The reference temperature dependence of Young’s modulus of two-temperature thermoelastic damping of gold nano-beam

This work is concerning with the study of the thermoelastic damping of a nanobeam resonator in the context of the two-temperature generalized thermoelasticity theory. An explicit formula of thermoelastic damping has been derived when Young’s modulus is a function of the reference temperature. Influences of the beam height and Young’s modulus have been studied with some comparisons between the Biot model and the Lord–Shulman model (L–S) for one- and two-temperature types. Numerical results show that the values of the thermal relaxation parameter and the two-temperature parameter have a strong influence on thermoelastic damping at nanoscales.     

Two-Temperature Generalized Thermoelastic Interactions in an Infinite Body with a Spherical Cavity

This paper is concerned with the determination of the thermoelastic displacement, stress, conductive temperature, and thermodynamic temperature in an infinite isotropic elastic body with a spherical cavity in the context of the two-temperature generalized thermoelasticity theory (2TT). The two-temperature Lord-Shulman (2TLS) model and two-temperature Green–Naghdi (2TGN) models of thermoelasticity are combined into a unified formulation introducing the unified parameters. The medium is assumed initially quiescent. The basic equations have been written in the form of a vector-matrix differential equation in the Laplace transform domain which is then solved by (a) the state-space approach and (b) the eigenvalue approach for any set of boundary conditions. The general solution obtained is applied to a specific problem when the boundary of the cavity is subjected to thermomechanical loading. The numerical inversion of the transform is carried out using Fourier-series expansion techniques. The computed results for thermoelastic stresses, conductive temperature, and thermodynamic temperature are shown graphically for the Lord Shulman model and for two models of Green–Naghdi and the effects of two temperatures are discussed. A comparative study of the two methods has also been carried out.     

Effects of thermal relaxation time on plane wave propagation under two-temperature thermoelasticity

The present paper is concerned with an in-depth investigation of the propagation of harmonic plane waves in elastic media in the context of the linear theory of two-temperature generalized thermoelasticity. The exact dispersion relation solutions for the longitudinal plane wave are determined analytically. Asymptotic expansions of several characterizations of the wave field, like phase velocity, specific loss and penetration depth of the dilatational waves, are obtained for both the high frequency as well as low frequency values. The effects of thermal relaxation parameter on the plane wave is analyzed in details by comparing the theoretical as well as numerical results of the present work with the corresponding results in the context of classical two-temperature thermoelasticity theory as reported earlier.     

Effect of Gravitational Field and Temperature Dependent Properties on Two-Temperature Thermoelastic Medium with Voids under G-N Theory

This investigation is aimed to study the two dimensional problem of thermoelastic medium with voids under the effect of the gravity. The modulus of elasticity is taken as a linear function of the reference temperature and employing the two-temperature generalized thermoelasticity. The problem is studied in the context of Green-Naghdi (G-N) theory of types II and III. The normal mode analysis method is used to obtain the exact expressions for the physical quantities which have been shown graphically by comparison between two types of the (G-N) theory in the presence and the absence of the gravity, the temperature dependent properties and the two-temperature effect.     

A Nonlinear Generalized Thermoelasticity Model of Temperature-Dependent Materials Using Finite Element Method

In this article, a general finite element method (FEM) is proposed to analyze transient phenomena in a thermoelastic model in the context of the theory of generalized thermoelasticity with one relaxation time. The exact solution of the nonlinear model of the thermal shock problem of a generalized thermoelastic half-space of temperature-dependent materials exists only for very special and simple initial- and boundary problems. In view of calculating general problems, a numerical solution technique is to be used. For this reason, the FEM is chosen. The results for the temperature increment, the stress components, and the displacement component are illustrated graphically with some comparisons.     

Study of deflection and damping in microbeam resonator based on microstretch thermoelastic theory

This article deals with the deflection and thermoelastic damping analysis in homogeneous, isotropic, micropolar microstretch generalized thermoelastic thin beam based on Euler–Bernoulli theory. Analytical expressions for deflection, thermoelastic damping, frequency shift, temperature distribution and microstretch functions have been obtained for various boundary conditions viz. clamped, simply supported and cantilever beam by using Laplace transform technique. The analytical results have been numerically analyzed with the help of MATLAB software in case of magnesium like materials. The computed results have been presented graphically in view of various boundary conditions.     

Fractional order two-temperature thermoelasticity with finite wave speed

In this paper, a new theory of two-temperature generalized thermoelasticity is constructed in the context of a new consideration of heat conduction with fractional orders. The two-temperature Lord–Shulman (2TLS) model and two-temperature Green–Naghdi (2TGN) models of thermoelasticity are combined into a unified formulation using the unified parameters. The basic equations have been written in the form of a vector-matrix differential equation in the Laplace transform domain which is then solved by using a state-space approach. The inversions of Laplace transforms are computed numerically using the method of Fourier series expansion technique. The numerical estimates of the quantities of physical interest are obtained and depicted graphically. Some comparisons of the thermophysical quantities are shown in figures to estimate the effects of the temperature discrepancy and the fractional order parameter.     

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

The propagation of plane waves in a fiber-reinforced, anisotropic thermoelastic half-space proposed by Lord–Shulman under the effect of a magnetic field is discussed. The problem has been solved numerically using a finite element method. Numerical results for the temperature distribution, the displacement components, and the thermal stress are given and illustrated graphically. Comparisons are made with the results predicted by the theory of generalized thermoelasticity with one relaxation time for different values of time. It is found that the reinforcement has a great effect on the distribution of field quantities.     

Transient Disturbance in a Half Space Under Thermoelasticity with Two Relaxation Times Due to Moving Internal Heat Source

In this paper transient waves caused by a line heat source moving with a uniform velocity inside isotropic homogeneous thermoelastic half-space are studied under the GL model of generalized thermoelasticity. The problem is reduced to the solution of three differential equations by introducing the elastic vector potential and the thermoelastic scalar potential. Using Laplace and Fourier transforms solutions are obtained in transforms domain. Applying inverse transforms approximate solutions of the displacement at the boundary valid in the small time range are given. Also the approximate region valid for the solutions is given and two special cases, (i) the source is motionless and (ii) the relaxation times vanish, are studied. Numerical evaluations are presented for the medium of copper.     

A 2D problem of time-fractional heat order for two-temperature thermoelasticity under hydrostatic initial stress

The present study solves the problem of thermoelastic interactions in a half-space medium under hydrostatic initial stress in the context of a fractional order heat conduction model with two-temperature theory. The analytical solutions of the field variables are obtained by using the normal mode analysis. The obtained solutions are then applied to a specific problem for a thermally insulated surface which is acted upon by a load. The distributions of the two temperatures, displacements, and the stress components inside the half-space are studied. The graphical results depict that the fractional parameter has significant effects on all the studied field variables. Comparisons are made within the theory in the presence and absence of the hydrostatic initial stress. Thus, we can conclude that the fractional order generalized thermoelasticity model may be an improvement on studying elastic materials.     

Thermoelastic vibration analysis of Mems/Nems plate resonators with voids

In this paper, the effect of voids, relaxation times, thermomechanical coupling, surface conditions, and plate dimensions on energy dissipation induced by thermoelastic damping in microelectronics mechanical systems (MEMS)/ nanoelectronics mechanical systems (NEMS) resonators are investigated. Closed form expressions for the transverse vibrations of a homogenous isotropic, thermoelastic thin plate with voids, based on Kirchhoff theory have been derived. The exact solutions for the free vibrations of plates under clamped-simply supported (CS) and simply supported-simply supported (SS) conditions are obtained. Analytical expressions for deflection, temperature change, frequency shifts, and thermoelastic damping in the plate have been derived. Some numerical results with the help of MATLAB programming software in case of silicon nitride and magnesium like material have also been presented.     

Dispersion of Thermoelastic Waves in a Plate With and Without Energy Dissipation

In this paper, the dispersion and energy dissipation of thermoelastic plane harmonic waves in a thin plate bounded by insulated traction-free surfaces is studied on the basis of three generalized theories of thermoelasticity. The frequency equations corresponding to the symmetric and antisymmetric modes of vibration of the plate are obtained. Some limiting and particular cases of the frequency equations are then discussed. Results obtained in three theories of generalized thermoelasticity are compared. The results for the coupled thermoelasticity can be obtained as particular cases of the results by setting thermal relaxations times equal to zero. Numerical evaluations relating to the lower modes of the symmetric and antisymmetric waves are presented for an aluminum alloy plate.     

Plane Strain Deformation in Generalized Thermoelastic Diffusion

The present investigation is concerned with plane strain deformation in homogeneous isotropic generalized thermoelastic diffusion subjected to a normal force, thermal source, and chemical potential source. Laplace and Fourier transform techniques are employed to solve the problem. The integral transform have been inverted by using a numerical technique to obtain the displacements, stresses, temperature distribution, and chemical potential distribution. The numerical results of these quantities are illustrated graphically to depict the response of various sources in the theories of thermoelastic diffusion and thermoelasticity for a particular model. Some particular cases have been deduced from the present investigation.     

A Generalized Thermoelasticity Problem for a Half-Space with Heat Sources and Body Forces

In this work, a two-dimensional problem of distribution of thermal stresses and temperature in a linear theory of a generalized thermoelastic half-space under the action of a body force and subjected to a thermal shock on the bounding plane is considered. Heat sources permeate the medium. The problem is in the context of the theory of generalized thermoelasticity with one relaxation time. 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.     

Propagation of Waves Through Cylindrical Bore in a Cubic Micropolar Generalized Thermoelastic Medium

The article deals with the propagation of axial symmetric cylindrical surface waves in a cylindrical bore through a micropolar thermoelastic medium of infinite extent possessing cubic symmetry. The theories of generalized thermoelasticity developed by Lord and Shulman and Green and Lindsay are used to study the problem. The frequency equations, connecting the phase velocity with the wave number, radius of bore, and other material parameters for empty and liquid-filled bores are derived. Some special cases have been deduced. The numerical results obtained have been illustrated graphically to understand the behavior of the phase velocity and attenuation coefficient versus the wave number.     

Generalized thermoelasticity with memory-dependent derivatives involving two temperatures

A new generalized model of two-temperature thermoelasticity theory with time-delay and Kernel function is constructed. Taylor theorem in terms of memory-dependent derivatives is proved. The governing coupled equations of the new generalized thermoelasticity with time-delay and Kernel function, which can be chosen freely according to the necessity of applications, are applied to a one-dimensional problem of a half-space. The bounding surface is taken to be traction free and subjected to a time-dependent thermal shock. Laplace transforms technique will be used to obtain the general solution in a closed form. A numerical method is employed for the inversion of the Laplace transforms. According to the numerical results and its graphs, conclusions about the new theory have been constructed. Some comparisons are shown in the figures to estimate the effects of the temperature discrepancy and time-delay parameter on all of the studied fields.     

Uniqueness and reciprocity theorems in generalized linear micropolar thermoviscoelasticity

A model of the equations of generalized linear micropolar thermoviscoelasticity is given. The formulation is 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 Chandrasekharaiah-Tzou theory with dual-phase-lag. Using Laplace transforms, a uniqueness theorem for this model is proved, restrictions on relaxation functions are deduced and the dynamic reciprocity theorem is derived. The cases of generalized linear micropolar thermoviscoelasticity of Kelvin-Voigt model, generalized linear micropolar thermoelasticity, generalized thermoviscoelasticity and generalized thermoelasticity can be obtained from the given general model.     

A finite element formulation for thermoelastic damping analysis

We present a finite element formulation based on a weak form of the boundary value problem for fully coupled thermoelasticity. The thermoelastic damping is calculated from the irreversible flow of entropy due to the thermal fluxes that have originated from the volumetric strain variations. Within our weak formulation we define a dissipation function that can be integrated over an oscillation period to evaluate the thermoelastic damping. We show the physical meaning of this dissipation function in the framework of the well‐known Biot's variational principle of thermoelasticity. The coupled finite element equations are derived by considering harmonic small variations of displacement and temperature with respect to the thermodynamic equilibrium state. In the finite element formulation two elements are considered: the first is a new 8‐node thermoelastic element based on the Reissner–Mindlin plate theory, which can be used for modeling thin or moderately thick structures, while the second is a standard three‐dimensional 20‐node iso‐parametric thermoelastic element, which is suitable to model massive structures. For the 8‐node element the dissipation along the plate thickness has been taken into account by introducing a through‐the‐thickness dependence of the temperature shape function. With this assumption the unknowns and the computational effort are minimized. Comparisons with analytical results for thin beams are shown to illustrate the performances of those coupled‐field elements. Copyright © 2008 John Wiley & Sons, Ltd.     

Impulsive effect on an elastic solid with generalized thermodiffusion

The theory of generalized thermoelastic diffusion with one relaxation time is employed to study the distribution of temperature, displacement components, stresses, concentration and chemical potential in a semi-infinite medium having an impulsive mechanical load at the origin. Using the joint Laplace and Fourier transforms, the governing equations are transformed into a vector–matrix differential equation which is then solved by the eigenvalue approach. The solution of the problem in the physical domain is obtained numerically using a numerical method for the inversion of the Laplace and Fourier transforms. Results of this work are presented graphically and are compared with the results of generalized thermoelasticity and classical elasticity deduced as special cases.     

Thermoelastic response in a symmetric spherical shell

This paper is concerned with the determination of thermoelastic stresses, strain and conductive temperature in a spherically symmetric spherical shell. The two-temperature three-phase-lag thermoelastic model (2T3P) and two-temperature Green–Naghdi model III (2TGNIII) are combined into a unified formulation. There is no temperature at the outer boundary, and thermal load is applied at the inner boundary. The basic equations have been written in the form of a vector–matrix differential equation in the Laplace transform domain which is then solved by the state-space approach. The numerical inversion of the transform is carried out using Fourier series expansion techniques. Because of the short duration of the second sound effects, small time approximations of the solutions are studied. The physical quantities have been computed numerically and presented graphically in a number of figures. A complete and comprehensive analysis of the results has been presented for the 2T3P and the 2TGNIII models. These results have also been compared with those of the one-temperature three-phase-lag thermoelastic model (1T3P) and one-temperature Green–Naghdi model III (1TGNIII).