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PurposeThe purpose of this paper is to analyse the transient effects in a functionally graded photo-thermoelastic (TE) medium with gravity and rotation by considering two generalised TE theories: Lord–Shulman (LS) and Green–Lindsay (GL). The governing equations are derived in rectangular Cartesian coordinates for a two dimensional problem.Design/methodology/approachAll the physical properties of the semiconductor are supposed to vary exponentially with distance. The analytical solution is procured by employing normal mode technique on the resulting non-dimensional coupled field equations with appropriate boundary conditions.FindingsFor the mechanically loaded thermally insulated surface, normal displacement, stress components, temperature distribution and carrier density are calculated numerically with the help of MATLAB software for a silicon semiconductor and displayed graphically. Some particular cases of interest have also been deduced from the present results.Originality/valueThe effects of rotation and non-homogeneity on the different physical fields are investigated on the basis of analytical and numerical results. Comparisons are made with the results predicted by GL theory in the presence and absence of gravity for different values of time. Comparisons are also made between the three theories in the presence of rotation, gravity and in-homogeneity. Such problems are very important in many dynamical systems.

PurposeThe purpose of this paper is to study the transient thermoelastic interactions in a nonlocal rotating magneto-thermoelastic medium with temperature-dependent properties. Three-phase-lag (TPL) model of generalized thermoelasticity is employed to study the problem. An initial magnetic field with constant intensity acts parallel to the bounding plane. Therefore, Maxwell's theory of electrodynamics has been effectively introduced and the expression for Lorentz's force is obtained with the help of modified Ohm's law.Design/methodology/approachThe normal mode technique has been adopted to solve the resulting non-dimensional coupled field equations to obtain the expressions of physical field variables.FindingsFor uniformly distributed thermal load, normal displacement, temperature distribution and stress components are calculated numerically with the help of MATLAB software for a copper material and the results are illustrated graphically. Some particular cases of interest are also deduced from the present study.Originality/valueInfluences of nonlocal parameter, rotation, temperature-dependent properties, magnetic field and time are carefully analyzed for mechanically stress free boundary and uniformly distributed thermal load. The present work is useful and valuable for analysis of problem involving thermal shock, nonlocal parameter, temperature-dependent elastic and thermal moduli.

Purpose The purpose of this study is to analyze the disturbances in a two-dimensional nonlocal, micropolar elastic medium under the dual-phase-lag model of thermoelasticity whose surface is subjected to an inclined mechanical load. The present study is carried out under the influence of gravity. Design/methodology/approach The normal mode technique is used to obtain the exact expressions of the physical fields. Findings For inclined mechanical load, the impact of micropolarity, nonlocal parameter, gravity and inclination angle have been highlighted on the considered physical fields. Originality/value The numerical results are computed for various physical quantities such as displacement, stresses and temperature for a magnesium crystal-like material and are illustrated graphically. The study is valuable for the analysis of thermoelastic problems involving gravitational field, nonlocal parameter, micropolarity and elastic deformations.

Purpose The purpose of this paper is to study the propagation of inhomogeneous waves in a partially saturated poro-thermoelastic media through the examples of the free surface of such media.. Design/methodology/approach The mathematical model evolved by Zhou et al. (2019) is solved through the Helmholtz decomposition theorem. The propagation velocities of bulk waves in partially saturated poro-thermoelastic media are derived by using the potential functions. The phase velocities and attenuation coefficients are expressed in terms of inhomogeneity angle. Reflection characteristics (phase shift, loci of vertical slowness, amplitude, energy) of elastic waves are investigated at the stress-free thermally insulated boundary of a considered medium. The boundary can be permeable or impermeable. The incident wave is portrayed with both attenuation and propagation directions (i.e. inhomogeneous wave). Numerical computations are executed by using MATLAB. Findings In this medium, the permanence of five inhomogeneous waves is found. Incidence of the inhomogeneous wave at the thermally insulated stress-free surface results in five reflected inhomogeneous waves in a partially saturated poro-thermoelastic media. The reflection coefficients and splitting of incident energy are obtained as a function of propagation direction, inhomogeneity angle, wave frequency and numerous thermophysical features of the partially saturated poro-thermoelastic media. The energy of distinct waves (incident wave, reflected waves) accompanying interference energies between distinct pairs of waves have been exhibited in the form of an energy matrix. Originality/value The sensitivity of propagation characteristics (velocity, attenuation, phase shift, loci of vertical slowness, energy) to numerous aspects of the physical model is analyzed graphically through a particular numerical example. The balance of energy is substantiated by virtue of the interaction energies at the thermally insulated stress-free surface (opened/sealed pores) of unsaturated poro-thermoelastic media through the bulk waves energy shares and interaction energy.

The present article is concerned with the propagation of plane waves in a homogeneous, fiber-reinforced orthotropic thermoelastic rotating half-space in the context of three-phase-lag model. There exist three coupled waves, namely, quasi-longitudinal P -wave ( q P ) , quasi-longitudinal thermal wave ( q T ) and quasi-transverse wave ( q S V ) in the medium. The reflection coefficients are computed numerically with the help of MATLAB programming and are depicted graphically to show the effects of rotation, fiber-reinforcement and phase lag parameters. The expressions of energy ratios have also been obtained in explicit form and are shown graphically as functions of angle of incidence. It has been verified that during reflection phenomena, the sum of energy ratios is equal to unity at each angle of incidence. Effect of anisotropy is depicted on velocities of various reflected waves. Some particular cases of interest have also been inferred from the present investigation.

Present work is aimed to study the solution of a problem on thermoelastic interactions in a functionally graded material under dual-phase-lag model in the presence of rotation and gravity. By emplo...

Current research is dedicated to study the influence of angular velocity and gravity field on the thermomechanical interactions in a non-homogeneous, nonlocal, micropolar elastic half-space whose s...

Purpose The purpose of this paper is to study two-dimensional deformations in a nonlocal, homogeneous, isotropic, rotating thermoelastic medium with temperature-dependent properties under the purview of the Green-Naghdi model II of generalized thermoelasticity. The formulation is subjected to a mechanical load. Design/methodology/approach The normal mode analysis technique is adopted to procure the exact solution of the problem. Findings For isothermal and insulated boundaries, discussions have been made to highlight the influences of rotational speed, nonlocality, temperature-dependent properties and time on the physical quantities. Originality/value The exact expressions for the displacement components, stresses and temperature field are obtained in the physical domain. These are also calculated numerically for a magnesium crystal-like material and depicted through graphs to observe the variations of the considered physical quantities. The present study is useful and valuable for the analysis of problems involving mechanical shock, rotational speed, nonlocal parameter, temperature-dependent properties and elastic deformation.

Present work deals with the investigation of disturbances in a two-dimensional functionally graded thermoelastic medium with microtemperatures. The study is carried out under the influence of rotat...

Present article is concerned with the propagation of plane waves in a nonlocal, microstretch thermoelastic half-space with temperature dependent properties. Five basic waves consisting of three set...

PurposeThe present investigation is concerned with the two-dimensional deformations in an inhomogeneous fiber-reinforced thermoelastic medium under the influence of gravity in the context of Green–Lindsay theory.Design/methodology/approachMaterial properties are supposed to be graded in x-direction, and normal mode technique is adopted to obtain the exact expressions for the temperature field, displacement components and stresses.FindingsNumerical computations have been carried out with the help of MATLAB software, and the results are depicted graphically to observe the disturbances induced in the considered medium. Comparisons made within the theory of the physical quantities are shown in figures to highlight the effects of fiber reinforcement, inhomogeneity parameter, gravity and time.Originality/valueIn the present work, we have investigated the effects of fiber reinforcement, inhomogeneity parameter, gravity and time in an inhomogeneous, fiber-reinforced thermoelastic medium under the influence of gravity. Although various investigations do exist to observe the disturbances in a thermoelastic medium under the effects of different parameters, the work in its present form i.e. thermally induced vibrations in an inhomogeneous fiber-reinforced thermoelastic material with gravity has not been studied till now. The present work is useful and valuable for analysis of problems involving thermal shock, gravity parameter, fiber reinforcement, inhomogeneous and elastic deformation.

PurposeThe purpose of this paper is to study the reflection of plane waves in an initially stressed rotating thermoelastic diffusive medium with micro-concentrations and two-temperature.Design/methodology/approachA two-dimensional model of generalized thermoelasticity is considered. The governing equations are transformed into the non-dimensional forms using the dimensionless variables. Then, potential functions are introduced for the decoupling of the waves. Further, appropriate boundary conditions are assumed to completely solve the problem. Finally, numerical computations are performed using MATLAB.FindingsThe problem is solved analytically and it is found that there exist five coupled waves in addition to an independent micro-concentration wave in the considered medium. The amplitude ratios and energy ratios of these reflected waves have also been computed numerically for a specific material.Originality/valueThe modulus values of amplitude ratios are presented graphically to exhibit the effects of angular velocity, initial stress, two-temperature, diffusion and micro-concentration parameters. The expressions of energy ratios obtained in explicit form are also depicted graphically as functions of angle of incidence. The law of conservation of energy at the free surface during reflection phenomenon is also verified.

This paper is devoted to discuss the features of various reflected waves in an infinite, homogeneous, isotropic magneto-thermoelastic medium with microconcentrations and diffusion. The problem is s...

Present research is concerned with the study of two-dimensional disturbances in a non-homogeneous, isotropic, thermoelastic medium with voids and gravity under the purview of Lord–Shulman (LS) model of generalized thermoelasticity. The formulation is subjected to a thermal shock. All the mechanical and thermal properties of the solid are supposed to vary exponentially with distance. Normal mode technique is employed to obtain the exact expressions for the displacement components, stresses, change in volume fraction field and temperature field. These are also calculated numerically for a magnesium crystal-like material and depicted through graphs to observe the variations of the considered physical quantities. Influences of non-homogeneity, gravitational field, voids and relaxation time on the physical quantities are carefully analyzed. A comparison between the models of coupled thermoelasticity theory and LS theory is also presented.

The present investigation is concerned with the reflection of plane waves at the free surface of a homogeneous, isotropic, nonlocal, micropolar rotating thermoelastic medium. The entire thermoelastic medium is rotating with a uniform angular velocity. It is observed that there exist four coupled plane waves, which travel through the medium with distinct speeds. Using appropriate boundary conditions, the reflection coefficients and energy ratios of various reflected waves are computed numerically with the help of the software MATLAB. The numerical values of modulus of reflection coefficients are presented graphically to show the effects of nonlocal, rotation and micropolar parameters. It has been verified that during reflection phenomena, the sum of modulus of energy ratios is approximately equal to unity at each angle of incidence. The effect of micropolarity on the phase velocities is also observed and shown graphically.

Present analysis is concerned with the propagation of plane waves in an initially stressed magneto-thermoelastic half-space with microtemperatures and voids. It is noticed that there exist four kin...

The purpose of present investigation is to study the reflection and transmission phenomena at the plane interface between an orthotropic thermoelastic half-space and an initially stressed orthotrop...

PurposeThe purpose of this paper is to establish a model of two-dimensional half-space problem of linear, isotropic, homogeneous, initially stressed, rotating thermoelastic medium with microtemperatures. The expressions for different physical variables such as displacement distribution, stress distribution, temperature field and microtemperatures are obtained in the physical domain.Design/methodology/approachNormal mode analysis technique is adopted to procure the exact solution of the problem.FindingsNumerical computations have been carried out with the help of MATLAB programming, and the results are illustrated graphically. Comparisons are made to show the effects of rotation, time and microtemperatures on the resulting quantities. The graphical results indicate that the effects of rotation, microtemperatures and time are very pronounced on the field variables.Originality/valueIn the present work, we have investigated the effects of rotation, time and microtemperature in an initially stressed thermoelastic medium. Although various investigations do exist to observe the disturbances in a thermoelastic medium under the effects of different parameters, the work in its present form, i.e. the disturbances in a thermoelastic medium in the presence of angular velocity, initial stress and microtemperature have not been studied till now. The present work is useful and valuable for analysis of problems involving coupled thermal shock, rotation parameter, microtemperatures and elastic deformation.

The present work is concerned with the 2D deformation in a nonhomogeneous, isotropic, micropolar, magneto-thermoelastic medium in the context of Lord-Shulman theory as a result of an inclined load....

The present analysis is aimed to model and study the characteristics of various reflected waves in a homogeneous and isotropic thermoelastic diffusive half-space with microtemperatures. It ...

The present investigation is concerned with the reflection and transmission phenomena of plane waves between a rotating thermoelastic transversely isotropic solid half space and a fiber-reinforced thermoelastic rotating solid half space under the effect of a magnetic field. Green–Lindsay and Lord–Shulman theories have been employed for addressing the mathematical analysis. Relevant boundary conditions are considered in order to determine the reflection and transmission coefficients. The phase speeds, reflection and refraction coefficients and energy ratios are computed numerically with the help of MATLAB. The numerical values of the moduli of reflection and transmission coefficients are depicted graphically to estimate and highlight the effects of fiber reinforcement, rotation parameter and angular frequency. The effect of anisotropy on the velocities of the reflected and transmitted waves is also observed. One particular case of interest has also been inferred from the present investigation.

In this article, a model of two dimensional problem of generalized thermoelasticity for an anisotropic magnetothermoelastic diffusive medium under the effect of temperature dependent properties is established. The enunciation is applied to generalized thermoelasticity theory based on Green-Lindsay model. There exist four coupled waves, namely, quasi-longitudinal P-wave (qP), quasi-longitudinal thermal wave (qT), quasi-longitudinal mass diffusive wave (qMD), and quasi-transverse wave (qSV) in the medium. Amplitude and energy ratios for these reflected waves are derived and the numerical computations have been carried out with the help of MATLAB programing. Effects of temperature dependent properties, magnetic and diffusion parameters on the amplitude and energy ratios are depicted graphically. Expressions of energy ratios have also been obtained in explicit form and are shown graphically as functions of angle of incidence. It has been verified that during the reflection phenomenon, the sum of energ...

The present investigation is concerned with the reflection of plane waves from the free surface of a homogeneous, anisotropic, fiber-reinforced thermoelastic rotating medium under two-temperature and dual-phase-lag model. It has been observed that three coupled plane waves travel in the medium with distinct speeds. Using appropriate boundary conditions, the amplitude and energy ratios for the reflected waves are derived and the numerical computations have been carried out with the help of MATLAB programming. The numerical values of the modulus of reflection coefficients are presented graphically to exhibit the two-temperature, phase lag and rotation parameter effects. The expressions of energy ratios have also been obtained in explicit form and are shown graphically as functions of angle of incidence. It has been verified that during reflection phenomena, the sum of energy ratios is equal to unity at each angle of incidence.

The current manuscript is an attempt to investigate the disturbances in a two dimensional isotropic, homogeneous, magneto-thermo-elastic diffusive material with microtemperatures. The formulation is subjected to a mechanical load. Normal mode analysis is applied to obtain the exact solution of the problem. The expressions for different field variables such as displacement, stresses, temperature, microtemperature and concentration are obtained in the physical domain. Numerical results are carried out for a specific material. Obtained results are compared with the existing models for verification and represented graphically using MATLAB software. Some comparisons are made to show the effects of magnetic field, diffusion parameter and time on the resulting quantities. The effects of these parameters under the consideration of present medium have not been appeared in the literature so far. The results depict that the effects of magnetic field, diffusion parameter and time on the field variables are very pronounced.

The present concept is related to the two-dimensional deformation in an initially stressed fiber-reinforced orthotropic thermoelastic model in the context of Green–Naghdi type III (GN III) theory as a result of the application of an inclined load. Normal and shear loads are assumed to be linear. The full expressions for the displacement components, temperature field and stresses are obtained by using normal mode technique. Comparisons are made in an orthotropic, transversely isotropic and an isotropic medium to illustrate the effects of fiber reinforcement on these physical quantities. The effects of initial stress, Green–Naghdi theories (type III and type II), inclination angle of load and time on the field variables are also considered.

Reflection and transmission phenomena at the plane interface between thermoelastic half-space and an initially stressed fiber-reinforced thermoelastic half-space are analyzed. The formulation is applied to generalized thermoelasticity based on the dual-phase-lag theory. Using convenient boundary conditions, the amplitude ratios and energy ratios for the reflected and transmitted waves are derived, and the numerical computations are carried out with the help of MATLAB programming. The numerical values of the modulus of reflection and transmission coefficients are presented graphically to highlight fiber-reinforced and initial stress parameter effects. The expressions of energy ratios obtained in explicit form are shown graphically as functions of angle of incidence. It has been verified that during reflection and transmission phenomena, the sum of energy ratios is equal to unity at each angle of incidence. The effect of anisotropy on velocities of reflected and transmitted waves is also depicted.

The present manuscript is aimed at studying the propagation of plane waves in a fiber-reinforced, anisotropic, thermoelastic half-space with diffusion. The formulation is applied to generalized thermoelasticity based on the Green–Lindsay (G–L) theory. A thermal shock is applied on the surface of the half-space, which is taken to be traction free. The analytical expressions for the displacement components, stresses, concentration and temperature field are obtained in the physical domain by using normal mode analysis. Moreover, the derived expressions are computed numerically, and corresponding graphs are plotted to illustrate and compare theoretical results. Comparisons are made within the theory in the presence and absence of fiber-reinforcement and diffusion. The effect of time on the physical fields is also observed. Some particular cases of interest have been deduced from the present investigation.

The aim of the present paper is to study the effects of rotation and three-phase-lag parameters in a micropolar generalized thermo-viscoelastic medium. By employing normal mode analysis, the analytical expressions for the displacement components, stresses and temperature field are obtained in the physical domain. These expressions are also calculated numerically, and corresponding graphs are plotted to illustrate and compare theoretical results. The effects of rotation, ramp and viscous parameters are also studied. Some particular cases of interest have been deduced from the present investigation.

The present paper deals with the problem of thermoviscoelastic interactions in a homogeneous isotropic thick plate whose upper surface is stress-free and is subjected to a known temperature distribution, while the lower surface rests on a rigid foundation and is thermally insulated. The problem is treated on the basis of fractional-ordered dual-phase-lag model of thermoelasticity. To study the viscoelastic nature of the material, Kelvin–Voigt model of linear viscoelasticity is employed. The governing equations are transformed into a vector-matrix differential equation with the use of joint Laplace and Fourier transforms, which is then solved by the eigenvalue approach. Numerical estimates of displacements, stresses and temperature are computed for copper material by using a numerical inversion technique. Finally, all the physical fields are represented graphically to estimate and highlight the effects of the fractional parameter, viscosity and time.

Purpose The 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/approach The exact expressions of the considered variables are obtained by using normal mode analysis. Findings Numerical 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/value This 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 current manuscript is devoted to scrutinize the effects of fractional parameter, micropolarity and diffusion on the interactions caused by a ramp type mechanical shock in a generalized thermo-viscoelastic solid half-space. The medium is assumed to be unstrained and unstressed initially and has uniform temperature. The problem has been modeled by employing the fractional generalization of the Lord–Shulman theory to carry the investigation. The governing equations in xz-plane are handled with an analytical–numerical technique based on Laplace–Fourier transforms. Expressions for displacement, stresses, temperature and mass concentration in the physical domain are obtained using a numerical inversion technique. The problem is illustrated by computing the numerical values of the field variables for a magnesium crystal like material. Comparisons of the physical quantities are shown in figures to study the effects of fractional parameter, micropolarity, diffusion and ramp parameter. Some particular cases of interest have also been inferred from the present problem.

The present study is attempted to analyze the thermoelastic interactions in a homogeneous isotropic electro-microstretch semi-space caused by mechanical source acting on the initially stressed surface. The problem is treated on the basis of two-temperature thermoelasticity without energy dissipation proposed by Youssef. Normal mode analysis is applied to derive the exact expressions for displacement components, force stresses, couple stress, microstress, conductive temperature, thermodynamic temperature and electric field. Numerical computations have been performed for magnesium crystal material to depict the response of mechanical source in the medium for thermally insulated boundary. Some comparisons have been made in figures to estimate the effects of two-temperature parameter and initial stress.

In the present article, a model of the equations of generalized electromicrostretch thermoelasticity in an initially stressed perfectly conducting elastic medium under the effect of temperature-dependent properties is studied. The entire elastic medium is rotating with a uniform angular velocity. Reflection phenomena of plane waves in electromicrostretch thermoelasticity is investigated under two theories proposed by Lord and Shulman (L–S) and Green and Lindsay (G–L). Amplitude ratios and energy ratios of various reflected waves are presented when an elastic wave is made incident obliquely at the plane boundary of an electromicrostretch thermoelastic solid half-space. It has been verified that there is no dissipation of energy at the boundary surface during reflection. Numerical examples calculate the amplitude ratios to evince the effects of initial stress parameter, rotation, and temperature-dependent properties, and the results obtained are depicted graphically.

The current manuscript is presented to study two-dimensional deformations in a nonhomogeneous, isotropic, rotating, magneto-thermoelastic medium in the context of Green-Naghdi model III. It is assumed that the functionally graded material has nonhomogeneous mechanical and thermal properties in the x-direction. The exact expressions for the displacement components, temperature field, and stresses are obtained in the physical domain by using normal mode technique. These are also computed numerically for a copper-like material and presented graphically to observe the variations of the considered physical variables. Comparisons of the physical quantities are shown in figures to depict the effects of angular velocity, nonhomogeneity parameter, and magnetic field.

In the present article, an appraisement is made to investigate the effects of gravity and initial stress in a fiber-reinforced, anisotropic, thermoelastic half-space with diffusion. The enuciation is applied to generalized thermoelasticity based on Lord–Shulman (L–S) theory. Solutions are obtained in the frequency domain, by using a standard mathematical technique. The physical quantities are established numerically and represented graphically in the presence and absence of gravity, initial stress, fiber-reinforcement and diffusion. The results indicate that the effects of gravity, initial stress and the parameters of fiber-reinforced material medium are very pronounced. Moreover, some particular cases of interest have been deduced from the present investigation. The datum of a finite speed of wave propagation is observed for each field.