Thermoelastic Solid Half-space Research Articles

Study of different theories of thermoelasticity under the propagation of Rayleigh waves in thermoelastic medium

The present research is on the propagation of Rayleigh waves in a homogenous thermoelastic solid half-space by considering the compact form of six different theories of thermoelasticity. The medium is subjected to an insulated boundary surface that is free from normal stress, tangential stress, and a temperature gradient normal to the surface. After developing a mathematical model, a dispersion equation is obtained with irrational terms. To apply the algebraic method, this equation must be converted into a rational polynomial equation. From this, only those roots are filtered out, which has satisfied both of the above equations for the propagation of waves decaying with depth. With the help of these roots, different characteristics are computed numerically, like phase velocity, attenuation coefficient, and path of particles. Various particular cases are compared graphically by using phase velocity and attenuation coefficient. The elliptic path of surface particles in Rayleigh wave propagation is also presented for the different theories using physical constants of copper material for different depths and thermal conductivity.

Three-phase-lag analysis of transversely isotropic double porous thermoelastic waves with liquid medium

This manuscript presents a mathematical framework for a double porous, thermoelastic solid half-space with transverse isotropy in contact with an inviscid liquid half-space. The analysis takes into account the three-phase-lag model within thermoelasticity theory. To gain deeper insights, we formulate the governing equations in a two-dimensional representation and subsequently employ normal mode analysis for their rigorous solution. The governing equations are influenced by both types of voids, anisotropy, thermal effect, and inviscid liquid. It has been discovered that thermoelastic half-space exhibits five coupled longitudinal waves, and in the liquid half-space, there is one mechanical wave. Secular equations are obtained by using thermal and mechanical conditions, resulting in a compact representation of phase velocity, specific loss, penetrating depth, and attenuation coefficient. Analytical presentations have been made to showcase the effects of anisotropy, voids, and liquid on various wave parameters. These effects are compared by illustrating the results graphically using the MATLAB software, allowing for a visual understanding of the comparative outcomes. This study has practical applications in engineering, materials science, geophysics, and environmental studies, contributing to advancements in various industries and scientific fields.

Propagation of plane waves at the initially stressed surface of an orthotropic nonlocal rotating half space under dual-phase-lag model

PurposeThe purpose of the current manuscript is to investigate the reflection of plane waves in a rotating, two-dimensional homogeneous, initially stressed, nonlocal orthotropic thermoelastic solid half-space based on dual-phase-lag model.Design/methodology/approachThe reflection phenomenon has been utilized to study the effects of initial stress, rotation and nonlocal parameter on the amplitude ratios. During the reflection phenomenon three coupled waves, namely quasi displacement primary wave (qP), quasi thermal wave (qT) and quasi displacement secondary wave (qSV) have been observed in the medium, propagating with distinct velocities. After imposing the suitable boundary conditions, amplitude and energy ratios of the reflected waves are obtained in explicit form.FindingsWith the support of MATLAB programming, the amplitude ratios and energy ratios are plotted graphically to display the effects of rotation, initial stress and nonlocal parameters. Moreover, the impact of anisotropy and phase lags is also observed on the reflection coefficients of the propagating waves.Originality/valueIn the current work, we have considered rotation and nonlocality parameters in an initially stressed orthotropic thermoelastic half-space, which is lacking in the published literature in this field. The introduction of these parameters in a nonlocal orthotropic thermoelastic medium provides a more realistic model for these studies. The present work is valuable for the analysis of orthotropic thermoelastic problems involving rotation, initial stress and nonlocality parameters.

Reflection and transmission characteristics of plane-P-wave at the interface of anisotropic nonlocal poroelastic and thermoelastic solid half-spaces

Reflection and transmission characteristics of plane-P-wave at the interface of anisotropic nonlocal poroelastic and thermoelastic solid half-spaces

Thermo-mechanical interactions in a functionally graded orthotropic thermoelastic medium with rotation and gravity

The current research identify the disturbances in a rotating two-dimensional nonhomogeneous, orthotropic thermoelastic solid half-space with gravity field in the context of Green and Lindsay (G-L) theory. A mechanical source is acting on the surface of the half-space. It is presumed that the mechanical and thermal properties are varying in the x-direction. With the application of normal mode analysis, different field variables are obtained in the physical domain. These field variables are also computed numerically with the help of MATLAB programming. Some collations are made to delineate the effects of anisotropy, non-homogeneity, gravity and rotation parameters on the physical fields.

Waves in a transversely isotropic poro-thermoelastic solid under inviscid fluid loadings

The generalized theory of thermoelasticity with one relaxation time has been extended to formulate the mathematical model for a homogeneous transversely isotropic thermoelastic solid half-space containing voids under inviscid fluid loading. The governing equations of motion have been derived by taking into account the thermal effect, effects of voids, anisotropy, and inviscid liquid. The complex secular equation has been derived by employing appropriate conditions at the solid–liquid boundary and particular cases have also been investigated. The theoretical portion has revealed the existence of five waves in the poro-thermoelastic anisotropic material and one mechanical wave traveling in the inviscid fluid. The wave motion has been examined with the help of a frequency equation by employing a numerical iteration method using MATLAB software tools that give complete information regarding the wave characteristics. Anisotropy, voids, and liquid effects on various parameters of wave have been presented analytically and comparisons have been made by depicting the results graphically. The study is useful in ultrasonics, navigation, and offshore engineering.

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.

Thermo-mechanical interactions in a nonlocal transversely isotropic material with rotation under Lord–Shulman model

The objective of this manuscript is to examine the thermodynamical disturbances in a rotating nonlocal transversely isotropic thermoelastic solid half-space. The enunciation is applied to Lord–Shulman model of generalized thermoelasticity with Eringen's nonlocal elasticity theory. The formulation is subjected to a mechanical load. The expressions for the displacement components, stresses and temperature field are obtained by using normal mode technique and the numerical computations have been carried out with the help of MATLAB software for zinc crystal-like material. The comparisons are made among the results obtained by taking into account the different values of rotation parameter ( Ω = 0.0 , 0.1 , 0.3 ) , nonlocal parameter ( ε = 0.195 × 10 − 9 , 0.195 × 10 − 4 , 0.195 × 10 − 1 ) and time ( t = 0.1 , 0.3 , 0.5 ) . The outcomes point out a strong impact of the rotation, nonlocality and time on the physical quantities and agree with the boundary conditions. Although various studies exist in the literature for local and isotropic thermoelastic medium, but the current results are presented in an anisotropic and nonlocal thermoelastic rotating medium, which have not been studied so far.

Reflection of plane waves in a micropolar thermo-diffusion porous medium

The research article deals with the reflection of plane waves in a micropolar thermoelastic diffusion solid half-space with voids in the context of Lord-Shulman theory of thermoelasticity. The governing equations are formulated to obtain two velocity equations. The plane wave solution of these velocity equations indicate the existence of six plane waves, a set of four coupled longitudinal displacement waves and a set of two coupled transverse displacement wave namely coupled longitudinal displacement wave ( LD − 1 ) , coupled thermal wave ( LD − 2 ) , coupled mass diffusion wave ( LD − 3 ) , coupled longitudinal void volume fraction wave ( LD − 4 ) and coupled transverse displacement wave ( TD − 1 ) , coupled transverse micro-rotational wave ( TD − 2 ) . A reflection of the plane wave from a stress-free thermally insulated surface is studied to obtain the reflection coefficients and energy ratios of reflected waves. The reflection coefficients and energy ratios of the reflected waves are computed for a particular material and the variations of the reflection coefficients and energy ratios against the angle of incidence are shown graphically.

Waves in magneto-thermoelastic solids under modified Green–Lindsay model

In this paper, the propagation of time-harmonic plane waves is investigated in an infinite elastic solid material by employing the modified Green–Lindsay (MGL) model of generalized thermoelasticity. It is found that three basic waves consisting of two sets of coupled longitudinal waves and one independent vertically shear-type (SV-type) wave may travel with distinct speeds. The sets of coupled waves are found to be dispersive, attenuating and influenced by the thermoelastic coupling effect. In contrast to the Green–Lindsay (GL) as well as the Lord–Shulman (LS) models, the SV-type wave is not only dispersive in nature but also experiences attenuation. Reflection phenomenon of an incident coupled longitudinal wave from stress-free and thermally insulated boundary surface of a thermoelastic solid half-space is addressed. 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 characteristics of employing the MGL model are discussed by comparing the numerical results obtained for the present model with those obtained in the case of the GL model.

Rayleigh-type surface waves in a nonlocal thermoelastic solid half space with voids

The present paper deals with the propagation of surface waves in an isotropic and homogeneous nonlocal generalized thermoelastic solid half-space with voids. The dispersion relations for Rayleigh-type surface wave are derived for both thermally insulated and isothermal boundaries. The non-dimensional wave speed of Rayleigh-type surface wave is computed for some specific constants of a material representing the present model. The dependence of non-dimensional wave speed on frequency, nonlocality, thermal and voids parameters is illustrated graphically.

Memory-dependent magneto–thermoelasticity for perfectly conducting two-dimensional elastic solids with thermal shock

Recently, Yu et al. (2014) proposed a new model in generalized thermoelasticity based on heat conduction with the memory-dependent derivative. The magneto–thermoelastic responses in a perfectly conducting thermoelastic solid half-space is investigated in the context of the above new theory. Normal mode analysis together with an eigenvalue expansion technique is used to solve the resulting non-dimensional coupled governing equations. The obtained solutions are then applied to a specific problem for thermoelastic half-space whose boundary is subjected to a time-dependent thermal shock and zero stress. The effects of the kernel function, time-delay parameter, magnetic field and thermoelastic coupling parameter on the variations of different field quantities inside the half-space are analyzed graphically. The results show that these parameters has significant influence on the variations of the considered variables.

Propagation of waves at an interface between a transversely isotropic rotating thermoelastic solid half space and a fiber-reinforced magneto-thermoelastic rotating solid half space

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.

Reflection of plane waves from a micropolar thermoelastic solid half-space with impedance boundary conditions

In this paper, the governing equations of linear, isotropic, homogeneous and generalized micropolar thermoelasticity are specialized in a plane. The governing equations are solved for plane harmonic wave solutions. Two separate velocity equations are obtained which indicate the existence of four plane waves with distinct speeds. A problem on reflection of plane waves from a thermally insulated/ isothermal surface is considered with impedance boundary conditions. Appropriate potentials for incident and reflected waves are formulated which satisfy the boundary conditions at a plane surface. Relations between reflection coefficients as well as the expressions of energy ratios for various reflected waves are obtained. For illustration, the reflection coefficients and energy ratios of reflected waves are computed for relevant material parameters of an aluminium-epoxy composite. Effect of impedance parameters on all reflected waves is shown graphically at each angle of incidence.

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.

Effect of Impedance Boundary on Reflection of Plane Waves from free Surface of a Rotating Thermoelastic Solid Half Space

The coupled partial differential equations governing a rotating thermoelastic medium in context of Lord and Shulman theory are solved for plane wave solutions. A cubic velocity equation is obtained, which correspond to the speeds of propagation of three coupled plane waves. A reflection phenomenon is considered in a rotating thermoelastic solid half-space for incidence of a coupled plane wave. The plane surface of the half-space is subjected to impedance boundary conditions, where normal and tangential tractions are proportional to normal and tangential displacement components time frequency, respectively. The expressions for energy ratios of all reflected waves are obtained and computed numerically for a particular material representing the medium. The dependence of energy ratios on rotation parameter, impedance parameters and angle of incidence is shown graphically.

Reflection of plane wave in a micropolar thermoelastic solid half-space with diffusion

ABSTRACTIn this article, the governing equations of micropolar thermoelasticity with diffusion are formulated in the context of Lord–Shulman theory of generalized thermoelasticity. The plane wave solutions of these equations indicate the existence of six plane waves, namely, coupled longitudinal displacement (CLD) wave, coupled thermal wave, coupled mass diffusion wave, coupled transverse microrotational wave, coupled transverse displacement wave, and longidudinal microrotational wave. Reflection of CLD wave from a stress-free thermally insulated/isothermal surface is considered. The appropriate potentials of incident and reflected waves satisfy the required boundary conditions at a stress-free thermally insulated/isothermal surface to obtain the reflection coefficients of various reflected waves for an incident CLD wave and to obtain an extension of Snell’s law. The expressions for energy ratios of various reflected waves are also obtained. A particular material aluminum–epoxy composite is chosen to compute the values of reflection coefficients and energy ratios of reflected waves. The effects of diffusion and thermal parameters are observed on the reflection coefficients and energy ratios.

Two-temperature dual-phase-lags theory in a thermoelastic solid half-space due to an inclined load

Abstract. This article addresses the thermoelastic interaction due to inclined load on a homogeneous isotropic half-space in context of two-temperature generalized theory of thermoelasticity with dual-phase-lags. It is assumed that the inclined load is a linear combination of both normal and tangential loads. The governing equations are solved by using the normal mode analysis. The variations of the displacement, stress, conductive temperature, and thermodynamic temperature distributions with the horizontal distance have been shown graphically. Results of some earlier workers have also been deduced from the present investigation as special cases. Some comparisons are graphically presented to estimate the effects of the two-temperature parameter, the dual-phase-lags parameters and the inclination angle. It is noticed that there is a significant difference in the values of the studied fields for different value of the angle of inclination. The method presented here maybe applicable to a wide range of problems in thermodynamics and thermoelasticity.

Generalized thermoelastic interactions due to an inclined load at a two-temperature half-space

The article presents a two-temperature theory to study the thermally insulated stress-free surface of a thermoelastic solid half-space due to an inclined load. The inclined load is a linear combination of a normal load and a tangential load. The normal mode analysis has been employed to solve the present problem. Variations of conductive and thermodynamic temperatures, displacements, and stresses distributions with the horizontal distance have been presented graphically. Some comparisons have been made to estimate the effects due to the two-temperature parameter and the inclination angle on the field quantities. Results of earlier works have been deduced from the present investigation as special cases.

Propagation of Rayleigh Surface Wave in a Two-Temperature Thermoelastic Solid Half-Space with Diffusion

Propagation of Rayleigh Surface Wave in a Two-Temperature Thermoelastic Solid Half-Space with Diffusion