THERMOELASTIC INTERACTIONS IN A TRANSVERSELY ISOTROPIC ELASTIC MEDIUM WITH A CYLINDRICAL HOLE SUBJECTED TO RAMP-TYPE INCREASE IN BOUNDARY TEMPERATURE OR LOAD

This paper deals with the study of thermoelastic interactions on the basis of the generalized theory of thermoelasticity and with a comparison of the generalized theory of thermoelasticity with the coupled dynamical theory of thermoelasticity for the case of a transversely isotropic elastic medium with a cylindrical cavity when the surface of the cavity is subjected to a ramp-type increase in temperature or load. The solution for the distributions of temperature and stresses are obtained with the help of the Laplace transform technique. Inversions of Laplace transforms are carried out analytically. Discontinuities of the field variables are analyzed. Numerical results for a particular material are also determined in order to extend the problem.     

Thermoelastic interactions without energy dissipation in an unbounded body with a cylindrical cavity

In this work, we apply Green and Naghdi's generalized thermoelasticity theory to a one-dimensional problem of an infinitely long cylindrical cavity. Laplace transform techniques are used to solve the problem. A comparison of generalized thermoelasticity theory with one relaxation time is made. Numerical results are computed and represented graphically for the temperature,displacement, and stress distributions.     

Normal Mode Method for Two-Temperature Generalized Thermoelasticity Under Thermal Shock Problem

The theory of two-temperature generalized thermoelasticity, based on Youssef's theory, was used to solve boundary value problems of one-dimensional generalized thermoelasticity half-space by heating its boundary with different types of heating. The governing equations are solved using new mathematical methods within the purview of the Lord-?hulman (L-S) theory and the classical dynamical coupled theory (CD). The general solution obtained is applied to a specific problem of a half-space subjected to one type of heating—thermal shock type. The separation of variables method is used to get the exact expressions for distributions of displacement, the stresses, and temperature distribution. Variations of the considered functions through the horizontal distance are illustrated graphically. Comparisons are made with results between the two theories. Numerical work is also performed for a suitable material and results are discussed, specifically the conductive temperature, the dynamical temperature, and the stress and strain distributions are shown graphically when discussed.     

Analysis of Thermoelastic Waves in Functionally Graded Hollow Spheres Based on the Green-Lindsay Theory

In this article, the Green–Lindsay theory of thermoelasticity is employed to study the thermoelastic response of functionally graded hollow spheres. This generalized coupled thermoelasticity theory admits the second sound phenomena and depicts a finite speed for temperature wave propagation. The materials of the hollow sphere are assumed to be graded through its thickness in the radial direction while a symmetric thermal shock load is applied to its boundary. The Galerkin finite element method via the Laplace transformation is used to solve the coupled form of governing equations. A numerical inversion of the Laplace transform is employed to obtain the results in time domain. Using the obtained solution, the temperature, displacement, radial stress, and hoop stress waves propagation are studied. Also the material distribution effects on temperature, displacement and stresses are investigated. Finally, the obtained results for the Green–Lindsay theory are compared with the results of classical thermoelasticity theory.     

Distinctive features of thermoelastic dissipation in microbeam resonators at nanoscale

In this work, thermoelastic damping in microbeam resonators is evaluated using the generalized thermoelasticity theory based on the dual-phase-lagging thermal conduction model with relaxation between temperature increment and thermal expansion. An explicit formula of thermoelastic damping has been derived. Influences of various affecting factors on thermoelastic damping, such as the beam height, aspect ratio, and relaxation time between temperature increment and thermal expansion, are examined. Numerical results show that the thermoelastic damping, obtained by the generalized thermoelasticity theory in the present study, exhibits distinctive features at nanoscale. This work reveals that non-Fourier thermal conduction and relaxation between temperature increment and thermal expansion may play a nonnegligible role at nanometer scale.     

Theory of Two-Temperature Thermoelasticity without Energy Dissipation

This paper deals with thermoelastic behavior without energy dissipation; it deals with linear theory of thermoelasticity. In particular, in this work, a new theory of generalized thermoelasticity has been constructed by taking into account two-temperature generalized thermoelasticity theory for a homogeneous and isotropic body without energy dissipation. The new theorem has been derived in the context of Green and Naghdi model of type II of linear thermoelasticity. Also, a general uniqueness theorem is proved for two-temperature generalized thermoelasticity without energy dissipation.     

Thermally nonlinear generalized thermoelasticity of a layer

This article addresses a clarification study on the thermally nonlinear Fourier/ non-Fourier dynamic coupled (generalized) thermoelasticity. Based on the Maxwell-Cattaneo’s heat conduction law and the infinitesimal theory of thermoelasticity, governing equations for the thermally nonlinear small deformation type of generalized thermoelasticity are derived. The Bubnov–Galerkin scheme is implemented for spatial discretization. The spatially discretized equations are directly discretized in time domain using the fully damped Newmark method. The Newton–Raphson procedure is used to linearize the finite element equations. The layers are exposed to a thermal shock, so that the displacement, temperature, and stress waves propagate in layers. The effects of the time evolution, thermoelastic coupling, and thermal relaxation time on the response of the layers are investigated. Results reveal the significance of the thermally nonlinear analysis of generalized thermoelasticity for the conditions where large temperature elevations exist.     

TWO-DIMENSIONAL PROBLEM IN GENERALIZED THERMOELASTICITY WITH HEAT SOURCES

In this work, a two-dimensional problem for a half-space is solved. The problem is in the context of the theory of generalized thermoelasticity with one relaxation time. The surface of the half-space is taken to be traction free and the temperature on it is specified. Heat sources permeate the medium. Laplace and exponential Fourier transform techniques are used. The solution in the transformed domain is obtained by a direct approach. The inverse double transform is evaluated numerically. Numerical results are obtained and represented graphically.     

A Domain of Influence Theorem for Thermoelasticity with Three-Phase-Lag Model

We establish the theory of domain of influence for a potential-temperature disturbance under the generalized theory of thermoelasticity with three-phase-lag model. For a finite time t > 0, it has been proved that the potential due to the displacement and the temperature fields does not produce any disturbances outside a bounded domain and the domain of influence is dependent on the support of load, the thermoelastic coupling constant and the phase-lag parameters. It has been shown that the domain of influence of the present case reduces to the domain of influence for classical thermoelasticity theory and the thermoelasticity theory with one relaxation parameter.     

On the Theory of Two-Temperature Thermoelasticity with Two Phase-Lags

The present paper is concerned with the theory of two temperature thermoelasticity with two phase-lags in which the theory of heat conduction in deformable bodies depends on two distinct temperatures – the conductive temperature and the thermodynamic temperature. A generalized heat conduction law with dual-phase-lag effects was proposed by Tzou (1995) for the purpose of considering the delayed response in times due to the microstructural interactions in the heat transport mechanism. Recently, Quintanilla (2008) has proposed to combine this constitutive equation with a two temperature heat conduction theory and has proved that a dual-phase-lag theory with two temperatures is a well-posed problem. In the present work we consider the basic equations concerning this dual-phase lag theory of two temperature thermoelasticity and make an attempt to establish some important theorems in this context. A uniqueness theorem has been established for a homogeneous and isotropic body. An alternative characterization of mixed boundary initial value problem is formulated and a variational principle as well as reciprocal principle have been established.     

GENERALIZED THERMOELASTIC PROBLEM FOR AN INFINITELY LONG HOLLOW CYLINDER FOR SHORT TIMES

In this work, we consider the one-dimensional problem for an infinitely long hollow cylinder in the context of the theory of generalized thermoelasticity with one relaxation time. The Laplace transform technique is used to solve the problem. The solution in the transformed domain is obtained by a direct approach. The inverse transforms are obtained in an approximate analytical manner using asymptotic expansions valid for small values of time. The temperature, displacement, and stress are computed and represented graphically.     

Fractional Order Generalized Thermo-Piezoelectric Semi-Infinite Medium with Temperature-Dependent Properties Subjected to a Ramp-Type Heating

The generalized thermoelasticity theory that, based on a fractional order model, is used to solve a one-dimensional boundary value problem of a semi-infinite piezoelectric medium. The resulting formulation is applied to a half-space subjected to ramp-type heating and traction free. The generalized thermo-piezoelectricity model in an isotropic elastic medium with temperature-dependent mechanical properties is established. The modulus of elasticity is taken as a linear function of the reference temperature. The Laplace transform technique is used to obtain the general solution for any set of boundary conditions. The inverse Laplace transforms are numerically computed using the Fourier expansion techniques. The effects of fractional order and the ramping of heating parameters are studied and comparison with different theories of thermoelasticity are considered. The results are also compared to results obtained in the case of a temperature-independent modulus of elasticity.     

Thermomechanical Interactions in a Generalized Thermo-Microstretch Elastic Half Space

Interactions caused by thermal and mechanical sources in a generalized thermo-microstretch elastic medium are studied by the use of Laplace-Fourier transform techniques. The formulation is applied to the coupled theory as well as to two generalizations, the Lord-Shulman and the Green-Lindsay theories. The integral transforms are inverted using a numerical technique to obtain the solutions field in the physical domain. Stretch effects lead to the existence of a new wave that is called longitudinal microstretch wave. The results of micropolar generalized thermoelasticity and generalized thermoelasticity are deduced as special cases from the present formulation.     

Two temperature fractional order thermoelasticity theory in a spherical domain

This article is an application of fractional thermoelasticity in association with two-temperature theory. The fractional heat conduction model has been proposed to investigate the thermal variations within the bounded spherical region. The corresponding heat conduction equation has been derived in the context of the generalized two-temperature theory of fractional thermoelasticity. The analytical solutions of thermal variations have been obtained in the Laplace domain, which are inverted using the Gaver–Stehfest algorithm in the time domain. Kuznetsov convergence criterion has been discussed for the bounded variations and stability of the problem. The delay time translations used in the heat flux vector and the temperature gradient result in the finite speed of thermal wave propagation. As a special case of time fractional derivative, the classical and generalized thermoelasticity theories have been recovered.     

An investigation on thermoelastic interactions under an exact heat conduction model with a delay term

The present work is concerned with a very recently proposed heat conduction model: an exact heat conduction model with a single delay term. A generalized thermoelasticity theory was proposed by Roy Choudhuri based on the heat conduction law with three-phase-lag effects for the purpose of considering the delayed response in time due to the microstructural interactions in the heat transport mechanism. However, the model defines an ill-posed problem in Hadamard sense. Quintanilla has recently proposed to reformulate this heat conduction model as an alternative heat conduction theory with a single delay term and subsequently, Leseduarte and Quintanilla investigated the spatial behavior of the solutions for this theory and they extended the results to a thermoelasticity theory by considering the Taylor series approximation of the equation of heat conduction with one delay term. In the present work, we consider the thermoelasticity theory based on this newly proposed heat conduction model and investigate a problem of thermoelastic interactions. State-space approach is used to formulate the problem and the formulation is then applied to a problem of an isotropic elastic half-space with its plane boundary subjected to sudden increase in temperature and zero stress. The integral transform method is applied to obtain the solution of the problem. A detailed analysis of analytical results is provided by finding the short-time approximated solutions of different field variables analytically and comparing the results of the present model with the corresponding results reported for other existing theories. An attempt has also been made to illustrate the problem and numerical values of field variables are obtained for a particular material. Results are analyzed with different graphs. To the best of the author\textquoteright s knowledge, this thermoelastic model is not yet investigated by any researcher in this direction.     

Eigenvalue Approach to Linear Micropolar Thermoelasticity Under Distributed Loading

The eigenvalue approach is developed for the two-dimensional problem in a micropolar thermoelastic medium for a half-space subjected to distributed loading and zero temperature change. The formulation is applied to the coupled theory as well as to two generalizations, the Lord–Shulman and the Green–Lindsay theories. The Fourier transforms are inverted analytically. The inversion of the Laplace transforms are carried out using the inversion formula of the transform together with Fourier expansion techniques. Numerical methods are used to accelerate the convergence of the resulting series and to evaluate the improper integrals involved to obtain temperature, displacement, force and couple stress in the physical domain. The results of micropolar elasticity and generalized thermoelasticity are deduced as special cases from the present formulation. Numerical results are represented graphically and discussed.     

Three-Dimensional Fractional Order Generalized Thermoelastic Problem Under the Effect of Rotation in a Half Space

The current article is concerned with three-dimensional problems for a homogeneous, isotropic thermoelastic half-space subjected to a time-dependent heat source on the surface, which is traction-free under the effect of rotation. The governing equations are taken in the context of fractional order generalized thermoelasticity (Green–Lindsay) theory. Normal mode analysis technique and eigenvalue approaches have been used to solve the non-dimensional equations. Numerical results for temperature, thermal stress and displacement distributions are presented graphically and discussed.     

Propagation of the photothermal waves in a semiconducting medium under L-S theory

The model of the equations of generalized thermoelasticity based on the Lord–Shulman theory with one relaxation time is used to study the photothermal waves in a semiconducting medium. The exact expressions for the displacement components, temperature, carrier density, and stress components are obtained using normal mode analysis. Numerically simulated results are obtained and presented graphically for silicon to depict the effect of time parameter on the different physical quantities.     

Thermoelastic Material Response Due to Laser Pulse Heating in Context of Four Theorems of Thermoelasticity

This article describes the study of induced temperature and stress fields in an elastic half-space in the context of classical coupled thermoelasticity (Biot) and generalized thermoelasticity (Lord–Shulman, Green–Lindsay and Green–Naghdi) in a unified system of equations. The medium is considered to be made of an isotropic homogeneous thermoelastic half-space. The bounding plane of the surface is heated by a non-Gaussian laser beam with pulse duration of 2 ps. An exact solution of the problem is first obtained in Laplace transform space. Because the response is of more interest in the transient state, the inversion of Laplace transforms were carried out numerically. The derived expressions were computed numerically for copper, and the results are presented in graphical form.