Reflection Of Thermoelastic Waves Research Articles

Thermal wave reflection and propagation in temperature rate-dependent non-local diffusive solids

The propagation and reflection of thermo-elastic waves through diffusive nonlocal isotropic medium had been studied in this paper. The Green–Lindsay model of thermo-elasticity is incorporated in the context of Temperature Rate Dependent Theory. Using Helmholtz vector decomposition rule, the system of governing equations has been transformed to their respective components. The dispersion relation in frequency indicates the existence of three coupled waves and one independent wave propagating through the medium. The coupled waves are affected by non-locality, temperature field and diffusivity in the medium; anyhow, un-coupled shear vertical wave is only affected by the non-local parameter. The reflection of [Formula: see text]-wave is also studied at the free boundary of the solid and their corresponding amplitude ratios are computed using set of suitable boundary conditions. The obtained results are further discussed graphically for significant physical parameters of interest. The results in the literature are obtained as a special case after ignoring the diffusivity in the solid.

Propagation and reflection of thermoelastic wave in a rotating nonlocal fractional order porous medium under Hall current influence

This investigation relates to the research on Hall current on propagation and reflection of elastic waves through non-local fractional-order thermoelastic rotating medium with voids. The system is split up into longitudinal and transverse components using the Helmholtz vector rule. It is observed that, through the frequency dispersion relation four coupled quasi-waves exist in the medium. The rotating solid modifies the nature of purely longitudinal and transverse waves toward the quasi-type waves. All the propagating waves are dispersive as they depend upon angular frequency. The quasi-longitudinal wave qP and quasi-transverse wave qSV faces cut-off frequencies. The nonlocal parameter affect all the waves except the quasi void wave. Analytically, the reflection coefficients of the wave are computed using suitable boundary conditions. MATLAB software is used to perform numerical computations for a chosen solid material. The amplitude ratios and the speed of propagation of the wave are plotted graphically for rotational frequency, nonlocal, fractional order, and Hall current parameter. The significant effect of the physical parameters on the computed results has been observed. The cut-off frequency of the waves is also presented graphically. The energy conservation law is proved in the form of energy ratios. The earlier findings in the literature are obtained as special case in the absence of rotation, Hall current parameter and porous voids.

Plane waves in nonlocal generalized thermoelasticity

AbstractThe Lord–Shulman (LS) model of generalized thermoelasticity and the Eringen's model of nonlocal elasticity are used to formulate the new constitutive relations and the field equations. The propagation of plane thermoelastic waves are then probed in a homogeneous isotropic nonlocal thermoelastic solid by employing this new model. We found two sets of the coupled longitudinal waves and one independent shear‐type wave. All these waves are found to be dispersive and attenuating in nature in the presence of nonlocality in the medium. We found that the shear‐type wave faces a critical frequency, while the coupled longitudinal waves may face critical frequency conditionally. A reflection of thermoelastic waves at a stress‐free thermally insulated and isothermal boundary of a thermoelastic half‐space are also considered in case of incident coupled longitudinal thermoelastic wave. The amplitude ratios of the reflected waves to that incident wave are determined analytically. For a particular model, various graphs are plotted to analyze the behavior of the phase speeds, attenuation coefficients and reflection coefficients. To investigate the effect of elastic nonlocal parameter on the variations of phase speeds, attenuation coefficients and amplitude ratios of the reflected waves are presented graphically. Some interesting results are noticed: All the waves are detected to be influenced by the nonlocality of the medium. The longitudinal waves are influenced by the thermal parameters but the shear‐type wave is independent of the thermal effect. Moreover the presence of elastic nonlocality reduces the classical shear‐type wave speed.

On the reflection of thermoelastic waves under an exact heat conduction model with a delay and temperature-dependent elastic parameters

The present work aims at describing the reflection of thermoelastic waves under a recently proposed thermoelasticity theory by Quintanilla [Some solutions for a family of exact phase-lag heat conduction problems. Mech Res Commun. 2011;38:355–360.]. Here the author has highlighted the condition for well-posedness by treating the three-phase-lag heat conduction theory differently and extended the results to obtain an alternative thermoelasticity theory with a single-delay term. In the present work, we formulate a mathematical model under this new theory to investigate the reflection of thermoelastic waves at the boundary of an elastic medium. The work is discussed for an isotropic medium with temperature-dependent elastic parameters. Unified field equations for Quintanilla's theory along with three other theories, namely, classical thermoelasticity theory, Lord-Shulman theory and Green-Naghdi theory, are considered for the analysis. The three waves, i.e. elastic-mode longitudinal wave, thermal-mode wave and transverse wave are found, among which only the first two are observed to be coupled. The amplitude ratio and phase velocity for various waves are obtained for incident longitudinal and incident transverse wave cases. The results are presented graphically for various angles of incidence and temperature dependence index parameter. Some important observations are highlighted and comparison between the considered theories is presented.

Reflection of thermo-elastic wave in semiconductor nanostructures nonlocal porous medium

The current work is an extension of the nonlocal elasticity theory to fractional order thermo-elasticity in semiconducting nanostructure medium with voids. The analysis is made on the reflection phenomena in context of three-phase-lag thermo-elastic model. It is observed that, four-coupled longitudinal waves and an independent shear vertical wave exist in the medium which is dispersive in nature. It is seen that longitudinal waves are damped, and shear wave is un-damped when angular frequency is less than the cut-off frequency. The voids, thermal and non-local parameter affect the dilatational waves whereas shear wave is only depending upon non-local parameter. It is found that reflection coefficients are affected by nonlocal and fractional order parameters. Reflection coefficients are calculated analytically and computed numerically for a material, silicon and discussed graphically in details. The results for local (classical) theory are obtained as a special case. The study may be useful in semiconductor nanostructure, geology and seismology in addition to semiconductor nanostructure devices.

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 photothermoelastic waves in a semiconductor material with different relaxations

In this article, reflection of thermoelastic waves in semiconducting medium is studied. The selected elastic medium is a half-space with an exponentially decaying heat source. Firstly, the governing equations are formulated with the help of generalized thermoelastic model initiated by Green and Lindsay. Interface of the solid is exposed to a heat flow having an exponentially decaying pulse. Harmonic wave solution is adopted to find the solution. It is found that, for the selected half-space model, four types of coupled waves are generated after reflection, namely quasi-longitudinal wave $${\text{P}}_{\text{q}}$$ , quasi-transverse wave $${\text{SV}}_{\text{q}}$$ , quasi-thermal wave $${\text{T}}_{\text{q}}$$ , and quasi-plasma wave $${\text{PL}}_{\text{q}}$$ . Different characteristics of waves subjected to angular frequency of incident wave are calculated numerically for the medium. Effect of the incident angle on amplitudes of reflected waves has also been calculated in terms of amplitude ratios for a semiconductor like material. Comparison of results obtained in the context three different models of thermoelastic theories is also presented, and the findings are highlighted.

Reflection phenomena of waves in a semiconductor nanostructure elasticity medium

ABSTRACT This paper presents a coupled nonlocal elasticity theory and a three-phase lag model to study the reflection of thermo-elastic wave in a semiconducting nanostructure medium. The nonlocal elasticity theory and three-phase lag thermal conduction model are used to formulate the governing equations. A heat equation with a fractional order is incorporated to study thermal effects on the propagation of the wave. Governing equations are decomposed into longitudinal and transverse components using the decomposition method. It is observed that four waves are propagating in the medium, in which three are longitudinal waves and one is a transverse wave. The reflection coefficients of the reflected waves are obtained analytically and are presented graphically for a particular material. The effects of the nonlocal parameters , and the fractional time derivative ‘’ are discussed on the basis of the numerical results. Some earlier published results can be obtained without nonlocal parameters .

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.

Reflection of Thermoelastic Waves at a Non-free Thermally Insulated Surface

ABSTRACT Sinha and Sinha (J. Phys. Earth, 22, 237-244, 1974) studied a problem on the reflection of thermoelastic waves at a stress free thermally insulated solid half-space in context of the Lord and Shulman theory of generalized thermoelastcity. He showed the existence of three plane waves (two longitudinal waves and a shear wave) in a homogeneous, linear and isotropic thermoelastic medium. He also obtained the reflection coefficients of reflected waves theoretically and numerically for the incident plane waves. Due to the engineering applications, a problem on the reflection of thermoelastic waves at a non-free boundary surface is considered in this paper. The reflection coefficients of various reflected waves are obtained by considering the new boundary conditions at non-free surface. For a particular material representing the half-space, the reflection coefficients are also computed numerically and are shown graphically against the angle of incidence for different values of boundary parameters.

Reflection of Thermoelastic Waves from Insulated Boundary Fibre-Reinforced Half-Space under Influence of Rotation and Magnetic Field

Reflection of Thermoelastic Waves from Insulated Boundary Fibre-Reinforced Half-Space under Influence of Rotation and Magnetic Field

Reflection of thermoelastic wave on the interface of isotropic half-space and tetragonal syngony anisotropic medium of classes 4, 4/m with thermomechanical effect

The thermoelastic wave propagation in a tetragonal syngony anisotropic medium of classes 4, 4/m having heterogeneity along z axis has been investigated by employing matrizant method. This medium has an axis of second-order symmetry parallel to z axis. In the case of the fourth-order matrix coefficients, the problems of wave refraction and reflection on the interface of homogeneous anisotropic thermoelastic mediums are solved analytically.

Математическая модель нестационарного термоупругого деформирования многослойных демпфирующих покрытий в радиоэлектронной аппаратуре

Generation of new multilayer coatings of units and blocks in electronics for effective damping of thermo-mechanical impact loads requires the development of mathematical models suitable for engineering practice. Mathematical model and calculation method proposed in this paper allows investigate the passing and reflection of thermo-elastic waves in a multilayer body excited by non-stationary magnetic field at the conductive layer boundary. Also, the problem of estimating relative influence of volume forces induced by the magnetic field in the electrically conductive nonferromagnetic layer on the wave propagation in thermo-elastic polymer compounds was considered. It is assumed that the velocity of heat propagation is finite. Assumptions are introduced to simplify the fully coupled system of magneto-thermo-elastic equations that allow applying the numerical solution based on the method of characteristics for obtaining concrete results. A method for finding required quantities at the nodal points of the boundary between the layers is indicated. The suggested mathematical model and calculation method makes it possible, without making any significant changes in the computing system, to carry out numerical experiments on researching the damping properties of multilayer coatings with different geometrical and mechanical parameters under the conditions of the thermo-mechanical loadings. This calculation method of heterogeneous multilayer thermo-elastic structures can be used to identify the areas most disposed to the damage.

Effect of Magnetic Field on Reflection of Thermo-elastic Waves from the Boundary of a Half-Space Using G–N Model of Type-II for Different Nature of the Boundary Surface

The aim of this paper is to investigate the problem of reflection of plane thermoelastic waves in presence of magnetic field from the boundary of a half-space using Green–Naghdi model of type-II. Analytical solutions for the ratios of the amplitude of the reflected waves to that of incident wave have been obtained in matrix form for stress-free insulated, stress-free isothermal, rigid insulated and rigid isothermal boundaries of the half-space. Numerical results have been carried out to obtain the values the amplitude ratios only for incident P and SV wave and shown graphically.

The effect of dual-phase-lag model on reflection of thermoelastic waves in a solid half space with variable material properties

The present article represents an analysis of reflection of P-wave and SV-wave on the boundary of an isotropic and homogeneous generalized thermoelastic half-space when the boundary is stress-free as well as isothermal. The modulus of elasticity is taken as a linear function of reference temperature. The basic governing equations are applied under four theories of the generalized thermoelasticity: Lord-Shulman (L-S) theory with one relaxation time, Green-Naghdi (G-N) theory without energy dissipation and Tzou theory with dual-phase-lag (DPL), as well as the coupled thermoelasticity (CTE) theory. It is shown that there exist three plane waves, namely, a thermal wave, a P-wave and an SV-wave. The reflection from an isothermal stress-free surface is studied to obtain the reflection amplitude ratios of the reflected waves for the incidence of P-and SV-waves. The amplitude ratios variations with the angle of incident are shown graphically. Also the effects of reference temperature of the modulus of elasticity and dual-phase lags on the reflection amplitude ratios are discussed numerically.

REFLECTION OF THERMOELASTIC WAVES AT A SOLID HALF-SPACE WITH TWO RELAXATION TIMES

The effect of two relaxation times, following Green and Lindsay's theory, on the reflection of thermoelastic waves at a homogeneous, isotropic, and thermally conducting elastic solid half-space is studied. The results for the partition of the energy for various values of the angle of incidence are presented and compared with that of Lord and Shulman's theory to show the importance of the second relaxation time.

Reflection of thermoelastic waves at a solid half-space with thermal relaxation.

The thermal and elastic plane wave motion of small amplitude in a homogeneous, isotropic and thermally conducting solid which occupies a half-space is considered. The presence of the thermal waves effect change in the angle of emergence.