Green And Lindsay Research Articles

Thermo-mechanical interactions in a functionally graded orthotropic thermoelastic medium with rotation and gravity

The current research identify the disturbances in a rotating two-dimensional nonhomogeneous, orthotropic thermoelastic solid half-space with gravity field in the context of Green and Lindsay (G-L) theory. A mechanical source is acting on the surface of the half-space. It is presumed that the mechanical and thermal properties are varying in the x-direction. With the application of normal mode analysis, different field variables are obtained in the physical domain. These field variables are also computed numerically with the help of MATLAB programming. Some collations are made to delineate the effects of anisotropy, non-homogeneity, gravity and rotation parameters on the physical fields.

Reflection and refraction of plane wave at the junction of two dissimilar pre-stressed functionally graded piezothermoelastic media under different interfacial conditions

The present paper deals with the study of the reflection and refraction of plane waves (quasi P wave, quasi SV wave, electroacoustic wave, and thermal wave) at the common interface of two dissimilar initially stressed functionally graded piezothermoelastic media. The problem has been formulated and solved using suitable boundary conditions, and the results are obtained in a closed matrix form. The effect of mechanical, electrical, and thermal loose bonding of the common interface on the reflection and refraction coefficients are analyzed and theoretical outcomes are presented through graphs under two generalized forms of thermoelasticity (namely, Lord and Shulman (LS) theory, Green and Lindsay (GL) theory). A particular model of CdSe and PZT-5A materials has been considered for the numerical illustration. Moreover, the effect of material gradient; horizontal, transverse, and normal initial stresses; thermal relaxation parameters; and material coefficients on the reflection and refraction coefficients are demonstrated with the help of graphs. The expressions for energy ratios of reflected and refracted waves are derived, and energy conservation is validated with the help of obtained graphs under LS and GL theories. The study finds its application toward the efficient optimization of force sensors, surface acoustic wave (SAW) devices, temperature sensors, and Love wave sensors.

Analysis of Thermoelastic Interaction in a Polymeric Orthotropic Medium Using the Finite Element Method.

In this work, the finite element technique is employed to evaluate the effects of thermal relaxation durations on temperature, displacements, and stresses in a two-dimensional, polymeric, orthotropic, elastic medium. The problem is considered in a homogeneous, polymeric, orthotropic medium in the context of the Green and Lindsay model with two thermal relaxation times. The bounding surface of the half-space was subjected to a heat flux with an exponentially decaying pulse. Finite element techniques were used to solve the governing formulations, with eight-node isoparametric rectangular elements with three degrees of freedom (DOF) per node. The developed method was calculated using numerical results applied to the polymeric, orthotropic medium. The findings were implemented and visually shown. Finally, the results were displayed to demonstrate the differences between classical dynamic coupling (CT), the Lord–Shulman (LS) and the Green and Lindsay (GL) models.

Mathematical Modeling on Rotational Magneto-Thermoelastic Phenomenon under Gravity and Laser Pulse considering Four Theories

The aim of this investigation is making mathematical model for the variation in laser pulse, rotational gravity, and magnetic fields on the generalized thermoelastic homogeneous isotropic half-space. The governing dynamical system equations have been formulated considering the four thermoelastic models: coupled (CT) model, Lord and Shulman (LS) model, Green and Lindsay (GL) theory, and Green and Naghdi (GN III) model. Normal mode analysis technique is used to obtain the analytical expressions for the displacement components, temperature, and mechanical and Maxwell’s stresses distribution. The effect of laser pulse, gravity, and magnetic field is studied by numerical examples and displayed graphically. A comparison has been made between the theories as well as the present results and agreement with it as a special case from this study. The results predict the strong effect of magnetic field, laser pulse, and gravity field on the wave propagation phenomenon.

On the fundamental solutions for the strain and temperature rate-dependent generalized thermoelasticity theory

The present paper concerns with the fundamental solutions for strain and temperature rate-dependent thermoelasticity theory recently developed by Yu et al. (2018). This recently developed model is theoretically established with the aid of principles of thermodynamics and by adding the strain-rate term in temperature rate-dependent thermoelasticity theory, which was proposed by Green and Lindsay (GL)(1972). This model has attempted to remove the drawback of discontinuity in the displacement field under Green-Lindsay (GL) model. We consider this modified Green-Lindsay (MGL) model for the case of homogeneous and isotropic bodies. Two cases, namely, concentrated body force and concentrated heat source have been taken for deriving the fundamental solutions for thermoelasticity in the context of MGL model. The fundamental solutions for the distributions of displacement components and temperature are obtained by the Laplace transform method. Fundamental solutions in the physical domain are obtained by Laplace inversion and the solution of displacement and temperature is obtained for short-time approximation. Lastly, we get the fundamental solution of the system of equations in the case of steady oscillations.

Fractional order GL model on thermoelastic interaction in porous media due to pulse heat flux

In this paper, the thermoelastic interactions in a two-dimension porous body are studied. This problem is solved by using the Green and Lindsay (GL) generalized thermoelasticity model under fractional time derivative. The derived approaches are estimated. with numeral results which are applied to the porous mediums in simplifying geometrical. The bounding plane surface of the present half-space continuum is subjected to a pulse heat flux. We use the Laplace-Fourier transforms methods with the eigenvalues approach to solve the problem. The numerical solutions for the field functions are obtained numerically using the numerical Laplace inversion technique. The effects of the fractional parameter and the thermal relaxation times on the temperature field, the displacement field, the change in volume fraction field of voids distribution and the stress fields have been calculated and displayed graphically and the obtained results are discussed.

Thermoelastic interaction in a thermally conducting cubic crystal subjected to ramp-type heating

In this paper, the thermoelastic interactions in a homogeneous, thermally conducting cubic crystal, elastic half-plane has been studied. A linear temperature ramping function is used to more realistically model. The general solution obtained is applied to a specific problem of a half space subjected to ramp-type heating. The components of displacement, stresses, and temperature distribution are obtained by applying a numerical finite element method. Some particular cases are also discussed in the context of the problem. The comparison in Lord and Shulman (LS), Green and Lindsay (GL) and Green and Naghdi (GN) theories have been shown graphically to estimate the effect of ramping parameter of heating for isothermal boundary.

Propagation of waves in micropolar generalized thermoelastic materials with two temperatures bordered with layers or half-spaces of inviscid liquid

The aim of the present paper is to study the propagation of Lamb waves in micropolar generalized thermoelastic solids with two temperatures bordered with layers or half-spaces of inviscid liquid subjected to stress-free boundary conditions in the context of Green and Lindsay (G-L) theory. The secular equations for governing the symmetric and skew-symmetric leaky and nonleaky Lamb wave modes of propagation are derived. The computer simulated results with respect to phase velocity, attenuation coefficient, amplitudes of dilatation, microrotation vector and heat flux in case of symmetric and skew-symmetric modes have been depicted graphically. Moreover, some particular cases of interest have also been discussed.

Wave Propagation in a Micropolar Transversely Isotropic Generalized Thermoelastic Half-Space

Rayleigh waves in a half-space exhibiting microplar transversely isotropic generalized thermoelastic properties based on the Lord-Shulman (L-S), Green and Lindsay (G-L) and Coupled thermoelasticty (C-T) theories are discussed. The phase velocity and attenuation coefficient in the previous three different theories have been obtained. A comparison is carried out of the phase velocity, attenuation coefficient and specific loss as calculated from the different theories of generalized thermoelasticity along with the comparison of anisotropy. The amplitudes of displacements, microrotation, stresses and temperature distribution were also obtained. The results obtained and the conclusions drawn are discussed numerically and illustrated graphically. Relevant results of previous investigations are deduced as special cases.

Wave propagation in micropolar monoclinic thermoelastic half space

Propagation of waves in a micropolar monoclinic medium possessing hermoelastic properties based on the Lord- Shulman (L-S),Green and Lindsay (G-L) and Coupled thermoelasticty (C-T) theories is discussed. The investigation is divided into two sections, viz., plane strain and anti-plane strain problem. After developing the solution, the phase velocities and attenuation quality factor have been derived and computed numerically. The numerical results have been plotted graphically.

Analysis of deformation due to inclined load in generalized thermodiffusive elastic medium

The present investigation deals with study of deformation in homogeneous, isotropic thermodiffusion elastic half-space as a result of inclined load. The inclined load is assumed to be a linear combination of normal load and tangential load. The integral transform technique is used to solve the problem. As an application of the approach distributed and moving forces have been taken. The transformed components of displacement, stresses, temperature distribution and concentration are inverted using numerical inversion technique. The effect of relaxation times and response of two theories of thermoelasticity i.e. Green and Lindsay (G-L) theory and coupled theory (CT) on these quantities have been depicted graphically for a particular model. Some particular cases are also deduced.

The Dynamic Response of a Rotating Thick Piezoelectric Plate with Thermal Relaxations

Based on the generalized thermoelastic theory postulated by Green and Lindsay(G-L), the dynamic response of an infinite rotating piezoelectric plate subject to thermal shocks on both up and bottom surfaces was investigated. To avoid the calculation precision loss caused by the integral transform technique, the so-called direct finite element method was used to solve the governing equations in time domain directly. The distributions of the dimensionless temperature, stress, displacement and electric potential were presented graphically. The results show that the direct finite element method provides an effective way for achieving high calculation precision in solving the generalized piezoelectric-thermoelastic problem. The results also show that the rotation effect tends to decrease the dimensionless displacement and electric potential and barely affects the dimensionless temperature and stress.

A study of axi-symmetric waves through an isotropic thermoelastic diffusive medium

The paper deals with the propagation of axial symmetric cylindrical surface waves in a cylindrical bore through a homogeneous isotropic thermoelastic diffusive medium of infinite extent. The three theories of thermoelasticity namely, Coupled Thermoelasticity (CT), Lord and Shulman (L-S) and Green and Lindsay (G-L) are used to study the problem. The frequency equations, connecting the phase velocity with wave number, radius of bore and other material parameters, for empty and liquid filled bore are derived. The numerical results obtained have been illustrated graphically to understand the behaviour of phase velocity and attenuation coefficient versus wave number of a wave. A particular case of interest has also been deduced from the present investigation.

Elastodynamic Behavior of Axisymmetric Vibrations in Micropolar Thermoelastic Cubic Crystal Plate

The present paper is aimed at studying elastodynamic behavior of axisymmetric vibrations in a homogenous isotropic micropolar thermoelastic cubic crystal plate in context of Lord and Shulman (L-S) and Green and Lindsay (G-L) theories of thermoelasticity. The upper and lower surfaces of the plate are subjected to stress free thermally insulated conditions. The secular equations for symmetric and skew-symmetric wave modes are derived. The amplitudes of displacement components, microrotation and temperature distribution are also computed during the symmetric and skew-symmetric motion of the plate. Finally, in order to illustrate and verify the analytical developments, numerical solution of secular equation corresponding to stress free thermally insulated micropolar thermoelastic cubic crystal plate is carried out for magnesium crystal material.

AXISYMMETRIC VIBRATIONS IN MICROPOLAR THERMOELASTIC CUBIC CRYSTAL PLATE BORDERED WITH LAYERS OR HALF SPACES OF INVISCID LIQUID

The present study is concerned with the propagation of ax- isymmetric vibrations in a homogenous isotropic micropolar thermoelas- tic cubic crystal plate bordered with layers or half spaces of inviscid liq- uid subjected to stress free boundary conditions in context of Lord and Shulman (L-S) and Green and Lindsay (G-L) theories of thermoelastic- ity. The secular equations for symmetric and skew-symmetric leaky and nonleaky Lamb wave modes of propagation are derived. The amplitudes of displacement components, microrotation and temperature distribution are also computed numerically and presented graphically. Finally, in or- der to illustrate the analytical developments, numerical solution of secu- lar equations corresponding to stress free thermally insulated micropolar thermoelastic cubic crystal plate is carried out for magnesium crystal material bordered with water layers of finite and infinite thickness.

Wave Propagation in Microstretch Thermoelastic Plate Bordered with Layers of Inviscid Liquid

The propagation of free vibrations in microstretch thermoelastic homogeneous isotropic, thermally conducting plate bordered with layers of inviscid liquid on both sides subjected to stress free thermally insulated and isothermal conditions is investigated in the context of Lord and Shulman (L‐S) and Green and Lindsay (G‐L) theories of thermoelasticity. The secular equations for symmetric and skewsymmetric wave mode propagation are derived. The regions of secular equations are obtained and short wavelength waves of the secular equations are also discussed. At short wavelength limits, the secular equations reduce to Rayleigh surface wave frequency equations. Finally, the numerical solution is carried out for magnesium crystal composite material plate bordered with water. The dispersion curves for symmetric and skew‐symmetric wave modes are computed numerically and presented graphically.

Propagation of Lamb waves in transversely isotropic thermoelastic diffusive plate

The constitutive relations and field equations for anisotropic generalized thermoelastic diffusion are derived and deduced for a particular type of anisotropy, i.e. transverse isotropy. Green and Lindsay (GL) theory, in which, thermodiffusion and thermodiffusion–mechanical relaxations are governed by four different time constants, is selected for study. The propagation of plane harmonic thermoelastic diffusive waves in a homogeneous, transversely isotropic, elastic plate of finite width is studied, in the context of generalized theory of thermoelastic diffusion. According to the characteristic equation, three quasi-longitudinal waves namely, quasi-elastodiffusive (QED-mode), quasi-massdiffusive (QMD-mode) and quasi-thermodiffusive (QTD-mode) can propagate in addition to quasi-transverse waves (QSV-mode) and the purely quasi-transverse motion (QSH-mode), which is not affected by thermal and diffusion vibrations, gets decoupled from the rest of the motion of wave propagation. The secular equations corresponding to the symmetric and skew symmetric modes of the plate are derived. The amplitudes of displacements, temperature change and concentration for symmetric and skew symmetric modes of vibration of plate are computed numerically. Anisotropy and diffusion effects on the phase velocity, attenuation coefficient and amplitudes of wave propagation are presented graphically in order to illustrate and compare the analytically results. Some special cases of frequency equation are also deduced from the existing results.

Dynamical behavior of generalized thermoelastic diffusion with two relaxation times in frequency domain

A general solution to the field equations of homogeneous isotropic generalized thermoelastic diffusion with two relaxation times (Green and Lindsay theory) has been obtained using the Fourier transform. Assuming the disturbances to be harmonically time.dependent, the transformed solution is obtained in the frequency domain. The application of a time harmonic concentrated and distributed loads have been considered to show the utility of the solution obtained. The transformed components of displacement, stress, temperature distribution and chemical potential distribution are inverted numerically, using a numerical inversion technique. Effect of diffusion on the resulting expressions have been depicted graphically for Green and Lindsay (G-L) and coupled (C-T) theories of thermoelasticity.

Effect of rotation on plane waves of generalized electro-magneto-thermoviscoelasticity with two relaxation times

A new model of the equations of generalized thermovisco-elasticity for a thermally, isotropic and electrically conducting half-space solid whose surface is subjected to a thermal shock is given. The formulation is applied to the generalized thermoelasticity based on the Green and Lindsay (GL) theory under the effect of rotation, where there is an initial magnetic field parallel to the plane boundary of the half-space. The medium is deformed because of thermal shock and due to the application of the magnetic field, it results an induced magnetic and electric fields in the medium. The normal mode analysis is used to obtain the expressions for the variables considered. The distributions of temperature, displacement, stress, induced magnetic and electric fields are represented graphically. Comparisons are made with the results predicted by the coupled theory (CD) in the presence and absence of rotation.

Reflection and Refraction of Micropolar Magneto-thermoviscoelastic Waves at the Interface between Two Micropolar Viscoelastic Media

Using micropolar generalized thermoviscoelastic theories, problems of reflection and refraction of magneto-thermoeviscoelastic waves at the interface between two viscoelastic media are studied when a uniform magnetic field permeates the media. Coefficient ratios of reflection and refraction are obtained using continuous boundary conditions. Some special cases are considered, i.e., the absence of micropolar and viscous effects. By numerical calculations, variations of the amplitude ratios of reflection and refraction coefficients with the angle of incidence are shown graphically for incident rotational and dilatational waves at the interface between two media (one medium is aluminium-epoxy micropolar iscoelastic material, and the other is magnesium crystal micropolar viscoelastic material). Comparing the generalized thermoelastic theories developed by Lord and Shulman (LS) and by Green and Lindsay (GL) in this paper to conventional dynamics (CD) theory the effects of a magnetic field and viscosity are shown numerically in this paper.