Thermoelastic Half-space Research Articles

Rayleigh waves in a layered thermoelastic structure

This paper aims to establish a general exact secular equation for Rayleigh surface waves propagating in an isotropic thermoelastic half-space coated by an isotropic thermoelastic layer of arbitrary thickness. The contact between the layer and the half-space is assumed to be welded on the interface. The outer surface of the layer is free of traction, and no heat transfer is allowed with the surrounding environment. When passing through the contact surface, the displacements and temperature fields, as well as the stresses and heat flux fields, are supposed to vary continuously, no jump being allowed. The explicit expressions of free Rayleigh waves in both the layer and the half-space are first presented, and then they are used to establish the general exact secular equation. Numerical illustrations are presented for a layered structure consisting of an aluminum layer welded on a half-space made of various thermoelastic materials outlining the main characteristics of Rayleigh wave propagation: the dimensionless propagation speed and the dimensionless damping in time of the wave’s amplitude. The exact effective boundary conditions for the Rayleigh waves are established in the thermoelastic half-spaces covered with thin films. Some limiting cases are also discussed: (1) when the thermoelastic layer is absent and (2) when the thermal effects are neglected.

Effect of Hall Current on Reflection Phenomenon of Plane Waves in a Two Temperature Fiber-Reinforced Orthotropic Thermoelastic Half-Space

Effect of Hall Current on Reflection Phenomenon of Plane Waves in a Two Temperature Fiber-Reinforced Orthotropic Thermoelastic Half-Space

Reflection phenomena of thermoelastic plane waves on a rigid surface within a size-dependent elastic media

The current investigation aims to comprehend the spread of time-harmonic thermoelastic plane waves in an isotropic and homogeneous nonlocal elastic material without bounds, within the framework of the Lord–Shulman model and Eringen’s nonlocal stress model. Our analysis reveals two sets of coupled longitudinal waves and one independent shear-type wave. The coupled longitudinal waves experience dispersion and damping over time due to the dissipative nature of the L-S model. In contrast, the vertically shear-type waves exhibit dispersion characteristics due to the presence of nonlocality in the medium. Furthermore, we observe that the shear-type wave encounters a critical frequency, while the coupled longitudinal waves may face critical frequency conditions under certain circumstances. We explore the reflection of thermoelastic waves at a rigid, thermally insulated, and isothermal boundary of a thermoelastic half-space, particularly in the case of an incident coupled longitudinal thermoelastic wave. We determine the amplitude ratios of the reflected waves to the incident wave through analytical methods. For a specific model, we generate various graphs to analyze the behavior of phase speeds, attenuation coefficients, and reflection coefficients. To assess the impact of the elastic nonlocal parameter on the variations of phase speeds, attenuation coefficients, and amplitude ratios of the reflected waves, we present graphical representations. Notably, our observations indicate that all waves are influenced by the nonlocality of the medium. Longitudinal waves exhibit sensitivity to thermal parameters, whereas the shear-type wave remains independent of thermal effects. Furthermore, the presence of elastic nonlocality results in a reduction in the classical shear-type wave speed.

Rayleigh Waves in a Thermoelastic Half-Space Coated by a Maxwell–Cattaneo Thermoelastic Layer

This paper investigates the propagation of in-plane surface waves in a coated thermoelastic half-space. First, it investigates a special case where the surface layer is described by the Maxwell–Cattaneo thermoelastic approach, while the half-space is filled by a thermoelastic material described by the classical Fourier law for the heat flux. The contact between the layer and the half-space is assumed to be welded, i.e., the displacements and the temperature, as well as the stresses and the heat flux are continuous through the interface of the layer and the half-space. The boundary and continuity conditions of the problem are formulated and then the exact dispersion relation of the surface waves is established. An illustrative numerical simulation is presented for the case of an aluminum thermoelastic layer coating a thermoelastic copper half-space, highlighting important aspects regarding the propagation of Rayleigh waves in such structures. The exact effective boundary conditions at the interface are also established replacing the entire effect of the layer on the half-space. The general case of the problem is also investigated when both the surface layer and the half-space are described by the Maxwell–Cattaneo thermoelasticity theory. This study helps to further understand the propagation characteristics of elastic waves in layered structures with thermal effects described by the Maxwell–Cattaneo approach.

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.

The Impact of Rotation and Inclined Load on a Nonlocal Fiber-Reinforced Thermoelastic Half-space via Simple-phase-lag Model

PurposeThe purpose of the present study is to discuss the impacts of rotation, inclined load, nonlocal parameter, and an empirical material constant on various physical variables of a fiber-reinforced thermoelastic medium.MethodsThe present problem was studied using the simple phase-lags (DPL) model. Using normal mode analysis, the precise expressions for the temperature, stress, and displacement components are found.ResultsMatlab software is used to do numerical computations. Comparisons are done between the outcomes obtained and those expected for various nonlocal parameter values, rotation, an empirical material constant, and inclined load.ConclusionThe nonlocal parameter and rotation play a big part in how the physical fields are distributed. The distributions of the physical fields are significantly influenced by the inclined load and an empirical material constant.

Analysis of an initially stressed functionally graded thermoelastic medium (type III) without energy dissipation

The current investigation deals with the deformation of a non-homogeneous thermoelastic half space under hydrostatic initial stress for the Green–Naghdi model III. The medium is supposed to be rotating with a constant angular velocity. The non-homogeneous properties of the material are along the x-direction. At the first instance, the problem has been solved analytically to obtain stress and displacement components. Further, the numerical values of these expressions are evaluated using a computer program for a particular medium. The numerical values obtained are then presented graphically to show the effect of initial stress parameter and non-homogeneity parameter on the quantities.

Temperature-dependent thermal conductivity in Green–Naghdi (type III) thermoelastic half-space with hydrostatic initial stress

Temperature-dependent thermal conductivity in Green–Naghdi (type III) thermoelastic half-space with hydrostatic initial stress

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 of plane wave at the interface between two distinct nonlocal triclinic micropolar generalized thermoelastic half spaces under DPL and LS theory

Reflection and transmission of plane wave at the interface between two distinct nonlocal triclinic micropolar generalized thermoelastic half spaces under DPL and LS theory

Thermoelastic diffusion in a half space due to fractional order theory

Based on the theory of fractional thermoelastic diffusion, a two dimensional problem for thermoelastic half space is considered. The upper surface of the half space is taken to be traction free and subjected to ramp type heating. Integral transform technique and a direct approach method are used to obtain the solution in the transformed domain. Numerical inversion techniques are used to obtain the inverse double transforms. The effect of Tempered-Caputo fractional derivative is studied. Numerical results are discussed and represented graphically.

Reflection phenomena of plane wave at a nonlocal monoclinic micropolar generalized thermoelastic half-space

In this study, we examined the reflection phenomena of plane wave occurring at the thermally insulated and stress-free surface of a nonlocal monoclinic micropolar generalized thermoelastic half-space. We have derived the reflection coefficients, phase velocities, and energy ratios of all the reflected waves. We explored the variation of phase velocity and reflection coefficients in presence and absence of nonlocal parameter against incident angle under LS and GL theory. The variation of energy ratios against incident angle in presence of nonlocal parameter is also obtained.

Rayleigh wave in rotating thermoelastic half-space under impedance boundary conditions, two-temperature, diffusion

Rayleigh wave in rotating thermoelastic half-space under impedance boundary conditions, two-temperature, diffusion

Effect of Magnetic and Thermal Parameters on the Reflected Waves in Generalized Magneto Thermoelastic Materials

The present paper is concerned with the problem of reflection of homogeneous plane waves from the free surface of a generalized magneto thermoelastic half-space. The phase speeds of corresponding to longitudinal, transverse and thermal waves are obtained and are independent of angle of propagation. The amplitude and energy ratios corresponding to the reflected waves are obtained theoretically and numerically with the help of boundary conditions. The effects of magnetic and thermal parameters on the reflected waves are examined. The results hold the conservation law of energy.

Behavior of higher-order MDD on energy ratios at the interface of thermoelastic and piezothermoelastic mediums

This paper investigates the intricate energy distribution patterns emerging at an orthotropic piezothermoelastic half-space interface by considering the influence of a higher-order three-phase lags heat conduction law, accompanied by memory-dependent derivatives (referred to as HPS) within the underlying thermoelastic half-space (referred to as TS). This study explores the amplitude and energy ratios of reflected and transmitted waves. These waves span various incident types, including longitudinal, thermal, and transversal, as they propagate through the TS and interact at the interface. Upon encountering the interface, an intriguing dynamic unfolds: three waves experience reflection within the TS medium, while four waves undergo transmission into the HPS medium. A graphical representation effectively illustrates the impact of higher-order time differential parameters and memory to offer comprehensive insights. This visual representation reveals the nuanced fluctuations of energy ratios with the incidence angle. The model astutely captures diverse scenarios, showcasing its ability to interpret complex interface dynamics.

Energy ratio response at the interface of elastic and dual-porous thermoelastic half-spaces

The present study delves into the intricate examination of energy distribution inherent in plane waves interfacing with an elastic half-space and a thermoelastic half-space characterized by a dual porosity framework. Employing the memory-dependent dual-phase-lag (DPL) hyperbolic two-temperature (H2T) thermoelastic paradigm, the investigation encompasses various incident wave types. The governing equations, rendered in a non-dimensional format, are meticulously addressed by applying the rigorous technique of eigenmode analysis. The intricate energy ratios are meticulously ascertained through the judicious imposition of boundary conditions and the discerning employment of reflection and transmission coefficients. Graphical representations have been exhibited, elucidating the effects of diverse parameters on distinct energy ratios within crystalline structures akin to magnesium materials. These parameters encompass but are not confined to the H2T paradigm, the absence of the two-temperature influence, the classical two-temperature approach, memory effects, and a spectrum of distinct kernel functions. The proposed model emanates cross-disciplinary utility, traversing the domains of seismology, acoustics, optics, materials science, structural engineering, and geophysics.

Energy transfer at the interface of monoclinic piezothermoelastic and thermoelastic half spaces with MDD

This research article presents an analysis of the behavior of an initially stressed monoclinic piezothermoelastic half-space based on memory-dependent three-phase lags heat transfer law (MPS) underlying a thermoelastic half-space (TS) with subject to the hyperbolic two-temperature (H2T), classical two-temperature (C2T), and without two-temperature (W2T) models. By applying the normal mode approach, calculate the amplitude ratios and further utilize them to obtain the waves’ energy ratios and interaction energy. The effect of memory-dependent derivatives (MDD), initial stresses, various kernel functions, and two temperature factors on the variation of energy ratios with incidence angle are graphically shown. The findings of this study have the potential to optimize material design, enhance seismic imaging techniques, improve thermal management in machinery, develop renewable energy systems, and facilitate materials characterization across diverse industries.

Stationary Boundary Problems of Coupled Thermoelasticity for a Half-Plane and Their Solution

Using the model of coupled thermoelasticity, the boundary value problems of the dynamics of a thermoelastic half-space are solved for plane deformation with periodic surface force and thermal effects associated with the desired boundary functions by linear algebraic relations. Green’s tensors are constructed for the stated boundary value problems, using their properties, analytical solutions of these problems are obtained. To solve them, we have used the method of incomplete separation of variables, the Fourier transform, and the properties of fundamental solutions. The presented algorithm solves the classical four boundary value problems of thermoelasticity, as well as non-classical ones with coupled thermal and force characteristics at the boundary of the half-plane.

Solution of a Half-Space in Generalized Thermoelastic Problem in the Context of Two Models Using the Homotopy Perturbation Method

This paper estimated the problem of one-dimensional generalized thermoelastic half-space in medium considering two models: the Lord and Shulman (LS) model and the Dual-Phase-Lag (DPL) model. We assumed that the surface of the half-space was free from traction force and under an exponentially varying external heat source at the boundary with time. The technique of homotopy perturbation has been applied to find the approximate solution for the interactions of thermoelasticity with the applied boundary condition. The effect of a heat source that varies with the time and the free traction force are investigated for the temperature, displacement, and stress. The numerical results obtained are presented graphically to show the influence of the new external parameters. The results obtained illustrate the strong impacts on the displacement, temperature, and stress with the variations in the two models as well as the relaxation time parameter. The results show the agreement between the present results and the previous obtained results of the phenomenon and applicable, especially in biology, acoustics, engineering, and geophysics.

Effect of Inclined Mechanical Load on a Rotating Microelongated Two Temperature Thermoelastic Half Space with Temperature Dependent Properties

Effect of Inclined Mechanical Load on a Rotating Microelongated Two Temperature Thermoelastic Half Space with Temperature Dependent Properties