then the error in the L2-norm is order of h+Δt. Furthermore, we demonstrate that the discrete energy decays as the time increases.

Electro-magnetic waves in generalized thermo-viscoelasticity for different theories

Some mathematical models of the equations of generalized magneto-thermo-viscoelasticty for isotropic media are given. The formulation is applied to each generalization of the Lord- Shulman theory, the Green-Lindsay theory and the Chan- drasekharaiah and Tzou theory as well as to the coupled theory. The state space approach is adopted for the solution of problems in the absence or presence of heat sources. The Laplace-transform technique is used. A numerical method is employed for the inversion of the Laplace transforms. Numerical results for the stress distribution are given and illustrated graphically for each problem. Comparisons are made with the results predicted by the four theories.

Wave reflection at a free interface in an anisotropic pyroelectric medium with nonclassical thermoelasticity

In this paper, the well-established two-dimensional mathematical model for linear pyroelectric materials is employed to investigate the reflection of waves at the boundary between a vacuum and an elastic, transversely isotropic, pyroelectric material. A comparative study between the solutions of (a) classical thermoelasticity, (b) Cattaneo–Lord–Shulman theory and (c) Green–Lindsay theory equations, characterised by none, one and two relaxation times, respectively, is presented. Suitable boundary conditions are considered in order to determine the reflection coefficients when incident elasto–electro–thermal waves impinge the free interface. It is established that, in the quasi-electrostatic approximation, three different classes of waves: (1) two principally elastic waves, namely a quasi-longitudinal Primary (qP) wave and a quasi-transverse Secondary (qS) wave; and (2) a mainly thermal (qT) wave. The observed electrical effects are, on the other hand, a direct consequence of mechanical and thermal phenomena due to pyroelectric coupling. The computed reflection coefficients of plane qP waves are found to depend upon the angle of incidence, the elastic, electric and thermal parameters of the medium, as well as the thermal relaxation times. The special cases of normal and grazing incidence are also derived and discussed. Finally, the reflection coefficients are computed for cadmium selenide observing the influence of (1) the anisotropy of the material, (2) the electrical potential and (3) temperature variations and (4) the thermal relaxation times on the reflection coefficients.

Reflection of a plane magneto-thermoelastic wave at the boundary of a solid half-space in presence of initial stress

The paper studies the effects of the magnetic field and initial stress on the reflection of a plane magneto-thermoelastic wave from the boundary of a solid half-space. The basic dynamical equations of thermoelasticity in presence of Lorentz force and the heat conduction equation of Green–Lindsay theory have been solved to derive the wave equations for the reflected P-, SV- and thermal waves. By considering the boundary to be a stress-free and insulated one, the boundary equations that contain the ratios of the amplitude of the reflected components to that of the incident wave have been obtained. The analytical solution has been cast in matrix form for each of the incident plane waves at the boundary, namely the P-wave, SV-wave and thermal wave. The numerical calculations of the absolute values of the amplitude ratios for an incident SV-wave have been carried out for different values of both magnetic pressure number and initial stress parameter. The initial stress parameter shows a marked influence on the magnitude of the amplitude ratios. The reflection coefficients for different values of magnetic pressure number in absence of initial stress have also been included for the sake of comparison.

The Effect of Rotation on a Fiber-Reinforced Medium under Generalized Magneto-Thermoelasticity with Internal Heat Source

In the present article, we discussed the transient waves caused by a line heat source with a uniform velocity inside a rotating half-space fiber-reinforced thermoelastic media permeated into a uniform magnetic field. The formulation of the problem is applied under the coupled theory (CD), Green-Lindsay (G-L) theory, and Lord-Shulman (L-S) theory. The normal mode analysis is used to obtain expressions for the temperature, displacement components, and thermal stresses. Numerical results are given and illustrated graphically. A comparison is made with the results predicted by three theories in the presence and absence of magnetic field and rotation as well as fiber-reinforced.

The influence of thermal loading due to laser pulse on generalized micropolar thermoelastic solid with comparison of different theories

Purpose – The purpose of this paper is to introduce the coupled theory, Lord-Shulman theory with one relaxation time and Green-Lindsay theory with two relaxation times to study the influence of rotation on generalized micropolar thermoelasticity subject to thermal loading due to laser pulse. The bounding plane surface is heated by a non-Gaussian laser beam with pulse duration of 8 ps. Design/methodology/approach – The problem has been solved numerically by using the normal mode analysis. Findings – The thermal shock problem is studied to obtain the exact expressions for the displacement components, force stresses, temperature, couple stresses and micro-rotation. The distributions of the considered variables are illustrated graphically. Comparisons are made with the results predicted by three theories in the presence and absence of laser pulse and for different values of time. Originality/value – Generalized micropolar thermoelastic solid.

Effect of rotation, magnetic field and a periodic loading on radial vibrations thermo-viscoelastic non-homogeneous media

In this paper, an analytical solution for the effect of the rotation in a magneto-thermo-viscoelastic non-homogeneous medium with a spherical cavity subjected to periodic loading is presented. The distribution of displacements, temperature, and stresses in the non-homogeneous medium in the context of generalized thermo-elasticity using GL (Green-Lindsay) theory is discussed and obtained in analytical form. The results are displayed graphically to illustrate the effect of rotation, relaxation, magnetic field, viscoelasticity, and non-homogeneity. Comparisons are made with the previous work in the absence of rotation and initial stress.

The effect of rotation on the problem of fiber-reinforced under generalized magnetothermoelasticity subject to thermal loading due to laser pulse: a comparison of different theories

In the present paper, we introduce the coupled theory, Lord–Schulman theory, and Green–Lindsay theory to study the influences of a magnetic field and rotation on a two-dimensional problem of fiber-reinforced thermoelasticity subject to thermal loading by a laser pulse. The material is a homogeneous isotropic elastic half-space and is heated by a non-Gaussian laser beam with pulse duration of 8 ps. The method applied here is to use normal mode analysis to solve a thermal shock problem. Deformation of a body depends on the nature of the force applied as well as the type of boundary conditions. Numerical results for the temperature, displacement, and thermal stress components are given and illustrated graphically in the absence and the presence of the magnetic field, rotation, reinforcement, and for two different values of time.

Reflection of plane waves from a thermo-microstretch elastic solid with temperature dependent elastic properties

Purpose– 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.Design/methodology/approach– 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.Findings– The effect of different temperature-dependent constants and frequency on the coefficient ratios of reflection is illustrated graphically in context of Lord-Shulman theory.Originality/value– 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.

Propagation of Plane Waves of a Mode-I Crack for a Generalized Thermoelasticity under Influence of Gravity for Different Theories

A general model of the equations of the generalized thermoelasticity for an infinite space weakened by a finite linear opening Mode-I crack is solved. The material is homogeneous isotropic elastic half space. The total deformation of a Mode-I crack in thermoelastic half-space in the context of Lord-Şhulman and Green-Lindsay theories is studied, as well as the coupled theory and the interaction with each other under the influence of gravity. The normal mode analysis is used to obtain the exact expressions for the physical quantities. Comparisons are made with the results between the three theories in the presence and absence of gravity.

Reflection of plane waves from a thermo-microstretch elastic solid under the effect of rotation

A reflection of a plane harmonic wave at the interface of thermo-microstretch elastic half space is studied. The formulation is applied to generalized thermo-elasticity theories, the Lord–Şhulman and Green–Lindsay theories, as well as the classical dynamical coupled theory. Using potential function, the governing equations reduce to ten differential equations. 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 in magnesium crystal micropolar material under three theories. Also the effect of frequency and rotation on the coefficient ratios of reflection is illustrated graphically in the context of Lord–Shulman theory.

Effect of magnetic field and a mode-I crack problem in micropolar thermoelastic medium possessing under three theories

Purpose – 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. Design/methodology/approach – The normal mode analysis is used to obtain the exact expressions for the displacement, microrotation, stresses and temperature distribution. Findings – 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. Originality/value – A comparison is also made between the three theories for different depths in 3D plots.

Gravitational effect and initial stress on generalized magneto-thermo-microstretch elastic solid for different theories

The present paper is aimed at studying the effect of gravity and initial stress on the general model of the equations of generalized magneto-thermo-microstretch for a homogeneous isotropic elastic half-space solid. The problem is in the context of the Lord–Şhulman and Green–Lindsay theories, as well as the 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 perpendicular to the axis of rotation are illustrated graphically. Comparisons are made with the results in the presence and absence of gravity and magnetic field of a particular case for the generalized micropolar thermoelastic medium (without microstretch constants) between the three theories.

The Effect of Magnetic Field on 2-D Problem for a Mode-I Crack of a Fiber-Reinforced in Generalized Thermoelasticity

In the present paper, the coupled theory, Lord–Şhulman theory, and Green–Lindsay theory are introduced to study the influence of a magnetic field on the 2-D problem of a fiber-reinforced thermoelastic. These theories are also applied to study the influence of reinforcement on the total deformation of an infinite space weakened by a finite linear opening Mode-I crack. The material is homogeneous and an isotropic elastic half-space. The crack is subjected to a prescribed temperature and stress distribution. Normal mode analysis is used to solve the problem of a Mode-I crack. Numerical results for the temperature, the displacement, and thermal stress components are given and illustrated graphically in the absence and the presence of the magnetic field. A comparison between the three theories is also made for different depths.

Reflection and Refraction of Coupled Transverse and Micro-Rotational Wave at Interface between Two Micropolar Elastic Solid

Using the model of micropolar generalized magneto-thermo-elasticity, the coupled transverse and micro-rotational wave at an interface between two micropolar solid mediums is discussed in the presence of a constant magnetic field. The model can be applied to the coupled theory as well as to five generalizations: the Lord-Shulman theory with one relaxation time, the Green-Lindsay theory with two relaxation times, the Green-Naghdi theories of type II(without energy dissipation) and of type III, and the theory with dual-phase-lag. Using continuous conditions at the interface, the amplitude ratios of reflected and refracted longitudinal displacement waves, longitudinal micro-rotational waves and the coupled transverse and micro-rotational waves are studied for incident coupled transverse and micro-rotational wave. The effect of thermal relaxation is discussed for C-D theory, G-L theory and L-S theory. The numerical results show that the effects of thermal relaxation times are very significant on the amplitude ratios.

The effect of magnetic field and rotation of the 2-D problem of a fiber-reinforced thermoelastic under three theories with influence of gravity

In the present paper, we introduced the coupled theory, Lord–Schulman theory with one relaxation time and Green–Lindsay theory with tow relaxation times to study the influence of magnetic field and rotation on the 2-D problem of a fiber-reinforced thermoelastic and the interaction with each other under the influence of gravity. The methodology applied here is the use of the normal mode analysis to solve the problem of a thermal shock problem to obtain the exact expressions for the displacement components, force stress and temperature. Some particular cases are also discussed in the context of the problem. Numerical results for the temperature, displacement and thermal stress components are given and illustrated graphically in the absence and presence of the magnetic field, rotation and gravity.

Plane Waves of a Fiber-Reinforcement Magneto-thermoelastic Comparison of Three Different Theories

In this article, the coupled theory, Lord–Shulman theory, and Green–Lindsay (GL) theory are used to study the influence of a magnetic field on a fiber-reinforced thermoelastic half-space. Normal mode analysis is used to solve a thermal shock problem. Numerical results for the temperature, displacement components, and stress components are given and illustrated graphically. A comparison is made between the coupled and GL theories in the absence and presence of a magnetic field and reinforcement.

Effects of Rotation and Gravity Field on Surface Waves in Fibre-Reinforced Thermoelastic Media under Four Theories

Estimation is done to investigate the gravitational and rotational parameters effects on surface waves in fibre-reinforced thermoelastic media. The theory of generalized surface waves has been firstly developed and then it has been employed to investigate particular cases of waves, namely, Stoneley waves, Rayleigh waves, and Love waves. The analytical expressions for surface waves velocity and attenuation coefficient are obtained in the physical domain by using the harmonic vibrations and four thermoelastic theories. The wave velocity equations have been obtained in different cases. The numerical results are given for equation of coupled thermoelastic theory (C-T), Lord-Shulman theory (L-S), Green-Lindsay theory (G-L), and the linearized (G-N) theory of type II. Comparison was made with the results obtained in the presence and absence of gravity, rotation, and parameters for fibre-reinforced of the material media. The results obtained are displayed by graphs to clear the phenomena physical meaning. The results indicate that the effect of gravity, rotation, relaxation times, and parameters of fibre-reinforced of the material medium is very pronounced.

OS0803 応力焦点化現象に及ぼす熱波の有限速度の影響

When an isotropic and homogeneous solid sphere and/or infinitely long solid cylinder are suddenly subjected to an instantaneous uniform heating, a stress wave occurs at the moment thermal impact is applied. The stress wave proceeds radially inward to the center of a sphere and/or cylinder. The wave may accumulate at the center and give rise to very large stress magnitudes, even though the initial thermal stress is relatively small. This phenomenon is called the stress-focusing effect. In this study, the stress focusing effect in a solid sphere and solid cylinder under instantaneous uniform heating at the free surface is studied on the basis of the generalized thermoelastic theories, that is, the Lord-Shulman's and the Green-Lindsay's theories. The combined governing equations of both theories are solved by the Laplace transform technique. The effects of the thermomechanical coupling and the relaxation time on the stress focusing phenomena as well as the singularity of stresses are discussed.