The equations of generalized thermoelasticity with one relaxation time with variable modulus of elasticity and the thermal conductivity were used to solve a problem of an infinite material with a spherical cavity.The ...The equations of generalized thermoelasticity with one relaxation time with variable modulus of elasticity and the thermal conductivity were used to solve a problem of an infinite material with a spherical cavity.The inner surface of the cavity was taken to be traction free and acted upon by a thermal shock to the surface. Laplace transforms techniques were used to obtain the solution by a direct approach.The inverse Laplace transforms was obtained numerically.The temperature,displacement and stress distributions are represented graphically.展开更多
The thermoelastic interaction for the three-phase-lag （TPL） heat equation in an isotropic infinite elastic body with a spherical cavity is studied by two-temperature generalized thermoelasticity theory （2TT）. The ...The thermoelastic interaction for the three-phase-lag （TPL） heat equation in an isotropic infinite elastic body with a spherical cavity is studied by two-temperature generalized thermoelasticity theory （2TT）. The heat conduction equation in the theory of TPL is a hyperbolic partial differential equation with a fourth-order derivative with respect to time. The medium is assumed to be initially quiescent. By the Laplace trans- formation, the fundamental equations are expressed in the form of a vector-matrix differ- ential equation, which is solved by a state-space approach. The general solution obtained is applied to a specific problem, when the boundary of the cavity is subjected to the ther- mal loading （the thermal shock and the ramp-type heating） and the mechanical loading. The inversion of the Laplace transform is carried out by the Fourier series expansion tech- niques. The numerical values of the physical quantity are computed for the copper like ma- terial. Significant dissimilarities between two models （the two-temperature Green-Naghdi theory with energy dissipation （2TGN-III） and two-temperature TPL model （2T3phase）） are shown graphically. The effects of two-temperature and ramping parameters are also studied.展开更多
In this work, a model of two-temperature generalized thermoelasticity without energy dissipation for an elastic half-space with constant elastic parameters is constructed. The Laplace transform and state-space techniq...In this work, a model of two-temperature generalized thermoelasticity without energy dissipation for an elastic half-space with constant elastic parameters is constructed. The Laplace transform and state-space techniques are used to obtain the general solution for any set of boundary conditions. The general solutions are applied to a specific problem of a half-space subjected to a moving heat source with a constant velocity. The inverse Laplace transforms are computed numerically, and the comparisons are shown in figures to estimate the effects of the heat source velocity and the two-temperature parameter.展开更多
The present work is concerned with the solution of a problem on thermoelastic interactions in a functional graded material due to thermal shock in the context of the fractional order three-phase lag model. The governi...The present work is concerned with the solution of a problem on thermoelastic interactions in a functional graded material due to thermal shock in the context of the fractional order three-phase lag model. The governing equations of fractional order generalized thermoelasticity with three-phase lag model for functionally graded materials(FGM)(i.e., material with spatially varying material properties) are established. The analytical solution in the transform domain is obtained by using the eigenvalue approach.The inversion of Laplace transform is done numerically. The graphical results indicate that the fractional parameter has significant effects on all the physical quantities. Thus, we can consider the theory of fractional order generalized thermoelasticity an improvement on studying elastic materials.展开更多
The present paper is concerned with the investigation of disturbances in＇a homogeneous, isotropic elastic medium with generalized thermoelastic diffusion, when a moving source is acting along one of the co-ordinate a...The present paper is concerned with the investigation of disturbances in＇a homogeneous, isotropic elastic medium with generalized thermoelastic diffusion, when a moving source is acting along one of the co-ordinate axis on the boundary of the medium. Eigen value approach is applied to study the disturbance in Laplace-Fourier transform domain for a two dimensional problem. The analytical expressions for displacement components, stresses, temperature field, concentration and chemical potential are obtained in the physical domain by using a numerical technique for the inversion of Laplace transform based on Fourier expansion techniques. These expressions are calculated numerically for a copper like material and depicted graphically. As special cases, the results in generalized thermoelastic and elastic media are obtained. Effect of presence of diffusion is analyzed theoretically and numerically.展开更多
This paper is concerned with the determination of thermoelastic displacement, stress and temperature in a functionally graded spherically isotropic infinite elastic medium having a spherical cavity, in the context of ...This paper is concerned with the determination of thermoelastic displacement, stress and temperature in a functionally graded spherically isotropic infinite elastic medium having a spherical cavity, in the context of the linear theory of generalized thermoelasticity with two relaxation time parameters （Green and Lindsay theory）. The surface of cavity is stress-free and is subjected to a time-dependent thermal shock. The basic equations have been written in the form of a vector-matrix differential equation in the Laplace transform domain, which is then solved by an eigenvalue approach. Numerical inversion of the transforms is carried out using the Bellman method. Displacement, stress and temperature are computed and presented graphically. It is found that variation in the thermo-physical properties of a material strongly influences the response to loading. A comparative study with a corresponding homogeneous material is also made.展开更多
The present problem is concerned with the study of deformation of a rotating generalized thermoelastic solid with an overlying infinite thermoelastic fluid due to different forces acting along the interface under the ...The present problem is concerned with the study of deformation of a rotating generalized thermoelastic solid with an overlying infinite thermoelastic fluid due to different forces acting along the interface under the influence of gravity.The components of displacement,force stress,and temperature distribution are first obtained in Laplace and Fourier domains by applying integral transforms,and then obtained in the physical domain by applying a numerical inversion method.Some particular cases are also discussed in the context of the problem.The results are also presented graphically to show the effect of rotation and gravity in the medium.展开更多
Based on the Lord and Shulman generalized thermoelasticity theory with one relaxation time, an isotropic semi-infinite plate subjected to a moving heat source has been studied by employing the finite element method di...Based on the Lord and Shulman generalized thermoelasticity theory with one relaxation time, an isotropic semi-infinite plate subjected to a moving heat source has been studied by employing the finite element method directly in time domain, whose distributions of nora dimensional temperature, displacement and stress are illustrated graphically. The results show that the present method is an effective and exact numerical one for solving the thermoelastic coupling problem and is capable of overcoming the defects of traditional integrated transformation and inverse integrated transformation methods. At the same time, the temperature step of the thermal wave front is obtained exactly in contrast with conventional numerical transformation methods.展开更多
The nonlinear thermoelastic responses of an elastic medium exposed to laser generated shortpulse heating are investigated in this article. The thermal wave propagation of generalized thermoelastic medium under the imp...The nonlinear thermoelastic responses of an elastic medium exposed to laser generated shortpulse heating are investigated in this article. The thermal wave propagation of generalized thermoelastic medium under the impact of thermal loading with energy dissipation is the focus of this research. To model the thermal boundary condition(in the form of thermal conduction),generalized Cattaneo model(GCM) is employed. In the reference configuration, a nonlinear coupled Lord-Shulman-type generalized thermoelasticity formulation using finite strain theory(FST) is developed and the temperature dependency of the thermal conductivity is considered to derive the equations. In order to solve the time-dependent and nonlinear equations, Newmark’s numerical time integration technique and an updated finite element algorithm is applied and to ensure achieving accurate continuity of the results, the Hermitian elements are used instead of Lagrangian’s. The numerical responses for different factors such as input heat flux and nonlinear terms are expressed graphically and their impacts on the system’s reaction are discussed in detail.The results of the study are presented for Green–Lindsay model and the findings are compared with Lord-Shulman model especially with regards to heat wave propagation. It is shown that the nature of the laser’s thermal shock and its geometry are particularly determinative in the final stage of deformation. The research also concluded that employing FST leads to achieving more accuracy in terms of elastic deformations;however, the thermally nonlinear analysis does not change the results markedly. For this reason, the nonlinear theory of deformation is required in laser related reviews, while it is reasonable to ignore the temperature changes compared to the reference temperature in deriving governing equations.展开更多
A mathematical model is elaborated for a thermoelastic infinite body with a spherical cavity.A generalized set of governing equations is formulated in the context of three different models of thermoelasticity:the Biot...A mathematical model is elaborated for a thermoelastic infinite body with a spherical cavity.A generalized set of governing equations is formulated in the context of three different models of thermoelasticity:the Biot model,also known as“coupled thermoelasticity”model;the Lord-Shulman model,also referred to as“generalized thermoelasticity with one-relaxation time”approach;and the Green-Lindsay model,also called“generalized thermoelasticity with two-relaxation times”approach.The Adomian’s decomposition method is used to solve the related mathematical problem.The bounding plane of the cavity is subjected to harmonic thermal loading with zero heat flux and strain.Numerical results for the temperature,radial stress,strain,and displacement are represented graphically.It is shown that the angular thermal load and the relaxation times have significant effects on all the studied fields.展开更多
The electron-phonon interaction can reveal the microscopic mechanism of heat transfer in metals.The two-step heat conduction considering electron-phonon interaction has become an effective theoretical model for extrem...The electron-phonon interaction can reveal the microscopic mechanism of heat transfer in metals.The two-step heat conduction considering electron-phonon interaction has become an effective theoretical model for extreme environments,such as micro-scale and ultrafast processes.In this work,the two-step heat transfer model is further extended by considering the Burgers heat conduction model with the secondorder heat flux rate for electrons.Then,a novel generalized electron-phonon coupling thermoelasticity is proposed with the Burgers electronic heat transfer.Then,the problem of one-dimensional semi-infinite copper strip subject to a thermal shock at one side is studied by the Burgers two-step(BTS)model.The thermoelastic analytical solutions are systematically derived in the Laplace domain,and the numerical Laplace inversion method is adopted to obtain the transient responses.The new model is compared with the parabolic two-step(PTS)model and the hyperbolic two-step(HTS)model.The results show that in ultrafast heating,the BTS model has the same wave front jump as the HTS model.The present model has the faster wave speed,and predicts the bigger disturbed regions than the HTS model.More deeply,all two-step models also have the faster wave speeds than one-step models.This work may benefit the theoretical modeling of ultrafast heating of metals.展开更多
The present paper is devoted to the study of Rayleigh wave propagation in a homogeneous, transversely isotropic, thermoelastic diffusive half-space, subject to stress free, thermally insulated/isothermal, and chemical...The present paper is devoted to the study of Rayleigh wave propagation in a homogeneous, transversely isotropic, thermoelastic diffusive half-space, subject to stress free, thermally insulated/isothermal, and chemical potential boundary conditions in the context of the generalized thermoelastic diffusion theory. The Green-Lindsay（GL） theory is used in the study. In this theory, thermodiffusion and thermodiffusion mechanical relaxations are governed by four different time constants. Secular equations for surface wave propagation in the considered media are derived. Anisotropy and diffusion effects on the phase velocity, attenuation coefficient are graphically presented in order to present the analytical results and make comparison. Some special cases of frequency equations are derived from the present investigation.展开更多
The present investigation is concerned with an axi-symmetric problem in the electromagnetic micropolar thermoelastic half-space whose surface is subjected to the mechanical or thermal source. Laplace and Hankel transf...The present investigation is concerned with an axi-symmetric problem in the electromagnetic micropolar thermoelastic half-space whose surface is subjected to the mechanical or thermal source. Laplace and Hankel transform techniques are used to solve the problem. Various types of sources are taken to illustrate the utility of the approach. Integral transforms are inverted by using a numerical technique to obtain the components of stresses, temperature distribution, and induced electric and magnetic fields. The expressions of these quantities are illustrated graphically to depict the magnetic effect for two different generalized thermoelasticity theories, i.e., Lord and Shulman （L-S theory） and Green and Lindsay （G-L theory）. Some particular interesting cases are also deduced from the present investigation.展开更多
The aim of this paper is to study the reflection of plane harmonic waves from a semi-infinite elastic solid under the effect of magnetic field in a vacuum.The expressions for the reflection coefficients,which are the ...The aim of this paper is to study the reflection of plane harmonic waves from a semi-infinite elastic solid under the effect of magnetic field in a vacuum.The expressions for the reflection coefficients,which are the relations of the amplitudes of the reflected waves to the amplitude of the incident waves,are obtained.Similarly,the reflection coefficient ratio variations with the angle of incident under different conditions are shown graphically.Comparisons are made with the results predicted by the dual-phase-lag model and Lord-Shulman theory in the presence and absence of magnetic field.展开更多
The generalized thermo-elasticity theory, i.e., Green and Naghdi （G-N） Ⅲ theory, with energy dissipation （TEWED） is employed in the study of time-harmonic plane wave propagation in an unbounded, perfectly electri...The generalized thermo-elasticity theory, i.e., Green and Naghdi （G-N） Ⅲ theory, with energy dissipation （TEWED） is employed in the study of time-harmonic plane wave propagation in an unbounded, perfectly electrically conducting elastic medium subject to primary uniform magnetic field. A more general dispersion equation with com- plex coefficients is obtained for coupled magneto-thermo-elastic wave solved in complex domain by using the Leguerre＇s method. It reveals that the coupled magneto-thermoelastic wave corresponds to modified dilatational and thermal wave propagation with finite speeds modified by finite thermal wave speeds, thermo-elastic coupling, thermal diffusivity, and the external magnetic field. Numerical results for a copper-like material are presented.展开更多
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 isotherma...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.展开更多
The thermal shock problems involved with fractional order generalized theory is studied by an analytical method. The asymptotic solutions for thermal responses induced by transient thermal shock are derived by means o...The thermal shock problems involved with fractional order generalized theory is studied by an analytical method. The asymptotic solutions for thermal responses induced by transient thermal shock are derived by means of the limit theorem of Laplace transform. An infinite solid with a cylindrical cavity subjected to a thermal shock at its inner boundary is studied. The propagation of thermal wave and thermal elastic wave, as well as the distributions of displacement, temperature and stresses are obtained from these asymptotic solutions. The investigation on the effect of fractional order parameter on the propagation of two waves is also conducted.展开更多
A problem concerned with the reflection and refraction of thermoelastic plane waves at an imperfect interface between two generalized thermally conducting cubic crystal solid half-spaces of different elastic and therm...A problem concerned with the reflection and refraction of thermoelastic plane waves at an imperfect interface between two generalized thermally conducting cubic crystal solid half-spaces of different elastic and thermal properties with two relaxation times has been investigated. The generalized thermoelastic theory with two relaxation times developed by Green and Lindsay has been used to study the problem. The expressions for the reflection and refraction coefficients which are the ratios of the amplitudes of reflected and refracted waves to the amplitude of incident waves are obtained for an imperfect boundary and deduced for normal stiffness, transverse stiffness, thermal contact conductance, slip and welded boundaries. Amplitude ratios of different reflected and refracted waves for different boundaries with angle of emergence have been compared graphically for different incident waves. It is observed that the amplitude ratios of reflected and refracted waves are affected by the stiffness and thermal properties of the media.展开更多
This paper deals with a two-dimensional （2D） problem for a transverselyisotropic thick plate having heat sources and body forces. The upper surface of the plate is stress free with the prescribed surface temperature...This paper deals with a two-dimensional （2D） problem for a transverselyisotropic thick plate having heat sources and body forces. The upper surface of the plate is stress free with the prescribed surface temperature, while the lower surface of the plate rests on a rigid foundation and is thermally insulated. The study is carried out in the context of the generalized thermoelasticity proposed by Green and Naghdi. The governing equations for displacement and temperature fields are obtained in the Laplace-Fourier transform domain by applying the Laplace and Fourier transforms. The inversion of the double transform is done numerically. Numerical inversion of the Laplace transform is done based on the Fourier series expansion. Numerical computations are carried out for magnesium （Mg）, and the results are presented graphically. The results for an isotropic material （Cu） are obtained numerically and presented graphically to be compared with those of a transversely isotropic material （Mg）. The effect of the body forces is also studied.展开更多
This paper is concerned with the thermoelastic behaviors of an elastic medium with variable thermal material properties. The problem is in the context of fractional order heat conduction. The governing equations with ...This paper is concerned with the thermoelastic behaviors of an elastic medium with variable thermal material properties. The problem is in the context of fractional order heat conduction. The governing equations with variable thermal properties were established by means of the fractional order calculus. The problem of a half-space formed of an elastic medium with variable thermal material properties was solved, and asymptotic solutions induced by a sudden temperature rise on the boundary were obtained by applying an asymptotic approach. The propagations of thermoelastic wave and thermal wave, as well as the distributions of displacement, temperature and stresses were obtained and plotted. Variations in the distributions with different values of fractional order parameter were discussed. The results were compared with those obtained from the case of constant material properties to evaluate the effects of variable material properties on thermoelastic behaviors.展开更多
文摘The equations of generalized thermoelasticity with one relaxation time with variable modulus of elasticity and the thermal conductivity were used to solve a problem of an infinite material with a spherical cavity.The inner surface of the cavity was taken to be traction free and acted upon by a thermal shock to the surface. Laplace transforms techniques were used to obtain the solution by a direct approach.The inverse Laplace transforms was obtained numerically.The temperature,displacement and stress distributions are represented graphically.
文摘The thermoelastic interaction for the three-phase-lag （TPL） heat equation in an isotropic infinite elastic body with a spherical cavity is studied by two-temperature generalized thermoelasticity theory （2TT）. The heat conduction equation in the theory of TPL is a hyperbolic partial differential equation with a fourth-order derivative with respect to time. The medium is assumed to be initially quiescent. By the Laplace trans- formation, the fundamental equations are expressed in the form of a vector-matrix differ- ential equation, which is solved by a state-space approach. The general solution obtained is applied to a specific problem, when the boundary of the cavity is subjected to the ther- mal loading （the thermal shock and the ramp-type heating） and the mechanical loading. The inversion of the Laplace transform is carried out by the Fourier series expansion tech- niques. The numerical values of the physical quantity are computed for the copper like ma- terial. Significant dissimilarities between two models （the two-temperature Green-Naghdi theory with energy dissipation （2TGN-III） and two-temperature TPL model （2T3phase）） are shown graphically. The effects of two-temperature and ramping parameters are also studied.
文摘In this work, a model of two-temperature generalized thermoelasticity without energy dissipation for an elastic half-space with constant elastic parameters is constructed. The Laplace transform and state-space techniques are used to obtain the general solution for any set of boundary conditions. The general solutions are applied to a specific problem of a half-space subjected to a moving heat source with a constant velocity. The inverse Laplace transforms are computed numerically, and the comparisons are shown in figures to estimate the effects of the heat source velocity and the two-temperature parameter.
文摘The present work is concerned with the solution of a problem on thermoelastic interactions in a functional graded material due to thermal shock in the context of the fractional order three-phase lag model. The governing equations of fractional order generalized thermoelasticity with three-phase lag model for functionally graded materials(FGM)(i.e., material with spatially varying material properties) are established. The analytical solution in the transform domain is obtained by using the eigenvalue approach.The inversion of Laplace transform is done numerically. The graphical results indicate that the fractional parameter has significant effects on all the physical quantities. Thus, we can consider the theory of fractional order generalized thermoelasticity an improvement on studying elastic materials.
文摘The present paper is concerned with the investigation of disturbances in＇a homogeneous, isotropic elastic medium with generalized thermoelastic diffusion, when a moving source is acting along one of the co-ordinate axis on the boundary of the medium. Eigen value approach is applied to study the disturbance in Laplace-Fourier transform domain for a two dimensional problem. The analytical expressions for displacement components, stresses, temperature field, concentration and chemical potential are obtained in the physical domain by using a numerical technique for the inversion of Laplace transform based on Fourier expansion techniques. These expressions are calculated numerically for a copper like material and depicted graphically. As special cases, the results in generalized thermoelastic and elastic media are obtained. Effect of presence of diffusion is analyzed theoretically and numerically.
文摘This paper is concerned with the determination of thermoelastic displacement, stress and temperature in a functionally graded spherically isotropic infinite elastic medium having a spherical cavity, in the context of the linear theory of generalized thermoelasticity with two relaxation time parameters （Green and Lindsay theory）. The surface of cavity is stress-free and is subjected to a time-dependent thermal shock. The basic equations have been written in the form of a vector-matrix differential equation in the Laplace transform domain, which is then solved by an eigenvalue approach. Numerical inversion of the transforms is carried out using the Bellman method. Displacement, stress and temperature are computed and presented graphically. It is found that variation in the thermo-physical properties of a material strongly influences the response to loading. A comparative study with a corresponding homogeneous material is also made.
文摘The present problem is concerned with the study of deformation of a rotating generalized thermoelastic solid with an overlying infinite thermoelastic fluid due to different forces acting along the interface under the influence of gravity.The components of displacement,force stress,and temperature distribution are first obtained in Laplace and Fourier domains by applying integral transforms,and then obtained in the physical domain by applying a numerical inversion method.Some particular cases are also discussed in the context of the problem.The results are also presented graphically to show the effect of rotation and gravity in the medium.
基金supported by the Funds of Xi’an University of Technology(No.104-211002)Shaanxi Province Natural Science Foundation research project(No.2014JM1024)
文摘Based on the Lord and Shulman generalized thermoelasticity theory with one relaxation time, an isotropic semi-infinite plate subjected to a moving heat source has been studied by employing the finite element method directly in time domain, whose distributions of nora dimensional temperature, displacement and stress are illustrated graphically. The results show that the present method is an effective and exact numerical one for solving the thermoelastic coupling problem and is capable of overcoming the defects of traditional integrated transformation and inverse integrated transformation methods. At the same time, the temperature step of the thermal wave front is obtained exactly in contrast with conventional numerical transformation methods.
文摘The nonlinear thermoelastic responses of an elastic medium exposed to laser generated shortpulse heating are investigated in this article. The thermal wave propagation of generalized thermoelastic medium under the impact of thermal loading with energy dissipation is the focus of this research. To model the thermal boundary condition(in the form of thermal conduction),generalized Cattaneo model(GCM) is employed. In the reference configuration, a nonlinear coupled Lord-Shulman-type generalized thermoelasticity formulation using finite strain theory(FST) is developed and the temperature dependency of the thermal conductivity is considered to derive the equations. In order to solve the time-dependent and nonlinear equations, Newmark’s numerical time integration technique and an updated finite element algorithm is applied and to ensure achieving accurate continuity of the results, the Hermitian elements are used instead of Lagrangian’s. The numerical responses for different factors such as input heat flux and nonlinear terms are expressed graphically and their impacts on the system’s reaction are discussed in detail.The results of the study are presented for Green–Lindsay model and the findings are compared with Lord-Shulman model especially with regards to heat wave propagation. It is shown that the nature of the laser’s thermal shock and its geometry are particularly determinative in the final stage of deformation. The research also concluded that employing FST leads to achieving more accuracy in terms of elastic deformations;however, the thermally nonlinear analysis does not change the results markedly. For this reason, the nonlinear theory of deformation is required in laser related reviews, while it is reasonable to ignore the temperature changes compared to the reference temperature in deriving governing equations.
文摘A mathematical model is elaborated for a thermoelastic infinite body with a spherical cavity.A generalized set of governing equations is formulated in the context of three different models of thermoelasticity:the Biot model,also known as“coupled thermoelasticity”model;the Lord-Shulman model,also referred to as“generalized thermoelasticity with one-relaxation time”approach;and the Green-Lindsay model,also called“generalized thermoelasticity with two-relaxation times”approach.The Adomian’s decomposition method is used to solve the related mathematical problem.The bounding plane of the cavity is subjected to harmonic thermal loading with zero heat flux and strain.Numerical results for the temperature,radial stress,strain,and displacement are represented graphically.It is shown that the angular thermal load and the relaxation times have significant effects on all the studied fields.
基金Project supported by the Fundamental Research Funds for the Central Universities of China(Nos.D5000230066 and D5000210117)the Natural Science Basic Research Plan in Shaanxi Province of China(No.2022JQ-358)。
文摘The electron-phonon interaction can reveal the microscopic mechanism of heat transfer in metals.The two-step heat conduction considering electron-phonon interaction has become an effective theoretical model for extreme environments,such as micro-scale and ultrafast processes.In this work,the two-step heat transfer model is further extended by considering the Burgers heat conduction model with the secondorder heat flux rate for electrons.Then,a novel generalized electron-phonon coupling thermoelasticity is proposed with the Burgers electronic heat transfer.Then,the problem of one-dimensional semi-infinite copper strip subject to a thermal shock at one side is studied by the Burgers two-step(BTS)model.The thermoelastic analytical solutions are systematically derived in the Laplace domain,and the numerical Laplace inversion method is adopted to obtain the transient responses.The new model is compared with the parabolic two-step(PTS)model and the hyperbolic two-step(HTS)model.The results show that in ultrafast heating,the BTS model has the same wave front jump as the HTS model.The present model has the faster wave speed,and predicts the bigger disturbed regions than the HTS model.More deeply,all two-step models also have the faster wave speeds than one-step models.This work may benefit the theoretical modeling of ultrafast heating of metals.
基金Council of Scientific and Industrial Research(CSIR)
文摘The present paper is devoted to the study of Rayleigh wave propagation in a homogeneous, transversely isotropic, thermoelastic diffusive half-space, subject to stress free, thermally insulated/isothermal, and chemical potential boundary conditions in the context of the generalized thermoelastic diffusion theory. The Green-Lindsay（GL） theory is used in the study. In this theory, thermodiffusion and thermodiffusion mechanical relaxations are governed by four different time constants. Secular equations for surface wave propagation in the considered media are derived. Anisotropy and diffusion effects on the phase velocity, attenuation coefficient are graphically presented in order to present the analytical results and make comparison. Some special cases of frequency equations are derived from the present investigation.
文摘The present investigation is concerned with an axi-symmetric problem in the electromagnetic micropolar thermoelastic half-space whose surface is subjected to the mechanical or thermal source. Laplace and Hankel transform techniques are used to solve the problem. Various types of sources are taken to illustrate the utility of the approach. Integral transforms are inverted by using a numerical technique to obtain the components of stresses, temperature distribution, and induced electric and magnetic fields. The expressions of these quantities are illustrated graphically to depict the magnetic effect for two different generalized thermoelasticity theories, i.e., Lord and Shulman （L-S theory） and Green and Lindsay （G-L theory）. Some particular interesting cases are also deduced from the present investigation.
文摘The aim of this paper is to study the reflection of plane harmonic waves from a semi-infinite elastic solid under the effect of magnetic field in a vacuum.The expressions for the reflection coefficients,which are the relations of the amplitudes of the reflected waves to the amplitude of the incident waves,are obtained.Similarly,the reflection coefficient ratio variations with the angle of incident under different conditions are shown graphically.Comparisons are made with the results predicted by the dual-phase-lag model and Lord-Shulman theory in the presence and absence of magnetic field.
文摘The generalized thermo-elasticity theory, i.e., Green and Naghdi （G-N） Ⅲ theory, with energy dissipation （TEWED） is employed in the study of time-harmonic plane wave propagation in an unbounded, perfectly electrically conducting elastic medium subject to primary uniform magnetic field. A more general dispersion equation with com- plex coefficients is obtained for coupled magneto-thermo-elastic wave solved in complex domain by using the Leguerre＇s method. It reveals that the coupled magneto-thermoelastic wave corresponds to modified dilatational and thermal wave propagation with finite speeds modified by finite thermal wave speeds, thermo-elastic coupling, thermal diffusivity, and the external magnetic field. Numerical results for a copper-like material are presented.
基金funded by the Deanship of Scientific Research(DSR),King Abdulaziz University,Jeddah,under grant No.(363/130/1431)
文摘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.
基金Project supported by the National Natural Science Foundation of China(No.11102073)the National Science Foundation for Post-doctoral Scientists of China(No.2012M511207)+1 种基金the Research Foundation of Advanced Talents of Jiangsu University(No.10JDG055)the Priority Academic Program Development of Jiangsu Higher Education Institutions
文摘The thermal shock problems involved with fractional order generalized theory is studied by an analytical method. The asymptotic solutions for thermal responses induced by transient thermal shock are derived by means of the limit theorem of Laplace transform. An infinite solid with a cylindrical cavity subjected to a thermal shock at its inner boundary is studied. The propagation of thermal wave and thermal elastic wave, as well as the distributions of displacement, temperature and stresses are obtained from these asymptotic solutions. The investigation on the effect of fractional order parameter on the propagation of two waves is also conducted.
文摘A problem concerned with the reflection and refraction of thermoelastic plane waves at an imperfect interface between two generalized thermally conducting cubic crystal solid half-spaces of different elastic and thermal properties with two relaxation times has been investigated. The generalized thermoelastic theory with two relaxation times developed by Green and Lindsay has been used to study the problem. The expressions for the reflection and refraction coefficients which are the ratios of the amplitudes of reflected and refracted waves to the amplitude of incident waves are obtained for an imperfect boundary and deduced for normal stiffness, transverse stiffness, thermal contact conductance, slip and welded boundaries. Amplitude ratios of different reflected and refracted waves for different boundaries with angle of emergence have been compared graphically for different incident waves. It is observed that the amplitude ratios of reflected and refracted waves are affected by the stiffness and thermal properties of the media.
文摘This paper deals with a two-dimensional （2D） problem for a transverselyisotropic thick plate having heat sources and body forces. The upper surface of the plate is stress free with the prescribed surface temperature, while the lower surface of the plate rests on a rigid foundation and is thermally insulated. The study is carried out in the context of the generalized thermoelasticity proposed by Green and Naghdi. The governing equations for displacement and temperature fields are obtained in the Laplace-Fourier transform domain by applying the Laplace and Fourier transforms. The inversion of the double transform is done numerically. Numerical inversion of the Laplace transform is done based on the Fourier series expansion. Numerical computations are carried out for magnesium （Mg）, and the results are presented graphically. The results for an isotropic material （Cu） are obtained numerically and presented graphically to be compared with those of a transversely isotropic material （Mg）. The effect of the body forces is also studied.
基金Project supported by the National Natural Science Foundation of China(Nos.51206062 and 11102073)the Six Talent Peaks Project of Jiangsu Province(No.2014-ZBZZ-016)+1 种基金the China Postdoctoral Science Foundation(No.2013M540420)the Jiangsu Planned Projects for Postdoctoral Research Funds(No.1501126B)
文摘This paper is concerned with the thermoelastic behaviors of an elastic medium with variable thermal material properties. The problem is in the context of fractional order heat conduction. The governing equations with variable thermal properties were established by means of the fractional order calculus. The problem of a half-space formed of an elastic medium with variable thermal material properties was solved, and asymptotic solutions induced by a sudden temperature rise on the boundary were obtained by applying an asymptotic approach. The propagations of thermoelastic wave and thermal wave, as well as the distributions of displacement, temperature and stresses were obtained and plotted. Variations in the distributions with different values of fractional order parameter were discussed. The results were compared with those obtained from the case of constant material properties to evaluate the effects of variable material properties on thermoelastic behaviors.
