Two-temperature Generalized Thermoelasticity Theory Research Articles

Fractional-order strain of an infinite annular cylinder based on Caputo and Caputo–Fabrizio fractional derivatives under hyperbolic two-temperature generalized thermoelasticity theory

Fractional-order strain of an infinite annular cylinder based on Caputo and Caputo–Fabrizio fractional derivatives under hyperbolic two-temperature generalized thermoelasticity theory

Characterization of the Vibration and Strain Energy Density of a Nanobeam under Two-Temperature Generalized Thermoelasticity with Fractional-Order Strain Theory

In this work, fractional-order strain theory was applied to construct a novel model that introduces a thermal analysis of a thermoelastic, isotropic, and homogeneous nanobeam. Under supported conditions of fixed aspect ratios, a two-temperature generalized thermoelasticity theory based on one relaxation time was used. The governing differential equations were solved using the Laplace transform, and their inversions were found by applying the Tzou technique. The numerical solutions and results for a thermoelastic rectangular silicon nitride nanobeam were validated and supported in the case of ramp-type heating. Graphs were used to present the numerical results. The two-temperature model parameter, beam size, ramp-type heat, and beam thickness all have a substantial influence on all of the investigated functions. Moreover, the parameter of the ramp-type heat might be beneficial for controlling the damping of nanobeam energy.

Diagonalization Method to Hyperbolic Two-Temperature Generalized Thermoelastic Solid Sphere under Mechanical Damage Effect

This study is the first to use the diagonalization method for the new modelling of a homogeneous, thermoelastic, and isotropic solid sphere that has been subjected to mechanical damage. The fundamental equations were derived using the hyperbolic two-temperature generalized thermoelasticity theory with mechanical damage taken into account. The outer surface of the sphere has been assumed to have been shocked thermally without cubical dilatation. The numerical results for the dynamical and conductive temperatures increment, strain, displacement, and average of the principal stresses components have been represented graphically with different values of the hyperbolic two-temperature parameter and mechanical damage parameters. The two-temperature model parameter and the mechanical damage parameter have significant effects. The propagations of the thermomechanical waves take place at finite speeds in the context of the hyperbolic two-temperature theory as well as in the usual context of the Lord–Shulman theory with one-temperature.

Effect of two-temperature parameter on thermoelastic vibration in micro and nano beam resonator

Thermoelastic vibration of micro and nano-beam resonators is described by the Euler-Bernoulli beam theory in context with two-temperature generalized thermoelasticity theory. The amplitude of deflection and thermal moment in the case of simply supported and the isothermal beam are obtained by the Laplace transform method along with the finite Fourier sine transform method and the vibration frequency is examined by the normal mode analysis when the beam-ends are clamped and isothermal. The effects of the two-temperature parameter and micro and nano-beam thickness on the amplitude of deflection, thermal moment, and thermoelastic vibration frequency of the micro and nano-beam resonator have been studied and shown with the numerical results. A comparison of the results with the corresponding results of the two-temperature generalized thermoelasticity (2TLS) and the Lord-Shulman (LS) theories is also presented. Besides, the size dependency nature of the micro and nano-beam is analyzed by analytical and numerical results.

The Fractional Strain Influence on a Solid Sphere under Hyperbolic Two-Temperature Generalized Thermoelasticity Theory by Using Diagonalization Method

This article constructs a mathematical model based on fractional-order deformations for a one-dimensional, thermoelastic, homogenous, and isotropic solid sphere. In the context of the hyperbolic two-temperature generalized thermoelasticity theory, the governing equations have been established. Thermally and without deformation, the sphere’s bounding surface is shocked. The singularities of the functions examined at the center of the world were decreased by using L’Hopital’s rule. Numerical results with different parameter fractional-order values, the double temperature function, radial distance, and time have been graphically illustrated. The two-temperature parameter, radial distance, and time have significant effects on all the studied functions, and the fractional-order parameter influences only mechanical functions. In the hyperbolic two-temperature theory as well as in one-temperature theory (the Lord-Shulman model), thermal and mechanical waves spread at low speeds in the thermoelastic organization.

Thermal-stress analysis of a damaged solid sphere using hyperbolic two-temperature generalized thermoelasticity theory

This work aims to study the influence of the rotation on a thermoelastic solid sphere in the context of the hyperbolic two-temperature generalized thermoelasticity theory based on the mechanical damage consideration. Therefore, a mathematical model of thermoelastic, homogenous, and isotropic solid sphere with a rotation based on the mechanical damage definition has been constructed. The governing equations have been written in the context of hyperbolic two-temperature generalized thermoelasticity theory. The bounding surface of the sphere is thermally shocked and without volumetric deformation. The singularities of the studied functions at the center of the sphere have been deleted using L’Hopital’s rule. The numerical results have been represented graphically with various mechanical damage values, two-temperature parameters, and rotation parameter values. The two-temperature parameter has significant effects on all the studied functions. Damage and rotation have a major impact on deformation, displacement, stress, and stress–strain energy, while their effects on conductive and dynamical temperature rise are minimal. The thermal and mechanical waves propagate with finite speeds on the thermoelastic body in the hyperbolic two-temperature theory and the one-temperature theory (Lord-Shulman model).

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.

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.

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.

Thermodynamical interactions in a two-temperature dual-phase-lag micropolar thermoelasticity with gravity

PurposeThe dual-phase-lag (DPL) model is applied to study the effect of the gravity field and micropolarity on the wave propagation in a two-temperature generalized thermoelastic problem for a medium. The paper aims to discuss this issue.Design/methodology/approachThe exact expressions of the considered variables are obtained by using normal mode analysis.FindingsNumerical results for the field quantities are given in the physical domain and illustrated graphically to show the effect of angle of inclination. Comparisons of the physical quantities are also shown in figure to study the effect of gravity and two-temperature parameter.Originality/valueThis paper is concerned with the analysis of transient wave phenomena in a micropolar thermoelastic half-space subjected to inclined load. The governing equations are formulated in the context of two-temperature generalized thermoelasticity theory with DPLs. A medium is assumed to be initially quiescent and under the effect of gravity. An analytical solution of the problem is obtained by employing normal mode analysis. Numerical estimates of displacement, stresses and temperatures are computed for magnesium crystal-like material and are illustrated graphically. Comparisons of the physical quantities are shown in figures to study the effects of gravity, two-temperature parameter and angle of inclination. Some particular cases of interest have also been inferred from the present problem.

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.

Generalized thermoelastic problem of an infinite body with a spherical cavity under dual-phase-lags

The aim of the present contribution is the determination of the thermoelastic temperatures, stress, displacement, and strain in an infinite isotropic elastic body with a spherical cavity in the context of the mechanism of the two-temperature generalized thermoelasticity theory (2TT). The two-temperature Lord–Shulman (2TLS) model and two-temperature dual-phase-lag (2TDP) model of thermoelasticity are combined into a unified formulation with unified parameters. The medium is assumed to be initially quiescent. The basic equations are 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 expressions for the conductive temperature and elongation are obtained at small times. The numerical inversion of the transformed solutions is carried out by using the Fourier-series expansion technique. A comparative study is performed for the thermoelastic stresses, conductive temperature, thermodynamic temperature, displacement, and elongation computed by using the Lord–Shulman and dual-phase-lag models.

Thermoelastic Damping in Nanomechanical Resonators Based on Two-Temperature Generalized Thermoelasticity Theory

This work is concerned with the study of the thermoelastic damping of nanobeam resonators in the context of the two-temperature generalized thermoelasticity theory. An explicit formula of thermoelastic damping has been derived. Influences of the beam height, the relaxation time parameter, the two-temperature parameter and the isothermal value of frequency have been studied with some comparisons between the Biot model and Lord–Shulman model (L–S). Numerical results show that the values of thermal relaxation parameter and the two-temperature parameter have a strong influence on thermoelastic damping in nanoscales.

Short-time Analysis of Magnetothermoelastic Wave Under Fractional Order Heat Conduction Law

This paper deals with the problem of magnetothermoelastic interactions in a perfectly conducting elastic medium in which the boundary is stress free and subjected to thermal loading in the context of the fractional-order, two-temperature generalized thermoelasticity theory (2TT). The two-temperature, three-phase-lag (2T3P) model and two-temperature Lord–Shulman (2TLS) model of thermoelasticity are combined into a unified formulation introducing unified parameters. The governing equations of generalized thermoelasticity of these models under the influence of a magnetic field are established. 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 by a method based on Fourier-series expansion techniques. Because of the short duration of the second sound effects, small time approximations of the solutions are studied. The numerical estimates of the quantities of physical interest are obtained and depicted graphically. The effect of the fractional-order parameter and the two-temperature and magnetic field parameters on the solutions has been studied and the comparisons among different thermoelastic models are made.

Eigenvalue Approach to Two-temperature Generalized Thermoelastic Interactions in an Annular Disk

Two-temperature generalized thermoelasticity theory has been applied to determine the conductive and thermodynamic temperature as well as the deformation and stresses in an annular disk. The basic equations have been written in the form of a vector-matrix differential equation in the Laplace transform domain and solved for the field variables in closed form. Finally, the time variation and space variation of temperatures, deformation and stresses have been estimated by numerical methods and presented in several graphs and the analysis of the results have been made.

A Two-Dimensional Problem for a Rotating Magneto-Thermoelastic Half-Space with Voids and Gravity in a Two-Temperature Generalized Thermoelasticity Theory

ABSTRACTThe present paper is concerned with an in-depth study of the effects of rotation, two-temperature parameter and voids on the magneto-thermoelastic interactions in a homogeneous, isotropic, generalized half-space with gravity field. The formulation is applied within the frame-work of two-temperature generalized thermoelasticity based on the hyperbolic heat conduction model with one relaxation time. Using normal mode analysis technique for the physical variables appearing in the governing equations, we get the analytical expressions for displacement components, stress, thermodynamic temperature, conductive temperature and change in volume fraction field. The general solution obtained is then applied to a specific problem of an infinite half-space having isothermal boundary subjected to mechanical load. Variations of the considered variables through the vertical distance are illustrated graphically.

Eigenvalue approach for an unbounded medium with a spherical cavity based upon two-temperature generalized thermoelastic theory

The thermoelastic interaction in an unbounded medium with a spherical cavity is studied using two-temperature generalized thermoelasticity theory. The medium is assumed to be initially quiescent. The inner surface of the cavity is taken traction free and subjected to a thermal shock. By the Laplace transformation, the basic equations are expressed in the form of a vector-matrix differential equation, which is solved by an eigenvalue approach. Some comparison have been shown in figures to estimate the effect of the two-temperature parameter.

Two-Temperature Generalized Thermoelasticity in a Fiber-Reinforced Hollow Cylinder Under Thermal Shock

This paper deals with the thermoelastic interactions in a transversely isotropic, infinite hollow cylinder in which the boundaries are stress-free. There is no temperature in the inner boundary and heat flux is applied on the outer boundary. In the context of two-temperature generalized thermoelasticity theory, the three-phase-lag thermoelastic model and Green Naghdi model III (GN-III) are employed to study the thermophysical quantities. The Laplace transform is used to transform the coupled equations into the Laplace transformed domain. Then two different methods, the Galerkin finite element technique and eigen-value approach, are employed to solve the resulting equations in the transformed domain. The numerical inversion of the transform is carried out using Fourier-series expansion techniques. The physical quantities have been computed numerically and presented graphically in a number of figures. A comparison of the results for different theories (GN-III and three-phase-lag model) and for two different methods are presented.

One-dimensional problem of a fractional order two-temperature generalized thermo-piezoelasticity

This paper is concerned with the determination of the thermoelastic stress, strain and conductive temperature in a piezoelastic half-space body in which the boundary is stress free and subjected to thermal loading in the context of the fractional order two-temperature generalized thermoelasticity theory (2TT). The two-temperature three-phase-lag (2T3P) model, two-temperature Green–Naghdi model III (2TGNIII) and two-temperature Lord–Shulman (2TLS) model of thermoelasticity are combined into a unified formulation introducing unified parameters. The basic equations have been written in the form of a vector-matrix differential equation in the Laplace transform domain that is then solved by the state-space approach. The numerical inversion of the transform is carried out by a method based on Fourier series expansion techniques. The numerical estimates of the quantities of physical interest are obtained and depicted graphically. The effect of the fractional order parameter, two-temperature and electric field on the solutions has been studied and comparisons among different thermoelastic models are made.

State-space approach for an infinite medium with a spherical cavity based upon two-temperature generalized thermoelasticity theory and fractional heat conduction

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. A general solution to the problem based on the two-temperature generalized thermoelasticity theory (2TT) is introduced. The theory of thermal stresses based on the heat conduction equation with Caputo’s time-fractional derivative of order α is used. Some special cases of coupled thermoelasticity and generalized thermoelasticity with one relaxation time are obtained. The general solution is provided by using Laplace’s transform and state-space techniques. It is applied to a specific problem when the boundary of the cavity is subjected to thermomechanical loading (thermal shock). Some numerical analyses are carried out using Fourier’s series expansion techniques. The computed results for thermoelastic stresses, conductive temperature, and thermodynamic temperature are shown graphically and the effects of two-temperature and fractional-order parameters are discussed.