Generalized Thermoelasticity Theory Research Articles

Elastic-thermal-diffusion model with a mechanical ramp type and variable thermal conductivity of electrons–holes semiconductor interaction

In this article, an elastic-thermodiffusion (ETD) model in the context of the coupled between the holes and electrons is constructed for the semiconductor material. The photothermal excitation in generalized thermoelasticity theory is used to describe this model. The governing equations are studied when the thermal conductivity is variable during the temperature graduation. The deformation occurrs in one-dimensional (1D) when thermoelastic (TD) and electronic(ED) transport processes are taken into consideration. The dimensionless field quantities are obtained analytically for the principle physical fields (hole charge field carrier, elastic, thermal, and electrons charge carrier density (plasma) waves). Laplace transform is used algebraically to solve the governing equations. When some conditions are taken at the boundary, the main physical fields are obtained and subjected to mechanical ramp type at rest. Laplace inverse with the approximate technique is used numerically during the transformation to get the closed-form in the time domain for the principle fields. Some comparisons are carried out graphically under the effect of variable thermal conductivity and thermal memories which are discussed for silicon material.

A thermoelastic model with higher order time derivatives for a crack in a rotating solid

This article represents a refined one-temperature thermoelastic model with higher order time derivatives and phase-lags for a Mode-I crack in a rotating fiber-reinforced solid. The crack is subjected to a stipulated temperature and normal stress. The exact expressions of displacement, temperature and stress components are obtained by normal mode analysis. Some generalized thermoelasticity theories are obtained as special cases. The convergency of the present refined model is tabulated and is compared with other theories. The variations of the temperature, displacements and stresses are presented graphically with the crack length to show the effect of phase-lags and thermal relaxation time through Refined-phase-lag (RPL), simple-phase-lag (SPL), Green-Naghdi (G-N) theory, Lord-Shulman (L-S) theory and the Coupled thermoelasticity (CTE) theory in the presence and absence of rotation.

On dynamic modeling of piezomagnetic/flexomagnetic microstructures based on Lord–Shulman thermoelastic model

We study a time-dependent thermoelastic coupling within free vibrations of piezomagnetic (PM) microbeams considering the flexomagnetic (FM) phenomenon. The flexomagneticity relates to a magnetic field with a gradient of strains. Here, we use the generalized thermoelasticity theory of Lord–Shulman to analyze the interaction between elastic deformation and thermal conductivity. The uniform magnetic field is permeated in line with the transverse axis. Using the strain gradient approach, the beam yields microstructural properties. The analytical solving process has been gotten via applying sine Fourier technique on displacements. Graphical illustrations are assigned to shape numerical examples concerning variations in essential physical quantities. It was observed that the flexomagnetic effect could be extraordinary if the thermal conductivity of the material is higher or the thermal relaxation time of the heat source is lesser. This theoretical study will provide the way of starting studies on magneto-thermoelastic small-scale piezo-flexomagnetic structures based on the heat conduction models.

Response of thermal-optical-elastic waves of a rotator microstretch semiconductor media during photothermal transport processes

A novel theoretical mathematical-physical model for elastic semiconductor material is investigated when the microstretch properties of the medium are considered. During the photo-generated processes, the generalized thermoelasticity theory in photo-thermal theory is studied for excited semiconductor medium. The governing equations describe the coupled propagation of the elastic-thermal-plasma (optical) waves when the thermomicrostretch elastic semiconductor material is considered during a rotation field. The photo-thermal transport processes occur during a two-dimension (2D) of elastic and electronic deformation when the microinertia of microelement is considered. The harmonic wave method can obtain the main solutions for the basic physical variables. The complete analytical solutions of the considered variables are obtained when some mechanical-thermal and plasma conditions are applied on the boundary of the semiconductor medium. The numerical simulations of silicon (Si) and Germanium (Ge) media are constructed graphically with many comparisons according to new parameters with thermal memories and rotation parameters.

"On instability in the theory of dipolar bodies with two-temperatures"

"In this paper we approach a generalized thermoelasticity theory based on a heat conduction equation in bodies with dipolar structure, the heat conduction depends on two distinct temperatures, the thermodynamic temperature and the conductive temperature. In our considerations the difference between two temperatures is highlighted by the heat supply. For the mixed initial boundary value problem defined in this context, we prove the uniqueness of a solution corresponding some specific initial and boundary conditions. Also, if the initial energy is negative or null, we prove that the solutions of the mixed problem are exponentially unstable."

Memory response in a nonlocal micropolar double porous thermoelastic medium with variable conductivity under Moore-Gibson-Thompson thermoelasticity theory

The present study enlightens the two-dimensional analysis of the thermo-mechanical response for a micropolar double porous thermoelastic material with voids (MDPTMWV) by virtue of Eringen’s theory of nonlocal elasticity. Moore-Gibson-Thompson (MGT) heat equation is introduced to the considered model in the context of memory-dependent derivative and variable conductivity. By employing the normal mode technique, the non-dimensional coupled governing equations of motion are solved to determine the analytical expressions of the displacements, temperature, void volume fractions, microrotation vector, force stress tensors, and equilibrated stress vectors. Several two-dimensional graphs are presented to demonstrate the influence of various parameters, such as kernel functions, thermal conductivity, and nonlocality. Furthermore, different generalized thermoelasticity theories with variable conductivity are compared to visualize the variations in the distributions associated with the prior mentioned variables. Some particular cases are also discussed in the presence and absence of different parameters.

Magnetic-thermal-elastic waves under the impact of induced laser pulses and hyperbolic two temperature theory with memory-dependent derivatives (MDD)

A novel model with theoretical investigations of generalized hyperbolic two-temperature theory in the context of the generalized thermoelasticity theory is studied. The elastic medium is excited at the outer surface by an external magnetic field and pulsed laser. The model is established in the context of the memory-depended derivative (MDD) when the elastic material time-dependent. The governing equations describe the interaction processes for isotropic homogeneous hyperbolic thermoelastic elastic medium in one-dimensional (1D) deformation when the non-Gaussian laser pulse model is applied with time delay. The Laplace transform is used to obtain the analytical solutions of the main physical fields. The medium is loaded when a traction is free and thermally shocked with time-dependent. The complete solutions are obtained in the Laplace time domain when used the inverse of Laplace transform numerically. Numerical results of the main physical quantities are discussed graphically under the effect of hyperbolic two-temperature, magnetic field and laser pulses when the time-delay parameter is taken into consideration.

Thermoelastic wave propagation in thin beams under thermal shock loading

An analytical solution is presented for the thermoelastic longitudinal and flexural wave propagation in transversely isotropic thin beams subjected to a thermal shock loading using the Lord–Shulman generalized thermoelasticity theory. The formulation considers a general through-thickness profile of the applied thermal loading, does not assume the across-thickness distribution of the temperature field and considers a general convective boundary condition at the beam surfaces. The thin beam is modeled using the Euler–Bernoulli beam theory. The governing equations of motion and the variationally consistent boundary conditions are derived from the extended Hamilton’s principle. The coupled thermoelastic equations are solved in the Laplace domain satisfying the thermal and mechanical boundary conditions using the homotopy perturbation method. The Laplace inversion to obtain the final solution in the time domain is performed numerically by using Durbin’s method. The formulation is validated by comparing the results for longitudinal wave propagation response under uniform thermal loading with those available in the literature. The developed solution is then employed to study the longitudinal and flexural wave propagation behaviour of a cantilever beam subject to uniform and non-uniform symmetric, and linear and non-linear anti-symmetric thermal shock loading applied at the free end. The effects of thermal boundary conditions at the beam surfaces and the relaxation time parameter on the response of the beam are illustrated.

Hall current effect in double poro-thermoelastic material with fractional-order Moore–Gibson–Thompson heat equation subjected to Eringen's nonlocal theory

The present study focuses on the analysis of one-dimensional thermoelastic interaction in an infinite medium consisting of double poro-thermoelastic material with voids (DPTMWV) in the presence of Hall current by developing the fundamental relations in light of Eringen's nonlocal elasticity theory. A fractional-order Moore–Gibson–Thompson (MGT) heat conduction equation is introduced to the model in the context of a continuous heat source. The Caputo fractional derivative is applied in the domain of Laplace transform. The displacement, temperature, volume fractions, and stresses are determined with the help of the eigenvalue approach and the numerical inversions of these physical variables are obtained by using Zakian's algorithm. The effects of several parameters, such as Hall current, fractional order, nonlocality, and time, are graphically executed. Furthermore, the nonlocal models under different generalized thermoelasticity theories are compared to visualize the variations in the distributions corresponding to the prior mentioned variables.

Thermoelastic vibrations in initially stressed rotating microbeams caused by laser irradiation

AbstractThe current paper has been presented to illustrate the thermoelastic vibration of a rotating microbeam based on generalized thermoelasticity theory, taking into account Euler–Bernoulli's assumptions. Using Hamilton's principle, the equation of motion of the initially stressed rotating microbeams has been derived. The microbeam is exposed to femtosecond laser pulses and sinusoidal varying heat. The Laplace transform technique is applied to obtain an analytical solution to the field variables. The influence of properties of various parameters, such as axial load, laser pulse duration, angular velocity, and material variation on the thermal and elastic waves of the rotating microbeam has been displayed graphically and discussed in detail.

Thermoelastic damping analysis in micro-beam resonators in the frame of modified couple stress and Moore–Gibson–Thompson (MGT) thermoelasticity theories

The thermoelastic coupling between strain and temperature fields arising out from temperature gradient, while bending of an oscillating structure, leads to irreversible heat conduction, which causes energy dissipation in such vibrating systems. The estimation of thermoelastic damping (TED) in micro- and nano-mechanical resonators is a significant aspect of acquiring a high quality factor (Q-factor). Yang et al. [Couple stress based strain gradient theory for elasticity. Int J Solids Struct. 2002;39(10):2731–2743.] developed the modified couple stress theory (MCST) that involves only one material length scale parameter. The present work attempts to investigate TED in micro/nano-beam resonators utilizing MCST and the recently proposed Moore–Gibson–Thompson (MGT) generalized thermoelasticity theory. Adopting the frequency approach method, we derive the size-dependent expression of the inverse quality factor for evaluating TED in rectangular micro/nano-beam resonators. Furthermore, the impact of the material length scale parameter on TED associated with MCST for silicon micro-beam resonator is investigated in detail by comparing the present results with those predicted by classical continuum theory (CCT). The obtained results are also compared with the existing results for the Lord–Shulman (LS) and Green–Naghdi (GN-III) thermoelasticity theories. Moreover, the effects of other important parameters like beam thickness, beam length, aspect ratio, phase-lag on TED in the present context are highlighted.

A visco-elastic layer overlaid by a thick layer on top of an elastic half space in the generalized theory of thermoelasticity

In this work, we presented a model which consists of three layers with different materials; the second layer was taken to be viscous-elastic material, while the first and third layers are made of elastic material. This model is solved in the context of the generalized thermoelasticity theory with one relaxation time. The first layer's upper surface is taken to be traction-free and is subjected to a constant thermal shock. Nobody forces or heat sources affecting the layer. Laplace transform techniques are used. The solution in the transformed domain is obtained by using a direct approach. The inverse Laplace transforms are obtained using a numerical method based on the Fourier expansion technique. The effect of thermal shock is discussed and studied of the three layers on the behavior of the solutions, in the presence of viscoelastic effects and its absence. Numerical results are computed and represented graphically for the temperature, displacement, and stress distributions.

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.

Two temperature generalized thermoelasticity involving memory-dependent derivative under fuzzy environment

A one-dimensional two-temperature model of generalized thermoelasticity theory in half-space has been studied in this present discussion with memory-dependent derivative. The fuzzy approach has been applied to construct the governing equations. The fuzzy variables such as stress, strain and so on are represented in r-cut. The coupled partial differential equations' analytical solutions are obtained in Laplace transform domain subject to a stress-free boundary with a time-dependent imprecise thermal shock. A suitable numerical inverse Laplace transformation technique is applied to get the space time-domain results for different time delay parameter values and several kernel functions. Two examples of numerical results in the fuzzy environment are performed and are compared with the crisp results graphically. The concluding remarks are made based on numerical results and graphs.

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.

Thermoelastic interactions on thick granular plate with three-phase-lag model under axisymmetric temperature distribution

The theory of thermoelasticity with three-phase-lag is used to study the phase lag effects on wave propagation in granular medium. A two-dimensional thick granular plate with axisymmetric temperature distribution is considered under the type III and three-phase-lag thermoelasticity. The plate’s lower and upper surfaces are assumed to be stress free and subjected to a thermal condition. The analytical solution of the different fields like temperature, displacement, stresses, rotation, and couple stresses is obtained by the Laplace together with the Hankel transform method. The characteristic features of the underlying theory are analyzed by the small-time approximation method with Boley’s theorem and by comparing these results with their counterparts in other generalized thermoelasticity theories (GN III and Lord Shulman theory). The numerical values are evaluated and displayed graphically in the middle plane for different models, and comparison is made.

Influence of nonlocal thermoelastic interactions for a half-Space overlaid via a thick layer

The model of nonlocal thermoelasticity is applied on a half-space overlaid by a thick layer of different materials, depending on generalized thermoelasticity theories (L. S). To solve this problem we take the upper surface is to be traction-free and is subjected to a constant thermal shock. The analytical expressions for temperature, displacement, and stresses were obtained by using the Laplace transform technique. Besides, comparisons are presented in graphs to illustrate the effects of different factors.

Initial Stress and Gravity on P-Wave Reflection from Electromagneto-Thermo-Microstretch Medium in the Context of Three-Phase Lag Model

The present paper studied the reflection of thermo-microstretch waves under the generalized thermoelasticity theory which is employed to study the reflection of plane harmonic waves from a semi-infinite elastic solid under the effect of the electromagnetic field, initial stress, and gravity. The formulation is applied under the thermoelasticity theory with three-phase lag, and the reflection coefficient ratio variations with the angle of incidence under different conditions are obtained. Numerical results obtained from the present study are presented graphically and discussed. It is observed that the initial stress, gravitation, and electromagnetic field exert some influence in the thermo-microstretch medium due to reflection of P-waves.

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.

Rotation and gravitational field on a poroelastic medium under the generalized thermoelasticity theory with two-temperature

The poro-thermoelastic problem with two-temperature, under the influence of the gravitational field and the rotation was investigated. The solution to the problem is presented in the context of lord and Shulman's theory of thermoelasticity with one relaxation time. We applied normal mode analysis to solve the resulting non-dimensional coupled partial differential equations. Effect of rotation, gravitational field, two-temperature parameter and porosity parameter on non-dimensional displacements, thermodynamic temperature, conductive temperature, excess pore water pressure and stresses has been discussed. Numerical analyses are given graphically in the square (2D) to illustrate the effect of these parameters. Some particular cases of interest are deduced from the present investigation.