Generalized Thermoelasticity Theory Research Articles

A domain of influence theorem under MGT thermoelasticity theory

The purpose of this article is to discuss domain of influence results under the Moore–Gibson–Thompson (MGT) thermoelasticity theory. We employ a mixed initial–boundary value problem concerning a homogeneous and isotropic material in view of the MGT thermoelasticity theory and establish the domain of influence theorem for potential–temperature disturbance. This theorem implies that the coupling of potential and temperature generates a thermoelastic disturbance, which vanishes outside the bounded domain for a prescribed bounded support of thermomechanical loading and for a finite time. The resulted bounded domain is subjected to the support of the prescribed load. The finite propagation of thermoelastic disturbance is also analyzed under the MGT theory, where the propagation speed depends on the parameters of the thermoelastic material. It is further shown that the domain of influence result for the present context reduces to the domain of influence result derived in the generalized thermoelasticity theory of Lord and Shulman under some conditions.

Ramp-type heating microtemperature for a rotator semiconducting material during photo-excited processes with magnetic field

The main objective of this discussion is to examine the interaction between the magnetic field and the excited semiconductor medium during the microtemperature process. The photothermal theory is used to obtain the main variables based on the generalized thermoelasticity theory of a rotator medium. The elastic-plasma-thermal transport processes in two-dimensions (2D) have been constructed. Moreover, the Fourier and Laplace integral transformations are used for the main governing equations under the influence of microtemperature vector field. The analytical solutions of the basic physical field quantities are obtained in the physical domain. The ramp type heating and some other mechanical-thermal-elastic-plasma conditions are applied on the free surface of the medium to determine the unknown parameters. To obtain the complete solutions of the main physical field quantities, the numerical inversion techniques of Fourier and Laplace transformations are used in space–time physical domain. Some comparisons are carried out for some several parameters graphically and discussed.

Effects of nonlocal thermoelasticity on nanoscale beams based on couple stress theory

A modified nonlocal Bernoulli–Euler model was established in this paper to analyze thermoelastic interactions in isotropic nanobeams subjected to ramp‐type heating, depending on the modified couple stress and generalized thermoelasticity theories. To solve this problem, the thermoelasticity theory with one thermal relaxation time (Lord–Shulman [LS]) is proposed. Due to the modified couple stress, the analytical expressions for deflection, temperature, flexure moment, and displacement in the nanobeam were obtained by using the Laplace transform technique. In addition, comparisons were shown in graphs to estimate the effects of the various parameters such as the couple stress, and the ramping time parameter on all the fields studied under consideration. Also, the numerical results are provided to demonstrate the small‐scale impact on the resonator of the nanobeams.

Generalized Thermoelastic Functionally Graded on a Thin Slim Strip Non-Gaussian Laser Beam

The present study utilizes the generalized thermoelasticity theory, with one thermal relaxation time (TR), to examine the thermoelastic problem of a functionally graded thin slim strip (TSS). The authors heated the plane surface bounding using a non-Gaussian laser beam with a pulse length of 2 ps. The material characteristics varied continually based on exponential functions. Moreover, the equations governing the generalized thermoelasticity for a functionally graded material (FGM) are recognized. The problem’s ideal solution was primarily obtained in the Laplace transform (LT) space. The LTs were converted numerically because of the considerable importance of the response in the transient state. For a hypothetical substance, the numerical procedures calculating the displacement, stress, temperature and strain were given. The analogous problem solution to an isotropic homogeneous material was provided by defining the parameter of non-homogeneity adequately. The obtained results were displayed using graphs to illustrate the extent to which non-homogeneity affected displacement, stress, temperature and strain. A comparison was been made between the present study and those previously obtained by others, when the new parameters vanish to show the impact of the non-homogeneity, TSS and laser parameters on the phenomenon. The results obtained indicate a significant strong impact of FGM, TSS and laser parameters.

A Modified Thermoelastic Fractional Heat Conduction Model with A Single-Lag and Two Different Fractional-Orders

Recently, fractional calculus theory has been successfully employed in generalized thermoelasticity theory and several models with fractional order have been introduced. In this work, a fractional thermoelastic modified Fourier's Law with phase lag and two different fractional-orders has been constructed. The previous fractional models of thermoelasticity introduced by Sherief et al. [1], Ezzat [2] and Lord and Shulman [3] as well as classical coupled thermoelasticity [4] follow as limiting cases. This proposed model is applied to an infinitely annular cylinder that is subject to time-dependent surface temperatures, and whose surfaces are free of traction. The method of the Laplace transform is employed to get the solutions of the field variables. A numerical technique is utilized to invert the Laplace transforms. Some results are presented in tables and figures to extract the effects of fractional order parameters on all variables studied. The theory's predictions have been checked and compared to previous models.

Eigenfunction approach to generalized thermo-viscoelasticity with memory dependent derivative due to three-phase-lag heat transfer

The present article investigates a new mathematical model of generalized thermo-viscoelasticity based on memory-dependent derivative in the context of three-phase-lag heat transfer subjected to an instantaneous point heat source. The governing coupled equations associated with kernel function and time delay are constituted for a two-dimensional problem of semi-infinite space in an isotropic medium. The bounding surface of the half-space is assumed to be subjected to a time-dependent thermal shock and rigidly fixed. The Eigenfunction expansion approach is proposed to analyze the problem and, consequently, the analytical solutions of the thermodynamic field variables viz. temperature, displacement and stresses are obtained in the Laplace-Fourier transformed domain. The effects of the kernel function and time-delay factor on the distributions of the non-dimensional thermodynamic field variables are presented graphically and compared with the several well-known generalized thermoelasticity theories present in the literature. Finally, some remarkable points are mentioned in conclusion.

Thermoelastic damping analysis in microbeam resonators based on Moore–Gibson–Thompson generalized thermoelasticity theory

Microbeam resonators are widely used due to their scientific and engineering applications. The accurate prediction of thermoelastic damping (TED) is necessary to evaluate the performance of resonators at micro- and nanoscales with less energy dissipation. This article aims to present an analytical method for analyzing TED and dynamic behavior of microbeam resonators based on the Moore–Gibson–Thompson (MGT) generalized thermoelasticity theory. The finite Fourier sine transform and Laplace transform methods are used to solve the coupled thermoelastic equations. The analytical solutions are obtained for deflection and thermal moment of beams. The vibration responses of deflection and thermal moment are established in microbeams with simply supported and isothermal boundary conditions. The responses of deflection and thermal moment in beams are analyzed by comparing the results obtained under the MGT model with the corresponding results under the Lord–Shulman (LS) and Green–Naghdi (GN-III) models. The obtained results show that the amplitudes of deflection and thermal moment are attenuated, and the vibration frequency is increased due to the effect of thermoelastic coupling. It has been observed that the amplitudes of deflection under these three models are approximately the same, while the amplitude of thermal moment under the MGT model is higher than under the GN-III model and agrees with the LS model. It has been further noticed that TED depends on the size of the beams when the thermoelastic coupling effect is considered.

Nonlinear vibrations of graphene piezoelectric microsheet under coupled excitations

Investigated herein are the nonlinear vibration characteristics of a rectangular microsheet comprising micro fiber composite with graphene (GP) skin under coupled excitations. Owing to the good thermal conductivity of GP, the heat sink performance of the GP skin is also considered. In this study, the constitutive relation for the microsheet is established by applying the Eringen theory and the governing equations for nonlinear dynamics of the microsheet are obtained from the principle of conservation of energy. The Green and Naghdi’s generalized thermo-elasticity theory and the Galerkin weighted residual method are employed to describe the thermo-elasticity coupling effect of the MFC-GP microsheet. The positive piezoelectric effects of graphene and MFC are also taken into consideration. Next, the coupled ordinary differential equations of thermo-elasticity-electricity are obtained by the Galerkin discrete method. Finally, the nonlinear frequency response equations of the microsheet are derived through the multi-scale method. By using the global residual harmonic balance method, nonlinear vibration characteristic of the MFC-GP microsheet are discussed with respect to nonlocal parameters, volume fraction of graphene, and aspect ratio, which have a significant impact on the dynamic behaviors of the microsheet. The findings will provide a theoretical guidance for engineering design of such microsheets.

Analysis of harmonic plane wave propagation predicted by strain and temperature-rate-dependent thermoelastic model

ABSTRACT The present work is concerned with a novel generalized thermoelasticity theory introduced by Yu et al. [A modified Green-Lindsay thermoelasticity with strain rate to eliminate the discontinuity. Meccanica. 2018;53:2543–2554] which considers the strain-rate along with temperature-rate term in the constitutive equations. This theory is an attempt to modify the Green-Lindsay (GL) thermoelasticity theory. For an unbounded isotropic homogeneous elastic medium, the present work analyzes the propagation of plane harmonic waves in the context of this new theory. In order to investigate the effects of strain-rate term, the unified governing equations related to three thermoelastic models namely, classical coupled thermoelastic model, GL model and new model have been considered. The dispersion relation for the propagation of longitudinal plane waves in the contexts of all three models has been derived in a unified way, which is further solved by the computational tool for a particular material. The behavior of different wave components for longitudinal waves is examined through graphical representation and the effects of temperature-rate and strain-rate terms on the plane wave propagation are investigated. Significant differences in predictions by this new model as compared to other models are highlighted.

A novel model of nonlocal thermoelasticity with time derivatives of higher order

The objective of this work is to introduce a new system of differential equations describing the nonlocal thermoelasticity theory with higher time derivatives and two‐phase lags. In order to obtain this model, we used the nonlocal continuum theory proposed by Eringen and the methodology of the Taylor series expansion of higher‐order time derivatives. Some generalized thermoelasticity theories follow as limited cases. This model is used to study the thermoelastic interaction in a nonlocal medium. The medium is exposed to an applied magnetic field and a periodic time heat source with a constant strength. Some comparisons have been displayed in figures to estimate the influences of the nonlocal parameter and magnetic field as well as the parameters of higher‐order on all the field quantities.

Waves in generalized thermo-viscoelastic infinite continuum with cylindrical cavity due to three-phase-lag time-nonlocal heat transfer

Generalized thermoelastic interactions due to three-phase-lag time-nonlocal heat transfer in a Kelvin-Voigt type infinitely extended visco-thermoelastic continuum with cylindrical cavity has been investigated. The two-temperature generalized thermoelasticity theory has also been taken into account. The problem has been solved in the domain of Laplace on the assumption that the surface of the cavity is free from traction and is subjected to a smooth and time-dependent-heating effect. Laplace inversion of the transformed solutions has been carried out numerically. The obtained numerical data for different considerations are plotted in graphs to study the effects of time-nonlocal parameter, two-temperature parameter and visco-thermoelastic relaxation parameter on different thermoelastic quantities of physical interest.

Nonlinear Dynamics of Composite Microsheet with Graphene Skins in Non-uniform Thermal Field

The effects of different parameters on the nonlinear dynamic characteristics of macrofiber composite (MFC) microsheet with graphene (GP) skin under non-uniform thermal field are investigated. Firstly, the physical parameters of the MFC–GP structure are calculated by the mixing rule, and the constitutive equations of the structure are set up by employing the Eringen theory. The nonlinear dynamic equations of the microsheet are obtained by using Hamilton’s principle. Then, the heat conduction equations of the microsheet are considered, adopting Green and Naghdi’s generalized thermoelasticity theory. According to the Galerkin weighted residual method, the thermoelasticity coupling equations of the structure are obtained. Meanwhile, the influence of the positive piezoelectric effect of GP and MFC on the vibration response of the structure is also investigated. The nonlinear dynamic governing equations including displacement, coupled thermoelasticity, and electricity field are discretized by the Galerkin method. The effects of non-local parameter, volume fraction of GP, and thermal and electricity coupling coefficients on structural dynamic behavior are discussed in the numerical simulation.

Thermoelastic interactions on hyperbolic two-temperature generalized thermoelasticity in an infinite medium with a cylindrical cavity

The thermoelastic interactions in an infinite elastic medium with a cylindrical cavity are described in the context of the hyperbolic two-temperature generalized thermoelasticity theory (recently proposed by Youssef and El-Bary, 2018) in which heat conduction in deformable bodies depends upon the difference between the acceleration of conductive temperature and the acceleration of dynamic temperature. The boundary of the cavity is assumed to be stress-free and is subjected to a thermal shock. The problem is formulated to compare between classical generalized thermoelastic model and hyperbolic two-temperature thermoelastic model, on the basis of Lord-Shulman model and hyperbolic two-temperature Lord-Shulman model in a unified way. The Laplace transform method and decoupling of the coupled differential equations are used to solve the problem. Explicit expressions for displacement, stresses and temperature fields are approximated for small-time. Numerical values are displayed graphically for different models and comparison is presented for the illustration of the problem.

On the fundamental solutions for the strain and temperature rate-dependent generalized thermoelasticity theory

The present paper concerns with the fundamental solutions for strain and temperature rate-dependent thermoelasticity theory recently developed by Yu et al. (2018). This recently developed model is theoretically established with the aid of principles of thermodynamics and by adding the strain-rate term in temperature rate-dependent thermoelasticity theory, which was proposed by Green and Lindsay (GL)(1972). This model has attempted to remove the drawback of discontinuity in the displacement field under Green-Lindsay (GL) model. We consider this modified Green-Lindsay (MGL) model for the case of homogeneous and isotropic bodies. Two cases, namely, concentrated body force and concentrated heat source have been taken for deriving the fundamental solutions for thermoelasticity in the context of MGL model. The fundamental solutions for the distributions of displacement components and temperature are obtained by the Laplace transform method. Fundamental solutions in the physical domain are obtained by Laplace inversion and the solution of displacement and temperature is obtained for short-time approximation. Lastly, we get the fundamental solution of the system of equations in the case of steady oscillations.

Analytical solution of magneto-photothermal theory during variable thermal conductivity of a semiconductor material due to pulse heat flux and volumetric heat source

In this investigation, the variable thermal conductivity, which depends on a linear function of temperature, is studied during photothermal excitation processes. The influence of the external magnetic field in the context of volumetrically heat source (optically external source) of an elastic semiconductor medium is investigated. The influence of pulse heat flux and thermal memory of the generalized thermoelasticity theory is taken into consideration. The governing equations are obtained in one dimension (1D) by cylindrical coordinates. The interactions between Photo (carrier density)-elastic and magneto-thermal waves are described analytically. The Laplace transform method in 1D is used to obtain the solutions of principal physical field quantities under investigation. The mechanical deformation during the mechanical loads and thermal gradient temperature are applied on the outer surface of the medium. Fourier series expansion and some numerical techniques are used to get the complete solution of physical fields in the physical time-domain. The resulting physical quantities are obtained numerically, discussed, and graphically presented for an example of a semiconductor material.

Fractional Order Two Temperature Generalized Thermoelasticity in a Symmetric Spherical Shell

This paper deals with the determination of thermoelastic stresses, strain and conductive temperature in a spherically symmetric spherical shell in the context of the fractional order two temperature generalized thermoelasticity theory (2TT). The two temperature three-phase-lag thermoelastic model (2T3P) and two temperature Green Naghdi model III (2TGN-III) 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. The physical quantities have been computed numerically and presented graphically. The effect of the fractional order parameter on the solutions has been studied and the comparisons among different thermoelastic models are made.

Photothermal excitation processes with refined multi dual phase-lags theory for semiconductor elastic medium

The aim of this investigation is to study a refined multi-phase-lags generalized thermoelasticity theory and coupled plasma theory for a semi-infinite semiconductor elastic medium. The model is studied in context of the Photothermal transport process for isoropic homogenous two dimension medium. The governing equations describe the interaction between elastic-plasma-thermal waves. The normal mode technique is used to get the exact solutions analytically of main physical quantities under investigation. The thermal-plasma and mechanical loads are applied at the free surface of semiconductor medium to obtain the complete solution of the temperature, displacement, stresses and carrier density distributions. Some special cases have been obtained. Results will be displayed graphically and discussed. Comparisons are made between the different theories in thermoelasticity.

Two-dimensional problem of two-temperature generalized thermoelasticity using memory-dependent heat transfer: an integral transform approach

We investigate the thermoelastic interactions in an isotropic and homogeneous perfectly conducting two-dimensional semi-infinite elastic medium. The bounding surface of the medium is assumed as stress free and subjected to a time-dependent thermal shock. A new two-temperature generalized thermoelasticity theory with memory-dependent derivative is employed for this study. The combined Laplace–Fourier transforms are applied to solve the non-dimensional governing equations to find the solutions for the field variables in the transform domain. An application is considered to enable us to get complete solutions. Numerical results of the field variables are presented graphically to discuss the effect of various parameters of interest.

Reflection of plane waves in generalized thermoelasticity of type III with nonlocal effect

The generalized thermoelasticity theory based upon the Green and Naghdi model III of thermoelasticity as well as the Eringen's nonlocal elasticity model is used to study the propagation of harmonic plane waves in a nonlocal thermoelastic medium. We found two sets of coupled longitudinal waves, which are dispersive in nature and experience attenuation. In addition to the coupled waves, there also exists one independent vertically shear‐type wave, which is dispersive but experiences no attenuation. All these waves are found to be influenced by the elastic nonlocality parameter. Furthermore, the shear‐type wave is found to face a critical frequency, while the coupled longitudinal waves may face critical frequencies conditionally. The problem of reflection of the thermoelastic waves at the stress‐free insulated and isothermal boundary of a homogeneous, isotropic nonlocal thermoelastic half‐space has also been investigated. The formulae for various reflection coefficients and their respective energy ratios are determined in various cases. For a particular material, the effects of the angular frequency and the elastic nonlocal parameter have been shown on phase speeds and the attenuation coefficients of the propagating waves. The effect of the elastic nonlocality on the reflection coefficients and the energy ratios has been observed and depicted graphically. Finally, analysis of the various results has been interpreted.

Memory response on thermoelastic deformation in a solid half-space with a cylindrical hole

The present article deals with the memory response on thermal wave propagation emanating from a cylindrical hole in an unbounded thermoelastic solid. Here, we have theoretically demonstrated two aspects of thermal waves in elastic materials with memory. First, the characteristics of thermoelastic disturbances originated from the hole in an unbounded elastic solid under the light of generalized thermoelasticity theory with memory-dependent derivatives (MDDs). For numerical implementation, cylindrical polar coordinate system with radial symmetry is considered. An integral transform method and, while in inverse transformation, an efficient and pragmatic NILT (numerical inverse Laplace transform) is adopted. Second, a comparison study is being made on the memory response of thermal waves with and without energy dissipation into the medium. Finally, parameter studies are performed to evaluate the effect of the kernel function and time delay. For thermal wave, the results show appreciable differences with those in the usual thermoelasticity theory.