Thermoelastic Material Response Due to Laser Pulse Heating in Context of Four Theorems of Thermoelasticity

This article describes the study of induced temperature and stress fields in an elastic half-space in the context of classical coupled thermoelasticity (Biot) and generalized thermoelasticity (Lord–Shulman, Green–Lindsay and Green–Naghdi) in a unified system of equations. The medium is considered to be made of an isotropic homogeneous thermoelastic half-space. The bounding plane of the surface is heated by a non-Gaussian laser beam with pulse duration of 2 ps. An exact solution of the problem is first obtained in Laplace transform space. Because the response is of more interest in the transient state, the inversion of Laplace transforms were carried out numerically. The derived expressions were computed numerically for copper, and the results are presented in graphical form.     

Stroh analysis of Rayleigh waves in anisotropic thermoelastic medium

The present article is concerned with the Stroh analysis of Rayleigh surface wave propagation in anisotropic homogeneous thermoelastic medium. The problem is considered in the context of three-phase-lag model of generalized thermoelasticity. The secular equation is with complex coe?cients and the surface wave is damped in time and dispersed. The results are illustrated for the case of an orthotropic homogeneous thermoelastic half space and an explicit bicubic form of the characteristic equation with complex coe?cients is obtained. The analysis of these Rayleigh waves for homogeneous orthotropic half space is numerically exemplified.     

Waves in nonlocal thermoelastic solids of type II

The present article deals with the investigation of the propagation of thermoelastic plane harmonic waves in a nonlocal thermoelastic medium. The Green and Naghdi theory II (without energy dissipation) of generalized thermoelasticity with elastic nonlocal effect is adopted to address this problem. The problem of reflection of thermoelastic waves due to an incident coupled longitudinal elastic wave from the rigid and thermally insulated boundary of a homogeneous, isotropic nonlocal thermoelastic half-space is also studied. The amplitude ratios of the reflected waves and their respective energy ratios are determined analytically. For a particular model, the effect of elastic nonlocality parameter on the variations of phase speeds, attenuation coefficients, amplitude ratios and corresponding energy ratios of the reflected waves is presented graphically and analysis of these results is given.     

Three-dimensional thermoelastic problem in orthotropic medium

Abstract

The present article is concerned with a thermoelastic boundary-value problem with a time-dependent thermal shock on traction-free half-space for a homogeneous orthotropic heat-conducting solid. The governing equations of the three-dimensional problem of generalized thermoelasticity in orthotropic medium are obtained as a vector-matrix differential equation form by employing normal mode analysis to the considered equations which is then solved by the eigenfunction expansion method. The distribution of thermal stress, displacements, and temperature are presented graphically and compared with other thermoelastic models.     

Theory of Two-Temperature Thermoelasticity without Energy Dissipation

This paper deals with thermoelastic behavior without energy dissipation; it deals with linear theory of thermoelasticity. In particular, in this work, a new theory of generalized thermoelasticity has been constructed by taking into account two-temperature generalized thermoelasticity theory for a homogeneous and isotropic body without energy dissipation. The new theorem has been derived in the context of Green and Naghdi model of type II of linear thermoelasticity. Also, a general uniqueness theorem is proved for two-temperature generalized thermoelasticity without energy dissipation.     

Eigenfunction expansion method to analyze thermal shock behavior in magneto-thermoelastic orthotropic medium under three theories

This article is concerned with a study of thermal shock response in infinite thermoelastic medium under the purview of Lord–Shulman model, Green–Naghdi theory III, and three-phase-lag model of generalized thermoelasticity. The medium under consideration is assumed to be homogeneous, orthotropic, and thermally conducting. The fundamental equations of the two-dimensional problem of generalized thermoelasticity with three-phase-lag model in an infinite elastic medium under the influence of magnetic field are obtained as a vector–matrix differential equation form using normal mode analysis which is then solved by the Eigenfunction expansion method. Numerical results for the temperature, displacements and thermal stress distribution are presented graphically.     

Thermoelastic Wave with Energy Dissipation in an Unbounded Medium with a Spherical Cavity

The generalized linear theory of thermoelasticity has been used to study waves emanating from the boundary of a spherical cavity in a homogeneous and isotropic infinite thermoelastic body. The basic equations are written in the form of a vector-matrix differential equation and solved by an eigenvalue approach. Solutions in closed form have been achieved in the Laplace transform domain, and the inversion in the space-time domain for the field variables are done numerically. Finally, the results are analyzed and represented graphically.     

Wave scattering through an orthotropic thermoelastic slab sandwiched between two isotropic elastic half-spaces

Abstract

Present study deals with the scattering of a plane wave through an orthotropic thermoelastic slab sandwiched between two elastic half-spaces. Unlike the classical theory of thermoelasticity, we have employed non-classical thermoelastic theories (LS-theory and GL-theory) to analyze the scattering of plane waves. The amplitude ratios for different waves have been computed numerically for the considered generalized theories of thermoelasticity. The effect of the slab thickness on the amplitude ratios has been shown graphically. Moreover, the amplitude ratios of different waves (i.e., reflected, transmitted, forward and backward waves) are compared for different values of slab thickness under both the LS-theory and GL-theory.     

PLANE HARMONIC WAVES IN A MICROPERIODIC LAYERED INFINITE THERMOELASTIC SOLID

A one-dimensional dynamical coupled refined averaged thermoelasticity for a microperiodic composite is used to study harmonic waves propagating in a layered infinite solid. In such a theory the waves are governed by an eighth-order-in-time partial differential equation in which the two intrinsic frequencies are present: a mechanical frequency Ω and a thermal frequency α; both these frequencies are high if the layering period l is small. The existence of harmonic waves of a given frequency ω propagating in a positive direction normal to the layering is established when (i) Ω→∞, α<∞ or (ii) Ω<∞, α→∞. It is shown that in each of the two cases there are two plane harmonic thermoelastic waves of a given frequency ω that are dispersive and attenuated. Also, a closed form of velocities and attenuation coefficients for the two waves are obtained. The velocities and attenuation coefficients, treated as the functions of ω, are illustrated graphically for a unit cell made of the two homogeneous isotropic thermoelastic layers: a zirconium oxide [Zr O₂] and a titanium alloy [Ti–6Al–4V].     

THERMAL BENDING ANALYSIS OF COMPOSITE LAMINATED CYLINDRICAL SHELLS USING A REFINED FIRST-ORDER THEORY

The problem of deducing two-dimensional theory from three-dimensional theory for a thermoelastic isotropic body is investigated. Based on thermoelasticity theory, the refined plate theory is derived by using Biot's solution of thermoelasticity and Lur'e method without ad hoc assumptions. For the homogeneous boundary conditions, the exact equations and solutions are derived and the equations can be decomposed into four governing differential equations: the biharmonic equation, the shear equation, the transcendental equation and the temperature equation. Moreover, the approximate equations and solutions for the plate under anti-symmetrical transverse loadings and temperature distribution are derived directly from the refined plate theory. By omitting coupling effect and higher-order terms, the refined plate theory can be degenerated into other well-known elastic and thermoelastic theoretical models.     

Dispersion Analysis of Generalized Magneto-Thermoelastic Waves in a Transversely Isotropic Cylindrical Panel

In this article the three-dimensional dispersion analysis of a homogeneous transversely isotropic magneto generalized thermoelastic cylindrical panel is discussed in the context of the linear theory of generalized thermoelasticity. Three displacement potential functions are introduced to uncouple the equations of motion. A Bessel function solutions with complex argument is used directly to analyze the frequency equations with traction-free boundary conditions and the special cases have also been deduced for magneto-elastic, thermoelastic and elasto-kinetic at various levels from the present analysis. Finally the numerical example demonstrates the present method and is studied for the material magnetostrictive cobalt iron oxide (CoFe₂O₄). The computed non-dimensional phase velocity, attenuation coefficient, specific loss and thermo-mechanical coupling factor are plotted in the form of dispersion curves with the support of MATLAB.     

Rayleigh surface wave propagation in orthotropic thermoelastic solids under three-phase-lag model

The present article deals with the propagation of Rayleigh surface waves in a homogeneous, orthotropic thermoelastic half-space in the context of three-phase-lag model of thermoelasticity. The frequency equations in closed form are derived and the amplitude ratios of surface displacements and temperature change during the Rayleigh wave propagation on the surface of half-space have been computed analytically. The path of particles during Rayleigh wave propagation is found elliptical and eccentricity of the ellipse is derived. To illustrate the analytical developments, the numerical solution is performed and the computer-simulated results in respect of phase velocity, attenuation coe?cient, and specific loss are presented graphically.     

THERMOELASTIC PROBLEM OF STEADY-STATE HEAT FLOW DISTURBED BY A CRACK PERPENDICULAR TO THE GRADED INTERFACIAL ZONE IN BONDED MATERIALS

The plane thermoelasticity equations are used to investigate the steady-state nonisothermal crack problem for bonded materials with a graded interfacial zone. The interfacial zone is modeled as a nonhomogeneous interlayer having continuously varying thermoelastic moduli in the exponential form between the dissimilar, homogeneous half-planes. A crack is assumed to exist in one of the half-planes oriented perpendicular to the nominal interface, disturbing a uniform heat flow. Based on the method of Fourier integral transform, formulation of the crack problem is reduced to solving two sets of Cauchy-type singular integral equations for temperature and thermal stress fields. The heat-flux intensity factors and the thermally induced mode II stress intensity factors are defined in order to characterize the singular behavior of temperature gradients and thermal stresses, respectively, in the vicinity of the crack tips. In the numerical results, the values of heat-flux and thermal-stress intensity factors are presented for various combinations of material and geometric parameters of the dissimilar media bonded through a thermoelastically graded interfacial zone. The influence of crack-surface partial conductance on the near-tip temperature and thermal stress fields is also addressed.     

REFLECTION OF GENERALIZED THERMOELASTIC WAVES FROM THE BOUNDARY OF A HALF-SPACE

We investigated the problem of thermoelastic wave reflection from the insulated and isothermal stress-free as well as rigidly fixed boundaries of homogeneous isotropic solid half-spaces in the context of various linear theories of thermoelasticity, namely, Lord-Shulman, Green-Lindsay, Green-Nagdhi, coupled thermoelasticity, and uncoupled thermoelasticity. The ratios of reflection coefficients to that of incident coefficients are obtained for P- and SV-wave incidence cases. The results for partition of the energy for various values of the angle of incidence are computed numerically and presented graphically for aluminum-epoxy composite material in case of incident P- and SV-waves from the stress-free and rigidly fixed thermally insulated boundaries. The results obtained are discussed and compared in various models of thermoelasticity.     

EFFECTS OF THERMAL RELAXATIONS ON THERMOVISCOELASTIC INTERACTIONS IN AN UNBOUNDED BODY WITH A SPHERICAL CAVITY SUBJECTED TO A PERIODIC LOADING ON THE BOUNDARY

Thermoviscoelastic interactions in an infinite homogeneous viscoelastic medium with a spherical cavity are studied. The cavity surface is subjected to a periodic loading and zero temperature change. The classical dynamical theory of thermoelasticity as well as the generalized theories of thermoelasticity are applied to consider the thermoelastic coupling. The analytical expressions for the closed-form solutions of displacement, temperature, and stresses are obtained; and the thermal relaxation effects on the interactions are studied to compare the three theories. The numerical values of the physical quantities are computed for a suitable material. The results are presented graphically to illustrate the problem.     

ON THE CHARACTERIZATION OF THE MIXED PROBLEM OF COUPLED,DYNAMIC, LINEAR THERMOELASTICITY IN TERMS OF THE TEMPERATURE

The temperature field in the coupled, dynamic theory of linear thermoelasticity for homogeneous and isotropic bodies satisfies a partial differential equation in which the temperature is the only unknown-the so-called temperature equation. Here, for certain classes of problems, appropriate boundary and initial conditions are derived for the temperature equation from the data for the corresponding mixed problem of thermoelasticity. It is shown that the resulting boundary-initial-value problem for the temperature has at most one solution. Furthermore, for these classes of problems, it is shown that a displacement field can be ex pressed directly in terms of the temperature field and that the corresponding thermoelastic process satisfies all of the conditions of the mixed thermoelasticity problem except for the tangential components of the mechanical boundary conditions. To this extent, our boundary-initial-value problem for the temperature uncouples the coupled theory.     

TIME-HARMONIC SOURCES IN A GENERALIZED THERMOELASTIC CONTINUUM

The disturbance due to a time-harmonic normal point load and thermal source in a homogeneous isotropic thermoelastic, half-space is investigated by applying the Hankel transform technique in the context of generalized theories of thermoelasticity. The inverse transform integrals are evaluated using Romberg integration with adaptive stepwise after using the results from successive refinements of the extended trapezoidal rule followed by extrapolation of the results to the limit when the step-size tends to zero. The displacement, temperature, and stresses so obtained in the physical domain are computed numerically and presented graphically in Figures 1-12 in different situations for Aluminium-epoxy composite material. A comparison of the results for different theories of generalized thermoelasticity is also presented.     

NUMERICAL SOLUTIONS OF THERMOELASTIC WAVE PROBLEMS BY THE METHOD OF CHARACTERISTICS

This article is concerned with the numerical treatment of thermal and thermal stress waves in thermoelastic solids. To keep the numerical treatment general, the development of the formulation is based on the generalized theory of thermoelasticity. A number of thermoelastic wave problems, which involve one or two space variables, are treated, in a uniform manner, by a system of first-order partial differential equations with stress, velocity, heat flow, and temperature as dependent variables. This system of equations is analyzed by the method of characteristics, yielding the characteristics and the characteristic equations. Procedures of numerical integration along the characteristics are established and carried out for several generalized and classical thermoelastic wave problems in homogeneous materials, composite materials, nonhomogeneous materials, and nonlinear elastic solids.     

Propagation of waves in an initially stressed generalized electromicrostretch thermoelastic medium with temperature-dependent properties under the effect of rotation

In the present article, a model of the equations of generalized electromicrostretch thermoelasticity in an initially stressed perfectly conducting elastic medium under the effect of temperature-dependent properties is studied. The entire elastic medium is rotating with a uniform angular velocity. Reflection phenomena of plane waves in electromicrostretch thermoelasticity is investigated under two theories proposed by Lord and Shulman (L–S) and Green and Lindsay (G–L). Amplitude ratios and energy ratios of various reflected waves are presented when an elastic wave is made incident obliquely at the plane boundary of an electromicrostretch thermoelastic solid half-space. It has been verified that there is no dissipation of energy at the boundary surface during reflection. Numerical examples calculate the amplitude ratios to evince the effects of initial stress parameter, rotation, and temperature-dependent properties, and the results obtained are depicted graphically.     

A thermoelastic spherical shell with and without energy dissipation

In this work, we apply the Green and Naghdi generalized thermoelasticity theory to a one-dimensional problem of distribution of thermal stresses and temperature in a generalized thermoelastic medium in the form of a spherical shell subjected to sudden change in the temperature of its external boundary. The results are compared to the generalized thermoelasticity theory with one relaxation time. Numerical results are computed and represented graphically for temperature, displacement, and stress distributions.