Isotropic Thermoelastic Half-space Research Articles

Two-dimensional deformations in a rotating functionally graded fiber-reinforced thermoelastic half-space with magnetic field

The present study is concerned with the two-dimensional deformations in a rotating functionally graded (non-homogeneous), fiber-reinforced, transversely isotropic thermoelastic half-space under the effect of magnetic field in the context of Lord-Shulman theory. Material properties are supposed to be graded in -direction and normal mode technique is adopted to obtain the exact expressions for the temperature field, displacement and stress components. These results are computed numerically and depicted graphically to highlight the effects of fiber reinforcement, non-homogeneity parameter, magnetic field, rotation parameter and time on the variations of different physical fields. Certain particular cases of interest have been deduced from the current investigation.

Representation of solutions of strain gradient dual-phase-lag thermoelasticity and effects of scale-length parameter in half-space

This work concerns the strain gradient theory of thermoelasticity with dual-phase-lag model. We obtain the Galerkin-type representation solution of the field equations. The strain gradient scale-length parameter plays an essential role in the material response. Therefore, we analyze the microstructural effect through the scale-length parameter on an isotropic thermoelastic half-space. We formulate the problem with a suitable boundary condition. The solution of the different field variables such as temperature, displacement, stresses, and double stresses is obtained in the Laplace transform domain. Then, we apply a numerical method for Laplace inversion to find the solution for different fields in the physical domain. The results are displayed in graphical form to show the microstructural effect through the scale-length parameter.

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

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

Effect of a Magnetic Field on the Propagation of Waves in a Homogeneous Isotropic Thermoelastic Half-Space

The prime objective of the present paper is to analyze the propagation of thermoelastic waves in a homogeneous isotropic elastic semi-infinite space that is exposed to a magnetic field at initial temperature T0 and whose boundary surface is subjected to the moving heat source and load moving with finite velocity. Temperature and stress distribution occurring due to heating or cooling have been determined using certain boundary conditions. Numerical results indicate that the effect of the magnetic field is very pronounced. Comparison is made with the results predicted by the theory of thermoelasticity in the absence of a magnetic field. Apart from geophysical applications, the consequences of the present study offer a better platform to design a surface wave sensor by means of its established results. The obtained results may be also used for acquiring a better performance in surface acoustic wave devices and waveguides.

Semi-analytical solution of three-dimensional thermoelastic problem for half-space with gradient coating

The article deals with a homogeneous isotropic thermoelastic half-space with an inhomogeneous gradient coating under thermal loadings over an elliptically shaped area. The shear modulus, the thermal expansion, and thermal conductivity coefficients depend exponentially on the depth from the boundary surface, and the Poisson ratio is constant in the coating layer. The considered three-dimensional problem is solved by using the double-Fourier transform method. The distributions of displacements, temperature, and stresses are presented in the integral forms and analyzed numerically.

Microstretch thermoelastic solid with temperature-dependent elastic properties under the influence of magnetic and gravitational field

In this article, propagation of plane waves in generalized microstretch homogeneous isotropic thermoelastic half-space is considered. The elastic modulus is considered as a function having linear relation with the initial temperature. The normal mode method is used to fine exact expression for field variables. The results predicted by both types of Green and Naghdi theory under the presence and absence of magnetic and gravitational field are presented graphically. Influence of temperature-dependent elastic constants is also considered on field variables.

Reflection of plane waves in thermoelastic medium with double porosity

Purpose The purpose of this paper is to study the reflection of plane waves in thermoelastic medium with double porosity structure. Design/methodology/approach A two-dimensional model is considered of an isotropic thermoelastic half-space with double porosity. Thermoelasticity with one relaxation time given by Lord and Shulman (1967) has been used to study the problem. It is found that there exists four coupled longitudinal waves, namely, longitudinal wave (P), longitudinal thermal wave (T), longitudinal volume fractional wave corresponding to pores (PVI) and longitudinal volume fractional wave corresponding to fissures (PVII), in addition to an uncoupled transverse wave (SV). Findings The formulae for amplitude ratios of various reflected waves are obtained in closed form. It is found that these amplitude ratios are functions of angle of incidence. Effect of porosity and thermal relaxation time is shown graphically on the amplitude ratios with angle of incidence for a particular model. Originality/value Reflection of plane waves is of great practical importance. There are many organic and inorganic deposits beneath the earth surface. Wave propagation is the simplest and most economical technique to detect these. The model discussed in the present paper can provide useful information for experimental researchers working in the field of geophysics and earthquake engineering, along with seismologist working in the field of mining tremors and drilling into the crust of the earth.

Wave propagation in an initially stressed transversely isotropic thermoelastic half-space

AbstractThe present paper deals with the study of reflection waves in an initially stressed transversely isotropic medium, in the context of Green and Naghdi (GN) thermoelasticity theory type II and III. The components of displacement, stresses and temperature distributions are determined through the solution of the wave equation by imposing the appropriate boundary conditions. Numerically simulated results are plotted graphically with respect to frequency in order to show the effect of anisotropy.

Effect of Rotation on Propagation of Waves in Transversely Isotropic Thermoelastic Half-Space

The present study is concerned with the effect of rotation on the propagation of plane waves in a transversely isotropic medium in the context of thermoelasticity theory of GN theory of types II and III. After solving the governing equations, three waves propagating in the medium are obtained. The fastest among them is a quasilongitudinal wave. The slowest of them is a thermal wave. The remaining is called quasitransverse wave. The prefix “quasi” refers to their polarizations being nearly, but not exactly, parallel or perpendicular to the direction of propagation. The polarizations of these three waves are not mutually orthogonal. After imposing the appropriate boundary conditions, the amplitudes of reflection coefficients have been obtained. Numerically simulated results have been plotted graphically with respect to frequency to evince the effect of rotation and anisotropy.

Reflection of waves in micropolar transversely isotropic thermoelastic half space of GN type II and III

AbstractThe present paper deals with the reflection of waves incident at the surface of a transversely isotropic micropolar medium under the theory of thermoelasticity of GN types II and III. The wave equations are solved by imposing proper conditions on the components of displacement, stresses, and temperature distribution. It is found that there exist four different waves, viz. quasi-longitudinal displacement (qLD) wave, quasi-transverse displacement (qTD) wave, quasi-transverse microrotational (qTM) wave, and quasi-thermal (qT) wave. The amplitude ratios of these reflected waves are presented, when different waves are incident. Numerically simulated results have been depicted graphically for the different angles of incidence with respect to the frequency. Some special cases of interest also have been deduced from the present investigation.

Exact Solution of Thermoelastic Problem for a One-Dimensional Bar without Energy Dissipation

We consider a homogeneous isotropic thermoelastic half-space in the context of the theory of thermoelasticity without energy dissipation. There are no body forces or heat source acting on the half-space. The surface of the half-space is affected by a time dependent thermal shock and is traction free. The Laplace transform with respect to time is used. The inverse transforms are obtained in an exact manner for the temperature, thermal stress, and displacement distributions. These solutions are represented graphically and discussed for several cases of the applied heating. Comparison is made between the predictions here and those of the theory of thermoelasticity with one relaxation time.

Asymmetric motion of a transversely isotropic thermoelastic half-space under time-harmonic buried source

With the aid of complete representations in terms of two scalar potential functions, the governing equations of coupled thermoelasticity are uncoupled into a sixth- and second-order partial differential equations in cylindrical coordinate system, which are solved by virtue of Fourier series expansion and Hankel integral transforms. Utilizing the transformed stresses-, displacements- and temperature-potential functions relationships, these functions are derived and represented in terms of improper line integrals. The general solutions are changed for point and circular patch load and heat flux Green’s functions in order to derive the related displacement and temperature Green’s functions. Some numerical evaluations of Greens functions are represented to portray the dependency of response on thermo-mechanical coupling as well as the anisotropy of the medium.

On Discontinuties in Thermoelastic Plane Waves without Energy Dissipation Due to a Thermo-Mechanical Shock

The present paper deals with the thermoelastic plane waves due to a thermo-mechanical shock in the form of pulse at the boundary of a homogeneous, isotropic thermoelastic half-space. The field equations of the Green- Naugdhi theory without energy dissipation for an thermoelastic solid in the generalized thermoelasticity theory are written in the form of a vector-matrix differential equation using Laplace transform techniques and then solved by an eigenvalue approach. Exact expressions for the considered field variables are obtained and presented graphically for copper-like material. The characteristic features of the present theory are analyzed by comparing these solutions with their counterparts in other generalized thcrmoelasticity theories.

Thermoelastic surface waves on an exponentially graded half-space

In this paper, we consider the propagation of Rayleigh surface waves in a functionally graded isotropic thermoelastic half-space, in which all thermoelastic characteristic parameters exponentially change along the depth direction. The propagation condition is established in the form of a bicubic equation whose coefficients are complex numbers while the analytical solutions (eigensolutions) of the thermoelastodynamic system are explicitly obtained in terms of the characteristic solutions. The concerned solution of the Rayleigh surface wave problem is subsequently expressed as a linear combination of the three eigensolutions while the secular equation is established in an implicit form. The explicit secular equation is written when an isotropic and homogeneous thermoelastic half-space is considered and some numerical simulations are given for a specific material.

Response of thermal source in a transversely isotropic thermoelastic half-space with mass diffusion by using a finite element method

The two-dimensional problem of generalized thermoelastic diffusion material with thermal and diffusion relaxation times is investigated in the context of the Lord—Shulman theory. As an application of the problem, a particular type of thermal source is considered and the problem is solved numerically by using a finite element method. The components of displacement, stress, temperature distribution, chemical potential, and mass concentration are obtained. The resulting quantities are depicted graphically for a special model. An appreciable effect of relaxation times is observed on various resulting quantities.

Analysis of wave motion in micropolar transversely isotropic thermoelastic half space without energy dissipation

The propagation of waves in a micropolar transversely isotropic half space in the theory of thermoelasticity without energy dissipation are discussed. After developing the solution, the phase velocities and attenuation quality factor has been obtained. The expressions for amplitudes of stresses, displacements, microrotation and temperature distribution have been derived and computed numerically. The numerical results have been plotted graphically.

Thermomechanical deformation in porous generalized thermoelastic body with variable material properties

The two-dimensional deformation of a homogeneous, isotropic thermoelastic half-space with voids with variable modulus of elasticity and thermal conductivity subjected to thermomechanical boundary conditions has been investigated. The formulation is applied to the coupled theory(CT) as well as generalized theories: Lord and Shulman theory with one relaxation time(LS), Green and Lindsay theory with two relaxation times(GL) Chandrasekharaiah and Tzou theory with dual phase lag(C-T) of thermoelasticity. The Laplace and Fourier transforms techniques are used to solve the problem. As an application, concentrated/uniformly distributed mechanical or thermal sources have been considered to illustrate the utility of the approach. The integral transforms have been inverted by using a numerical inversion technique to obtain the components of displacement, stress, changes in volume fraction field and temperature distribution in the physical domain. The effect of dependence of modulus of elasticity on the components of stress, changes in volume fraction field and temperature distribution are illustrated graphically for a specific model. Different special cases are also deduced.

Debonding of a thermoelastic material from a rigid substrate at any constant speed: thermal relaxation effects

A linear isotropic thermoelastic half-space is debonded from a rigid insulated substrate at constant speed by moving shear and normal line loads. A dynamic steady state is examined, and an exact transform solution for the related problem of an insulated half-space subjected to a moving zone of specified surface displacements is obtained. Asymptotic forms are extracted that are valid near the zone edge and for high speeds, and which highlight thermal relaxation effects. They are used to derive analytical results for debonding at any constant speed. In particular, field variables on the debonded surface and the still-bonded interface are given for the sub-Rayleigh, super-Rayleigh/subsonic, lower and upper transonic, and supersonic speed ranges. The degenerate cases that arise at the three body wave speeds and at twice the rotational wave speed are also given. Calculations for the dynamic fracture energy rate and debonding zone temperature change at sub-Rayleigh speeds in 4340 steel indicate that thermal relaxation enhances energy rate, but mutes thermal response. The latter effect, however, itself decreases as the Rayleigh speed is approached.

Rapid sliding indentation with friction on a transversely isotropic thermoelastic half-space

A rigid insulated die slides at a constant sub-critical speed on a transversely isotropic half-space in the presence of friction. In a two-dimensional analysis of the dynamic steady-state, the coupled equations of thermoelasticity are invoked. All elements of the Coulomb friction model are strictly enforced, thus giving rise to auxiliary conditions, including two unilateral constraints. Robust asymptotic forms of an exact solution to a related problem with unmixed boundary conditions lead to analytical solutions for the sliding indentation problem. The solution expressions, abetted by calculations for zinc, show the role of frictional heating on the half-space surface. The effects of friction and sliding speed on contact zone size and location and average contact zone temperature are also studied. The analysis is aided by factoring procedures that simplify the complicated forms that arise in anisotropic elasticity. A scheme that renders expressions for roots of certain irrational functions analytic to within a single quadrature also plays a role.

MECHANICAL AND THERMAL SOURCES IN A GENERALIZED THERMOELASTIC HALF-SPACE

The disturbance due to mechanical point loads and thermal sources acting on the boundary of a homogeneous isotropic thermoelastic half-space has been investigated upon applying the Laplace and Hankel transforms in the context of generalized theories of thermoelasticity. The integral transforms have been inverted using a numerical technique to obtain the displacements, temperature, and stresses in the physical domain. The numerical technique expresses the integrand as a Fourier series representation with respect to the Laplace transform parameter and evaluates the inverse Hankel transform integral via Romberg integration with an adaptive stepsize after using the results from successive refinements of the extended trapezoidal rule followed by extrapolating the results to the limit when the stepsize tends to zero. The results for various physical quantities are computed and presented graphically. A comparison of the results for different generalized theories of thermoelasticity are also presented.