Thermoelastic Half-space Research Articles

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.

Waves in a nonlocal micropolar thermoelastic half-space with voids under dual-phase-lag model

The present article is concerned with the reflection of plane harmonic waves in a nonlocal micropolar thermoelastic medium having void pores in the context of dual-phase-lag and Lord-Shulman models. Two sets of coupled shear waves and three sets of coupled longitudinal waves are shown to exist. When a coupled longitudinal displacement wave is made incident, the reflection coefficients of the various reflected waves and their respective energy ratios are computed analytically and the numerical computation is carried out with the help of MATLAB software. For a particular model, the influence of nonlocal, voids and micropolar parameters on the variations of reflection coefficients and energy ratios of various reflected waves is presented graphically. It is verified that during reflection phenomenon, the sum of energy ratios is equal to unity at each angle of incidence. A comparison between the dual-phase-lag model and Lord-Shulman model is also depicted graphically.

State space approach to characterize Rayleigh waves in a layer lying over a half-space with nonlocal thermoelasticity

The paper deals with a new model based on Eringen's nonlocal thermoelasticity. The propagation of Rayleigh waves in a nonlocal thermoelastic layer which is lying over a nonlocal thermoelastic half-space is considered in the context of energy dissipation theory. The normal mode analysis is employed to the considered equations to obtain vector matrix differential equation which is then solved by state space approach.The frequency equation of Rayleigh surface wave is derived. The effect of the nonlocal parameter on phase velocity, attenuation coefficient, specific loss and penetration depth of Rayleigh surface waves is presented graphically.

Reflection of coupled waves from the flat boundary surface of a nonlocal micropolar thermoelastic half-space containing voids

Reflection behavior of a set of coupled longitudinal/transverse waves incident obliquely at the flat boundary surface of a nonlocal micropolar thermoelastic half-space containing voids is investigated. Appropriate boundary conditions are setup for mechanically stress-free and thermally insulated boundary surface of the half-space. The equations yielding the reflection coefficients and the expressions of corresponding energy ratios of various reflected waves are presented. The nature of dependence of the reflection coefficients and their corresponding energy ratios against the angle of incidence is studied numerically for a specific model. Effect of several parameters on the reflection coefficients as well as on the corresponding energy ratios is noticed and depicted graphically. It is found that the sum of the energy ratios is approximately equal to unity at each angle of incidence. Some earlier known results are also recovered as special cases of the present formulation.

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.

Surface absorption illumination in a 2D thermoelastic semi-infinite medium under modified Green and Lindsay model

In this study, the modified Green and Lindsay model is utilized to discuss the effects of heating caused by surface absorption of laser radiation in a two-dimensional thermoelastic half-space. The temporal profile of the pulsed laser is taken as a non-Gaussian and the spatial one is a Gaussian. The medium surface is taken to be traction free. The integral transform method is utilized to obtain the general solution by applying the two transformations Hankel and Laplace, in which the inverse of Laplace is performed numerically. The Silicon material is considered as an example to verify the consistency of the obtained results of the new model.

Magneto-thermoelastic interactions in generalized thermoelastic half-space for varying thermal and electrical conductivity

Significant variations are observed over the working temperature range of the various engineering problems such as designing the structures heated by sudden heat flux in engineering. At that time, major variations in the coefficient of the thermal conductivity of the material are observed. Electrical conductivity is also found to be directly dependent on the thermal conductivity. Therefore, present problem enlightens the influence of the variable thermal conductivity and electrical conductivity inside a half space medium permeated by the magnetic field in context of dual phase lag thermoelasticity. Thermal shock has been applied to the non-traction boundary of the medium. Analytical solutions are calculated by adopting Laplace transform technique. Physical fields such as conductive temperature, displacement as well stress of the medium are evaluated in time-domain numerically by using a suitable method of numerical inversion of Laplace transform. Further, to predict the utility of the present model, computational results are compared to the corresponding results of heat conduction model with single phase lag (Lord and Shulman model). By examining the numerical results that have been graphically represented, significant differences have been attributable to the studied fields due to the variable thermal conductivity and different heat conduction models.

Rayleigh wave propagation at the boundary surface of dry sandy ($SiO_2$) thermoelastic solids

PurposeThe purpose of study to this article is to analyze the Rayleigh wave propagation in an isotropic dry sandy thermoelastic half-space. Various wave characteristics, i.e wave velocity, penetration depth and temperature have been derived and represented graphically. The generalized secular equation and classical dispersion equation of Rayleigh wave is obtained in a compact form.Design/methodology/approachThe present article deals with the propagation of Rayleigh surface wave in a homogeneous, dry sandy thermoelastic half-space. The dispersion equation for the proposed model is derived in closed form and computed analytically. The velocity of Rayleigh surface wave is discussed through graphs. Phase velocity and penetration depth of generated quasi P, quasi SH wave, and thermal mode wave is computed mathematically and analyzed graphically. To illustrate the analytical developments, some particular cases are deliberated, which agrees with the classical equation of Rayleigh waves.FindingsThe dispersion equation of Rayleigh waves in the presence of thermal conductivity for a dry sandy thermoelastic medium has been derived. The dry sandiness parameter plays an effective role in thermoelastic media, especially with respect to the reference temperature for η = 0.6,0.8,1. The significant difference in η changes a lot in thermal parameters that are obvious from graphs. The penetration depth and phase velocity for generated quasi-wave is deduced due to the propagation of Rayleigh wave. The generalized secular equation and classical dispersion equation of Rayleigh wave is obtained in a compact form.Originality/valueRayleigh surface wave propagation in dry sandy thermoelastic medium has not been attempted so far. In the present investigation, the propagation of Rayleigh waves in dry sandy thermoelastic half-space has been considered. This study will find its applications in the design of surface acoustic wave devices, earthquake engineering structural mechanics and damages in the characterization of materials.

Plane wave propagation in dual-phase-lag generalized thermoelastic transversely isotropic structure with rotation effect

The aim of this work is to investigate the influence of rotation and dual-phase-lag (DPL) theory of generalized thermoelasticity on the reflection of plane waves in a transversely isotropic thermoelastic half-space. It is supposed that the elastic half-space rotates with steady angular velocity. Since the basic equations were solved in a two-dimensional space, so three types of quasi-plane waves are found based on the three of velocities of plane waves. The amplitude ratios and their coefficients of these diverse plane waves according to a suitable boundary conditions are obtained analytically. The impact of incident angle, rotation and thermal relaxation times of DPL theory are computed numerically for a specific material and represented graphically.

A Mode-I crack for a rotational fibre-reinforced thermoelastic medium with thermal relaxation time

A general model of the equations with coupled theory (CD) and Lord-Shulman (L-S) theory with one relaxation time is applied to study the influence of reinforcement on the total deformation for an infinite space weakened by a finite linear opening Mode-I Crack is solving. We study the influence of reinforcement on the total deformation of rotating thermoelastic half-space and the interaction with each other. The material is homogeneous isotropic elastic half space. The crack is subjected to prescribed temperature and stress distribution. The normal mode analysis is used to obtain the exact expressions for the displacement components, force stresses and temperature. The variations of the considered variables with the horizontal distance are illustrated graphically. Comparisons are made with the results in two theories in the presence and absence of rotation. A comparison also is made between the two theories for different depths.

Thermal wave propagation in a two-dimensional problem under gravitational field due to time-dependent thermal loading and memory effect

This paper presents a comprehensive study on developing a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena for an infinite thermoelastic half-space under the action of ramp-type thermal loading and due to the influence of a gravitational field. The bounding plane of the half-space is subjected to rough and rigid foundation so that the rough surface prevents the vertical displacement. Due to the shortcomings of power-law distributions, some other forms of derivatives with few other kernel functions are proposed. The present analysis deals with the heat transport which involves the memory-dependent derivative (MDD) on a slipping interval in the context of Lord–Shulman model to describe the physical phenomena which is defined in the form of convolution with the kernels in the form of power functions. Employing the Laplace and the Fourier transform techniques as tools, the analytical expressions for different physical fields have been obtained on the transformed domain. The numerical inversion of the Fourier transforms have been performed analytically, whereas numerical inversion of the Laplace transform is carried out using the Riemann-sum approximation method. Excellent predictive capability is demonstrated due to the presence of MDD, delay time and gravitational field also.

Effect of magnetic field and voids on Rayleigh waves in a nonlocal thermoelastic half-space

This work is concerned with the propagation of surface waves is considered in an isotropic elastic homogeneous nonlocal generalized thermoelastic solid medium in the presence of a magnetic field and voids. The normal mode analysis and Lame’s potential theory are used to solve the resulting non-dimensional coupled equations. Dispersion relation for Rayleigh surface wave are derived for both thermally insulated and isothermal surfaces. The non-dimensional wave speed of Rayleigh surface wave is computed for a specific material. The non-dimensional wave speed of Rayleigh surface waves are found to be influenced by the presence of voids, magnetic field, thermal field, and elastic nonlocal parameter. For a particular model, the effect of magnetic field, void parameters, thermal parameter, and nonlocality has been studied numerically on the Rayleigh surface waves. All the computed results obtained have been depicted graphically and explained.

Dynamics of thermoelastic half-plane by action of periodic loads and heat flows at its boundary

The problem of the dynamics of a thermoelastic half-space under periodic surface forces and heat flows is solved using the model of coupled thermoelasticity. The Green’s tensor for one boundary value problem is constructed utilizing Fourier transformation. Analytical solutions for arbitrary surface forces and heat flow using the theory of generalized functions are constructed. To solve this boundary value problem, generalized function theory, tensor and differential algebra, the operator method, and integral transformations were used. The solutions obtained make it possible to investigate the thermal stress–strain state of an array with natural and artificial thermal sources and mass power forces acting at its surface.

Solution of three-dimensional generalized thermodiffusive elastic half-space with phase lag in the presence of chemical potential shock and thermal pulse

An isotropic homogeneous thermoelastic half-space has been considered with permeating gas, thermal pulse, and chemical potential on the bounding plane. A three-dimensional generalized thermo-diffusion model with three-phase lag has been constructed in the context of Memory-dependent derivative (MDD). Laplace transform (time domain) and Double Fourier transform (space domain) have been used in the formulation of the problem and thus the solutions for temperature increment, invariant stress, chemical potential and diffusion concentration are obtained using eigenvalue approach. Finally the effect of kernel function has been discussed and also the results are depicted in several dimensions.

Mathematical Modeling on Rotational Magneto-Thermoelastic Phenomenon under Gravity and Laser Pulse considering Four Theories

The aim of this investigation is making mathematical model for the variation in laser pulse, rotational gravity, and magnetic fields on the generalized thermoelastic homogeneous isotropic half-space. The governing dynamical system equations have been formulated considering the four thermoelastic models: coupled (CT) model, Lord and Shulman (LS) model, Green and Lindsay (GL) theory, and Green and Naghdi (GN III) model. Normal mode analysis technique is used to obtain the analytical expressions for the displacement components, temperature, and mechanical and Maxwell’s stresses distribution. The effect of laser pulse, gravity, and magnetic field is studied by numerical examples and displayed graphically. A comparison has been made between the theories as well as the present results and agreement with it as a special case from this study. The results predict the strong effect of magnetic field, laser pulse, and gravity field on the wave propagation phenomenon.

Rayleigh waves in porous nonlocal orthotropic thermoelastic layer lying over porous nonlocal orthotropic thermoelastic half space

ABSTRACT The present paper deals with the propagation of Rayleigh surface waves in a nonlocal thermoelastic orthotropic layer which is lying over a nonlocal thermoelastic orthotropic half space. The problem is considered in the context of Green-Naghdi type III model of hyperbolic thermoelasticity and Eringen’s nonlocal elasticity theory in the presence of voids. The problem is solved using eigenfunction expansion method. Frequency equation of Rayleigh waves is derived and different particular cases are also deduced. The effects of voids and nonlocality on different characteristics of Rayleigh waves are presented graphically.

Plane wave propagation in functionally graded isotropic couple stress thermoelastic solid media under initial stress and gravity

The work is concerned with the wave propagation at the interface of isolated exponentially graded couple stress thermoelastic media under initial stress and gravity. We analyse the influence of initial stress and gravity on reflection and refraction coefficients for both upper and lower couple stress thermoelastic half-spaces. Further, we found there are three waves, viz. quasi-SV and set of two longitudinal waves propagating with different speeds. The phase speeds, equation of motions, reflection and refraction coefficients are calculated in closed form. The impact of gravity and initial stress parameter has also been calculated numerically and shown graphically.

Rotational Effect on the Propagation of Waves in a Magneto-Micropolar Thermoelastic Medium

The present paper aims to explore how the magnetic field, ramp parameter, and rotation affect a generalized micropolar thermoelastic medium that is standardized isotropic within the half-space. By employing normal mode analysis and Lame’s potential theory, the authors could express analytically the components of displacement, stress, couple stress, and temperature field in the physical domain. They calculated such manners of expression numerically and plotted the matching graphs to highlight and make comparisons with theoretical findings. The highlights of the paper cover the impacts of various parameters on the rotating micropolar thermoelastic half-space. Nevertheless, the non-dimensional temperature is not affected by the rotation and the magnetic field. Specific attention is paid to studying the impact of the magnetic field, rotation, and ramp parameter of the distribution of temperature, displacement, stress, and couple stress. The study highlighted the significant impact of the rotation, magnetic field, and ramp parameter on the micropolar thermoelastic medium. In conclusion, graphical presentations were provided to evaluate the impacts of different parameters on the propagation of plane waves in thermoelastic media of different nature. The study may help the designers and engineers develop a structural control system in several applied fields.

On a thermoelastic magnetized half-space problem considering presence and absence of rotation in the context of GN (II) model

In this paper, having or lacking a rotating, magnetic field, and a time-dependent source of heat on a two-dimensional homogeneous, isotropic, and thermoelastic half-space was illustrated. The governing equations were formulated in the considering Maxwell's stresses. The surface boundary settings were explored considering the thermoelasticity model of Green and Naghdi (type II). The techniques of the eigenvalue method and the normal mode analysis were utilized to resolve the non-dimensional coupled equations. We analyzed theoretically and computed numerically the rotation, time, wave number, frequency, and magnetic field. A comparison between having or lacking of the rotation was made with the results obtained. The displacement components, temperature, dilatation, and average of the normal stress were displayed in graphs to illustrate the physical meaning of the wavenumber, frequency, rotation, magnetic field, and time-dependent heat source. Normal stresses have been displayed graphically to show the physical meaning of the magnetic field, rotation, frequency, wave number, and time-dependent heat source. The results obtained show that having rotation, magnetic field, and time affects significantly eigenvalue issue, especially in astrophysics, aircraft, engineering, astronomy, petroleum extracting, and structures.

Reflection of plane waves in a nonlocal microstretch thermoelastic medium with temperature dependent properties under three-phase-lag model

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 sets of coupled longitudinal waves and two sets of coupled transverse waves travel with distinct speeds in the considered medium. The numerical values of amplitude ratios are shown graphically to explore the effects of temperature dependent properties, nonlocal and microstretch parameters. The effect of nonlocality on the phase speeds and attenuation coefficients of propagating waves have also been observed. It has also been verified that there is no dissipation of energy during reflection phenomenon.