Thermoelastic Plane Waves Research Articles

Correction: Effect of Impedance Boundary on the Reflection of Plane Waves in Fraction-Order Thermoelasticity in an Initially Stressed Rotating Half-Space with a Magnetic Field

Correction: Effect of Impedance Boundary on the Reflection of Plane Waves in Fraction-Order Thermoelasticity in an Initially Stressed Rotating Half-Space with a Magnetic Field

Micropolar thermoelastic plane waves in microscopic materials caused by Hall-current effects in a two-temperature heat conduction model with higher-order time derivatives

Micropolar thermoelastic plane waves in microscopic materials caused by Hall-current effects in a two-temperature heat conduction model with higher-order time derivatives

Reflection of Plane Waves in Nonlocal Fractional-Order Thermoelastic Half Space

The problem of plane waves in nonlocal fractional-order thermoelasticity has been studied. We have considered the x-y plane for the governing equation of nonlocal fractional thermoelasticity and solved these governing equations to calculate the equation in terms of frequency. This frequency shows that three sets of waves exist, in which two are coupled and one is uncoupled. The reflection coefficient of plane waves for classical theory and LS theory has been calculated. The effect of phase speeds, specific losses, and attenuation coefficients with respect to the frequency and nonlocal parameter for the two theories (LS theory and the classical theory of thermoelasticity) has been studied numerically for all propagating waves, and the same has been plotted graphically and explained thoroughly.

Plane wave propagation in a fiber-reinforced thermoelastic rotating medium with variable thermal conductivity under modified Green–Lindsay model

The present investigation is concerned with the reflection of thermoelastic plane waves in an anisotropic, rotating, fiber-reinforced medium having variable thermal conductivity. Modified Green–Lindsay theory (MGL) is used to formulate the problem. It is shown that there exist three kinds of coupled quasi-waves, namely, (quasi longitudinal displacement), (quasi thermal) and (quasi transverse displacement). Using appropriate boundary conditions, the reflection coefficients, phase velocities and energy ratios of these reflected waves have been calculated numerically and shown graphically to exhibit the effects of rotational and fiber-reinforcement parameters. The characteristics of MGL model are discussed by comparing the numerical results procured for the present model with those procured in the case of Green–Lindsay (GL) model. It has been shown that during reflection phenomenon, the sum of energy ratios is equal to unity at each angle of the incident.

Reflection of temperature rate–dependent coupled thermoelastic waves on a non-local elastic half-space

Based upon the Green–Lindsay (GL) theory of thermoelasticity and the Eringen non-local elasticity theory, we describe the new constitutive relations and the field equations for generalized non-local thermoelastic model. The propagation of harmonically time-dependent thermoelastic plane waves of assigned frequency is studied in a homogeneous, isotropic, non-local infinite elastic solid by employing these equations. Reflection phenomenon of thermoelastic waves at a stress-free thermally insulated or isothermal flat boundary of a non-local thermoelastic solid half-space is also studied in case of incident coupled longitudinal wave. The amplitude ratios of the reflected waves to that of incident wave are determined analytically and numerically by considering an appropriate material. The numerical results are presented graphically to highlight the effects of various parameters of interest.

Thermoelastic Plane Waves in Materials with a Microstructure Based on Micropolar Thermoelasticity with Two Temperature and Higher Order Time Derivatives

The study of the effect of the microstructure is important and is most evident in elastic vibrations of high frequency and short-wave duration. In addition to deformation caused by temperature and acting forces, the theory of micropolar thermoelasticity is applied to investigate the microstructure of materials when the vibration of their atoms or molecules is increased. This paper addresses a two-dimensional problem involving a thermoelastic micro-polar half-space with a traction-free surface and a known conductive temperature at the medium surface. The problem is treated in the framework of the concept of two-temperature thermoelasticity with a higher-order time derivative and phase delays, which takes into consideration the impact of microscopic structures in non-simple materials. The normal mode technique was applied to find the analytical formulas for thermal stresses, displacements, micro-rotation, temperature changes, and coupled stress. The numerical results are graphed, and the effect of the discrepancy indicator and higher-order temporal derivatives is examined. There are also some exceptional cases that are covered.

Reflection of thermoelastic coupled plane waves under the MGL model

The present study is concerned with the reflection phenomenon of thermoelastic plane waves at the thermally insulated stress-free surface of a homogeneous isotropic thermally conducting elastic half-space in the frame of modified Green-Lindasy (MGL) model of generalized thermoelasticity with strain rate. The thermoelastic coupling effect creates two types of coupled longitudinal waves which are dispersive in nature as well as exhibit attenuation. Different from the thermoelastic coupling effect, there also exist one independent vertically shear-type (SV-type) wave. In contrast to the classical Green-Lindsay (GL) and the Lord-Shulman (LS) theories of generalized thermoelasticity, the SV-type wave is not only dispersive in nature but also experiences attenuation. Analytical expressions for the amplitude ratios and their respective energy ratios for the reflected thermoelastic waves are determined when a coupled longitudinal wave is made incident on a surface. The paper concludes with the numerical results on the phase speeds, amplitude ratios and their respective energy ratios for specific parameter choices. Various graphs are plotted to analyzed the analytical solution. The characteristics of employing the MGL model are discussed by comparing the numerical results obtained for the MGL model with those obtained in case of the GL, LS and the coupled thermoelasticity (CTE) models.

Effect of Impedance Boundary on the Reflection of Plane Waves in Fraction-Order Thermoelasticity in an Initially Stressed Rotating Half-Space with a Magnetic Field

In this research article, the propagation of the plane waves in an initially stressed rotating magneto-thermoelastic solid half-space in the context of fractional-order derivative thermoelasticity is studied. The governing equations in the x–z plane are formulated and solved to obtain a cubic velocity equation that indicates the existence of three coupled plane waves. A reflection phenomenon for the incidence of a coupled plane wave for thermally insulated/isothermal surface is studied. The plane surface of the half-space is subjected to impedance boundary conditions, where normal and tangential tractions are proportional to the product of normal and tangential displacement components and frequency, respectively. The reflection coefficients and energy ratios of various reflected waves are computed numerically for a particular material and the effects of rotation, initial stress, magnetic field, fractional-order, and impedance parameters on the reflection coefficients and energy ratios are shown graphically.

Reflection of thermoelastic plane waves at a stress-free insulated solid boundary with memory-dependent derivative

In the present manuscript, a two-dimensional generalized thermoelastic model is used to study the problem of reflection of thermoelastic plane waves from a stress-free and thermally insulated boundary of thermally conducting isotropic homogeneous elastic material. The Lord–Shulman model under the heat transfer law with memory-dependent derivative is employed to model this problem. The case of total reflection is taken into account to calculate the critical angle. Phase velocities and corresponding attenuation factors of the coupled dilatational elastic-thermal waves and the ratios of the reflection coefficients are calculated and illustrated graphically for copper-like material and highlighted the effects of various parameters of interest.

Thermoelastic plane waves under the modified Green–Lindsay model with two‐temperature formulation

AbstractThe present study is concerned with the reflection and propagation of thermoelastic plane waves from the stress‐free and thermally insulated surface of a homogeneous, isotropic thermally conducting elastic half‐space in the frame of modified Green–Lindsay theory of generalized thermoelasticity with two‐temperature (2TMGL). The thermoelastic coupling effect creates two types of coupled longitudinal waves which are dispersive as well as exhibit attenuation. Different from the thermoelastic coupling effect, there also exists one independent vertically shear‐type (SV‐type) wave. In contrast to the classical Green–Lindsay (GL) and Lord–Shulman (LS) theories of generalized thermoelasticity, the SV‐type wave is not only dispersive in nature but also experiences attenuation. Analytical expressions for the amplitude ratios and their respective energy ratios for reflected thermoelastic waves are determined when a coupled longitudinal wave is made incident on the free surface. The paper concludes with the numerical results on the phase speeds, amplitude ratios and their respective energy ratios for specific parameter choices. Various graphs have been plotted to analyze the behavior of these quantities. The characteristics of employing the 2TMGL model are discussed by comparing the numerical results obtained for the present model with those obtained in case of the two‐temperature Green–Lindsay (2TGL) and two‐temperature Lord–Shulman (2TLS) models.

Reflection of Thermoelastic Waves From the Insulated Surface of a Solid Half-Space With Time-Delay

Abstract This paper is devoted to study the reflection of thermoelastic plane waves from the thermally insulated stress-free boundary of a homogeneous, isotropic and thermally conducting elastic half-space. A new linear theory of generalized thermoelasticity under heat transfer with memory-dependent derivative (MDD) is employed to address this study. It has been found that three basic waves consisting of two sets of coupled longitudinal waves and one independent vertically shear-type wave may travel with distinct phase speeds. The formulae for various reflection coefficients and their respective energy ratios are determined in case of an incident coupled longitudinal elastic wave at the thermally insulated stress-free boundary of the medium. The results for the reflection coefficients and their respective energy ratios for various values of the angle of incidence are computed numerically and presented graphically for copper-like material and discussed.

Reflection of plane waves on generalized thermoelastic medium under effect of temperature dependent properties and initial stress with three-phase-lag model

The present paper investigates the reflection coefficient of thermoelastic plane waves at the free surface of an elastic half-space influenced by initial stress and temperature-dependent properties in the presence of thermal loading bounded by the three-phase-lag (3PHL) thermoelastic model. It revealed three plane waves, i.e. (thermal wave (T-wave), P-wave, and SV-wave). It provided the numerical solution and presented the effect of initial stress and temperature-dependent properties of the reflection coefficient graphically. Moreover, the paper utilized the altered reflected elastic waves because of initial stress and temperature-dependence to identify the more accurate nature of waves reflection, especially seismic waves.

Waves in nonlocal thermoelastic solids of type III

AbstractIn this paper, the propagation of time‐harmonic thermoelastic plane waves is studied in an infinite nonlocal elastic continuum. The type III Green‐Naghdi model (with energy dissipation) of generalized thermoelasticity and the Eringen's nonlocal elasticity model are adopted to address this problem. We found two sets of the 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. Reflection phenomenon of an incident coupled longitudinal waves from a rigid and thermally insulated boundary surface of a homogeneous and isotropic nonlocal thermoelastic half‐space is investigated. Using these boundary conditions, the formulae for various reflection coefficients and their respective energy ratios are presented. For a particular model, various graphs are plotted to analyze the behavior of the phase speeds, reflection coefficients and their respective energy ratios. The amplitude ratios of the reflected waves and their respective energy ratios are determined analytically. For a particular model, the effect of elastic nonlocality parameter on the variations of phase speeds, attenuation coefficients, amplitude ratios and corresponding energy ratios of the reflected waves are presented graphically. Finally, analysis of the various results have been interpreted.

Modified Green–Lindsay model on the reflection and propagation of thermoelastic plane waves at an isothermal stress-free surface

The present study is concerned with the reflection and propagation of thermoelastic harmonic plane waves from the stress-free and isothermal surface of a homogeneous, isotropic thermally conducting elastic half-space in the frame of the modified Green–Lindasy (MGL) theory of generalized thermoelasticity with strain rate proposed by Yu et al. (Meccanica 53:2543–2554, 2018). The thermoelastic coupling effect creates two types of coupled longitudinal waves which are dispersive as well as exhibit attenuation. Different from the thermoelastic coupling effect, there also exists one independent vertically shear-type (SV-type) wave. In contrast to the classical Green–Lindsay (GL) and Lord–Shulman (LS) theories of generalized thermoelasticity, the SV-type wave is not only dispersive in nature but also experiences attenuation. Analytical expressions for the amplitude ratios of the reflected thermoelastic waves are determined when a coupled longitudinal wave is made incident on the free surface. The paper concludes with the numerical results on the phase speeds and the amplitude ratios for specific parameter choices. Various graphs have been plotted to analyze the behavior of these quantities. The characteristics of employing the MGL model are discussed by comparing the numerical results obtained for the present model with those obtained in case of the GL and LS models.

Reflection of thermoelastic waves from the isothermal boundary of a solid half-space under memory-dependent heat transfer

ABSTRACT In this paper, we investigated the reflection of thermoelastic plane waves from the isothermal stress-free boundary of a homogeneous, isotropic and thermally conducting solid half-space in the context of the new linear theory of generalized thermoelasticity under heat transfer with memory-dependent derivative. It has been found that three types of basic waves consisting of two sets of coupled longitudinal waves and one independent vertically shear type wave may travel with distinct phase speeds. The formulae for various reflection coefficients are determined in case of an incident coupled dilatational elastic wave at an isothermal stress-free boundary of the medium. For an appropriate material, the reflection coefficients are computed numerically and presented graphically for various values of the angle of incidence and discussed the effect of various parameters of interest. At the end, the phase speeds and the attenuations coefficients of the coupled longitudinal waves are shown graphically to compare our results with the existing results.

Propagation of waves in an initially stressed generalized electromicrostretch thermoelastic medium with temperature-dependent properties under the effect of rotation

ABSTRACTIn 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.

Structure and intrinsic properties of dispersion relation in hyperbolic thermoelasticity

ABSTRACTFor a system of field equations of hyperbolic thermoelasticity, we derive a propagation condition for a thermoelastic disturbance in a form of homogeneous plane wave in deformation and temperature. The corresponding dispersion relation is given in an explicit form, together with the dependence of characteristic coefficients on the principal invariants of the tensor of isothermal elasticity, heat conductivity, and thermoelasticity. Discussion of different types of homogeneous thermoelastic plane waves is given as well. Derived methodology is applied in the analysis of Green–Naghdi model.

On Discontinuties in Thermoelastic Plane Waves without Energy Dissipation Due to a Thermo-Mechanical Shock

The present paper deals with the thermoelastic plane waves due to a thermo-mechanical shock in the form of pulse at the boundary of a homogeneous, isotropic thermoelastic half-space. The field equations of the Green- Naugdhi theory without energy dissipation for an thermoelastic solid in the generalized thermoelasticity theory are written in the form of a vector-matrix differential equation using Laplace transform techniques and then solved by an eigenvalue approach. Exact expressions for the considered field variables are obtained and presented graphically for copper-like material. The characteristic features of the present theory are analyzed by comparing these solutions with their counterparts in other generalized thcrmoelasticity theories.

Propagation of thermoelastic plane waves at an imperfect boundary of thermal conducting viscous liquid/generalized thermoelastic solid

The reflection and transmission of thermoelastic plane waves at an imperfect interface between a thermal conducting viscous-liquid and generalized thermoelastic solid half-space has been investigated. The amplitude ratios of various reflected and transmitted waves are obtained for an imperfect boundary. Particular cases of normal stiffness, transverse stiffness, slip and welded boundaries are deduced. Some special cases of interest are also obtained from the present investigation. It is found that the amplitude ratios of various reflected and transmitted waves are affected by the stiffness and thermal properties of the media.

Thermoelastic plane waves for an elastic solid half-space under hydrostatic initial stress of type III

In this paper, we constructed the equations of generalized thermoelastic isotropic and homogeneous half-space under hydrostatic initial stress in the context of the Green and Naghdi (GN) theory of types II and III. Normal mode analysis is used to obtain the exact expressions of temperature, displacement and stress. Comparisons are made with the results predicted by GN theory of types II and III in the presence and absence of the hydrostatic initial stress. The temperature, displacement and stress distributions are represented graphically.