Green Lindsay Theory Research Articles

Rayleigh wave propagation in a modified couple stress visco-thermoelastic diffusion medium

The present investigation is devoted to Rayleigh wave propagation in modified couple stress visco-thermoelastic medium with mass diffusion under Lord–Shulman and Green–Lindsay theories of thermoelasticity. After formulating the problem mathematically, the secular equation is derived for stress free, insulated, and impermeable boundary. The wave characteristics like phase velocity and attenuation coefficient have been obtained numerically by developing numerical algorithm. For a particular material, the numerically simulated results are shown graphically to display the physical meaning of the phenomenon. The current inquiry also leads to several specific cases of interest. A comparison has been conducted with the earlier findings that suggested how the additional parameters might affect the phenomena of Rayleigh waves propagating. The results obtained indicate to the strong impact for the diffusivity and viscosity of Rayleigh thermoelastic waves propagation and applicable on the related phenomenon in geology, geophysics, acoustics, astronomy, and geophysics and agreement with the physical meaning of the phenomenon.

An investigation of the thermomechanical effects of mode-I crack under modified Green–Lindsay theory

An investigation of the thermomechanical effects of mode-I crack under modified Green–Lindsay theory

Magneto–thermoelastic behavior of an orthotropic hollow cylinder based on Lord–Shulman and Green–Lindsay theories

Magneto–thermoelastic behavior of an orthotropic hollow cylinder based on Lord–Shulman and Green–Lindsay theories

Thermoelastic interactions in a micropolar poroelastic medium

The present problem investigates the two-dimensional disturbances in a homogeneous, isotropic, micropolar thermoelastic saturated porous medium under the purview of Green-Lindsay (GL) theory of thermoelasticity. The medium is assumed to be unstrained and unstressed initially and has uniform temperature. The formulation is subjected to a moving thermal shock. Normal mode technique is employed to obtain the exact expressions for the displacement components, stresses, pore pressure and temperature. Numerical computations have been carried out with the help of MATLAB software and the results are illustrated graphically. Comparisons are made to show the effects of time, velocity of the load, micropolar and porous parameters on the resulting quantities. The outcomes point out a strong impact of these parameters on the physical quantities and agree with the boundary conditions. Some particular cases of interest have been deducted from the current investigation to validate the results. The present work is useful and valuable for analysis of problems involving thermal shock, micropolar and poroelastic deformations.

Wave packet enriched finite element for accurate modelling of thermoelectroelastic wave propagation in functionally graded solids

A wave packet enriched finite element (FE) formulation featuring electrothermomechanical coupling is presented for solving two-dimensional wave propagation problems in functionally graded elastic and piezoelectric media. The FE equations for the Lord-Shulman and Green-Lindsay theories of generalized piezothermoelasticity are derived, where the standard Lagrangian interpolation functions of the temperature, electric potential, and displacement field variables are extrinsically enriched with element-domain sinusoidal wave-packet functions and are solved using the Newmark–β direct time integration. The effective properties of the functionally graded material (FGM) are computed using the volume-fraction-based micromechanics models, the Mori-Tanaka model and Voigt's rule of mixture (ROM) model. A variety of wave propagation problems, including the mechanically and electrically excited high-frequency Lamb wave propagation in FGM plates, impact waves in FGM bars, and thermal shock waves in functionally graded piezoelectric cylinders, are solved using the present formulation, and results are validated with available solutions. The efficacy of the current solution in comparison with the conventional FE is evaluated for all the studied problems. The effect of the inhomogeneity parameter on the transient wave behaviour is also presented for all the problems. The results of the Mori–Tanaka model are compared with those of the widely used ROM.

Influence of thermal load on a rotating thermoelastic medium with diffusion and double porosity

In the present work, we have studied the thermodynamical interactions in a two-dimensional thermoelastic medium with diffusion, rotation and double porosity in the context of Green–Lindsay theory. A thermal load is applied at the outer free surface of the medium. The normal mode technique is employed to derive the analytic expressions of the field quantities such as stresses, displacement components, temperature field and mass concentration. Numerical computations are performed with the help of MATLAB software for a specific material for illustrating the results. To the author’s best knowledge, no attempt has been made to investigate the therodynamical interactions in a rotating double porous thermoelastic medium with diffusion under the influence of a thermal load. Comparisons of the physical quantities are shown in figures to study the effects of time, double porosity, rotation, thermal load and diffusion. Some particular cases of interest have also been inferred from the present problem. The theoretical and numerical computations are found to be in close agreement.

A new model of rotating nonlocal fiber-reinforced visco-thermoelastic solid using a modified Green–Lindsay theory

The effect of rotation on a nonlocal fiber-reinforced visco-thermoelastic media was examined in this work using an modified Green and Lindsay theory (MGL). The problem was resolved by using normal mode method to derive the precise expressions of field quantities. In this technique, one gets exact solution without any assumed restrictions on the field variables. The normal mode technique is applicable to a wide range of problems in thermodynamics and thermoelasticity. Graphical representations of the thermal temperature, displacements and stresses are obtained. Comparisons of the physical quantities are shown in figures to study the effects of nonlocal parameter, rotation, viscosity and reinforcement parameters. Some special cases of interest have also been inferred from the present problem. The results indicate that rotation, nonlocal parameter, viscosity and reinforcing factors have a considerable impact on the fluctuations of the variables under consideration. These impacts are examined and described in depth.

Simulation and modeling of polymer concrete panels using deep neural networks

The most often utilized construction material worldwide is concrete. Extensive experiments are carried out each year to study the physical, mechanical, and chemical properties of concrete, which are costly and time-consuming. This study focuses on avoiding redundant tests by applying the machine learning (ML) method to predict temperature-dependent polymer concrete qualities. In this work, as a strong tool of the ML method, a deep neural network (DNN) is used to examine the five temperature-dependent mechanical characteristics of concrete, including Poisson's ratio, Young's modulus, specific heat, coefficient of thermal expansion, and thermal conductivity. A 5-fold cross-validation method was used to verify the strategy in this research and get rid of split bias in testing and training. This study demonstrates the material properties of temperature-dependent polymer concrete followed by mathematical modeling of a steel-polymer concrete panel used for various civil applications. Temperature-dependent equations are determined using constitutive heat transfer and Cartesian coordinates. In addition, a thermal shock load acts on the upper part, and the lower part becomes an isothermal state with no heat flow. In order to account for the limited speed at which temperature waves travel, two distinct theories of generalized thermoelasticity are employed: the Lord-Shulman (LS) and the Green-Lindsay (GL) theories. The Fast Laplace Inverse Transform Method (FLITM) is used to transfer the results from the Laplace domain to the time domain. In addition, a three-dimensional differential quadrature approach (3D-DQA) using three Chebyshev-Gaussian-Robat functions for solving temperature-dependent equations is presented. In conclusion, some suggestions for improving the stability of polymer concrete panels are detailed and will be compiled in a future manual.

Effect of thermal conductivity in a semiconducting medium under modified Green-Lindsay theory

Effect of thermal conductivity in a semiconducting medium under modified Green-Lindsay theory

Eigenvalue Approach on a Fiber-Reinforced Magneto-Visco-Thermoelastic Rotating Medium with Initial Stress

PurposeThe aim of this work is to study the wave propagation in a rotating fiber-reinforced thermo-viscoelastic solid.MethodsThe analytical technique used to obtain the ordinary differential equations was normal mode analysis. In this article using the modified Green-Lindsay (MGL) theory and the Green-Lindsay (G-L) theory.ResultsThe numerical calculations have been completed, and the physical fields have been determined using the proper boundary conditions. The effects of rotation, viscosity, and magnetic field are discussed.ConclusionOverall, the research on the rotation and magnetic field effect on fiber-reinforced thermo-viscoelastic have a significant influence on all the physical variables and several potential practical implications and engineering applications in various fields such as environmental, chemical, and energy engineering.

Transient responses of two temperature, fractional thermo-diffusive-elastic half space with temperature dependent properties

In scientific disciplines such as control engineering, astrophysics, geomechanics, nuclear physics, etc., thermoelastic diffusion plays a crucial role. When physical processes involve high temperature, considering two temperature theories and temperature-dependent material properties contribute to more rational results. The inclusion of fractional calculus in such studies provides results with significant accuracy. In this light, a model is formulated under two temperatures, fractional order Lord Shulman and Green Lindsay's theories of generalized thermo-diffusive-elasticity. The medium under consideration is a half space which is kept unstressed initially at a uniform temperature The material properties are considered to be a function of temperature. Governing equations and constitutive relations of the model are non-dimensionalized and simplified using potential functions. The field variables are determined analytically in the closed form in Laplace-Fourier transformed domain. Numerical computations are conducted with the assistance of MATLAB software. The study aims to observe the behavior of physical quantities for different values of two temperature, temperature-dependent, and fractional order parameters. Graphical representation is displayed with respect to space variables x and z. The results reveal that physical quantities express varying degrees of influence corresponding to different effects involved in the study.

Multifield asymptotic homogenization for periodic materials in non-standard thermoelasticity

This article presents a multifield asymptotic homogenization scheme for the analysis of Bloch wave propagation in non-standard thermoelastic periodic materials, leveraging on the Green-Lindsay theory that accounts for two relaxation times. The procedure involves several steps. Firstly, an asymptotic expansion of the micro-fields is performed, considering the characteristic size of the microstructure. By utilizing the derived microscale field equations and asymptotic expansions, a series of recursive differential problems are solved within the repetitive unit cell Q. These problems are then expressed in terms of perturbation functions, which incorporate the material’s geometric, physical, and mechanical properties, as well as the microstructural heterogeneities. The down-scaling relation, which connects the microscopic and macroscopic fields along with their gradients through the perturbation functions, is then established in a consistent manner. Subsequently, the average field equations of infinite order are obtained by substituting the down-scaling relation into the microscale field equations. To solve these average field equations, an asymptotic expansion of the macroscopic fields is performed based on the microstructural size, resulting in a sequence of macroscopic recursive problems. To illustrate the methodology, a bi-phase layered material is introduced as an example. The dispersion curves obtained from the non-local homogenization scheme are compared with those generated from the Floquet-Bloch theory. This analysis helps validate the effectiveness and accuracy of the proposed approach in predicting the wave propagation behavior in the considered non-standard thermoelastic periodic materials.

Thermodynamical interactions in a micropolar magneto-thermoelastic medium with photothermal effect

PurposeThe purpose of this paper is to establish a two-dimensional model of Green–Lindsay theory for micropolar magneto-thermoelastic medium to study the photothermal effect. The model is used to study the coupling between elastic waves and plasma waves generated due to thermal changes in a micropolar elastic medium.Design/methodology/approachNormal mode analysis is used to obtain the analytical solutions of the governing equations.FindingsEffects of magnetic field, micropolarity, photothermal and time are highlighted on various physical fields such as stresses, temperature, displacement and carrier density. The above physical fields also conform to the boundary conditions. It is further observed that all the physical quantities become zero outside some bounded region of space, thus confirming the notion of generalized theory of thermoelasticity.Originality/valueThe values of physical fields are computed numerically using MATLAB software considering material constants for silicon. Furthermore, the effects are depicted graphically and analyzed accordingly. The study is valuable for the analysis of thermoelastic problems involving magnetic field, micropolarity and elastic deformations.

Analysis of two thermoelastic problems with the Green–Lindsay model

In this paper, we analyze, from the numerical point of view, two thermo-elastic problems involving the Green–Lindsay theory. The coupling term is different for each case, involving second order or first order spatial derivatives, respectively. The variational formulation leads to a linear coupled system which is written in terms of the velocity and temperature speed. An existence and uniqueness results and the exponential energy decay for the problem with the stronger coupling are recalled. The polynomial energy decay for the weaker coupling is then proved but using the theory of linear semigroups. Then, a fully discrete approximation is introduced using the finite element method and an implicit scheme. A discrete stability property and a main a priori error estimates result are shown, from which we can derive the linear convergence of the approximations. Finally, some numerical simulations are presented to demonstrate the accuracy of the algorithm, the discrete energy decay and the dependence on the relaxation parameter.

Wave motion in homogeneous isotropic micropolar porous thermoelastic plate under memory-dependent Lord-Shulman and Green-Lindsay theories

The homogeneous isotropic micropolar porous thermoelastic plate under memory-dependent derivatives (MDD) has been taken into consideration to investigate the wave propagation regarding Lord-Shulman (LS) and Green-Lindsay (GL) theories. The governing equations are non-dimensionalized and solved using normal mode analysis. The dispersion equations for both symmetric and anti-symmetric modes of wave propagation are obtained in the assumed model. The comparisons between the variation of phase velocity and attenuation coefficient corresponding to LS and GL theories are shown graphically using MATLAB software. The amplitudes of dilatation, volume fraction, micro-rotation and temperature distribution are computed analytically and presented in the form of graphs for LS and GL theories in the presence of MDD. Various particular cases are discussed in detail.

Variation on propagation of Rayleigh waves in thermo-poroelastic solids

We analyse the dispersion and attenuation of Rayleigh-wave propagation along on isothermal free surface of a thermo-poroelastic medium. The thermo-poroelastic theory, including the Lord-Shulman (LS) and Green-Lindsay (GL) theories, predicts three compressional waves and one shear wave, which induce two Rayleigh-type surface waves, R1 and R2 modes along the interface by evanescent potential functions specified by vertical imaginary wavenumbers. The GL model can give a stronger P1 and P2 wave thermal attenuation and consequently a stronger velocity dispersion than the LS model. We investigate the influence of frequency and surface boundary condition. The additional thermal diffusion exhibits the inverse dispersion in R1 waves, and makes the pseudo surface-wave transition under the closed (CP) and partial permeable (PP) surface toward high frequencies. Another T wave affects the energy inference along the surface and induce the other R2 waves under the open surface (OP). The thermal dispersion occurs at characteristic frequencies around the thermal relaxation peaks, which induces the high-velocity T wave toward low frequencies when the Maxwell–Vernotte–Cattaneo relaxation time increases. Until the T wave propagates faster than the P2 wave, the Rayleigh equations lose the R2 poles making the prohibition of R2-wave propagation.

Thermodynamical interactions in a rotating functionally graded semiconductor material with gravity

PurposeThe purpose of this paper is to analyse the transient effects in a functionally graded photo-thermoelastic (TE) medium with gravity and rotation by considering two generalised TE theories: Lord–Shulman (LS) and Green–Lindsay (GL). The governing equations are derived in rectangular Cartesian coordinates for a two dimensional problem.Design/methodology/approachAll the physical properties of the semiconductor are supposed to vary exponentially with distance. The analytical solution is procured by employing normal mode technique on the resulting non-dimensional coupled field equations with appropriate boundary conditions.FindingsFor the mechanically loaded thermally insulated surface, normal displacement, stress components, temperature distribution and carrier density are calculated numerically with the help of MATLAB software for a silicon semiconductor and displayed graphically. Some particular cases of interest have also been deduced from the present results.Originality/valueThe effects of rotation and non-homogeneity on the different physical fields are investigated on the basis of analytical and numerical results. Comparisons are made with the results predicted by GL theory in the presence and absence of gravity for different values of time. Comparisons are also made between the three theories in the presence of rotation, gravity and in-homogeneity. Such problems are very important in many dynamical systems.

Effect of thermal conductivity in a semiconducting medium under modified Green-Lindsay theory

Effect of thermal conductivity in a semiconducting medium under modified Green-Lindsay theory

A Modified Two-Relaxation Thermoelastic Model for a Thermal Shock of Rotating Infinite Medium.

A unified form of thermoelasticity theory that contains three familiar generalized thermoelasticity. The Lord-Shulman theory, Green-Lindsay theory, and the classical one can be outlined in this form. The field quantities of a rotating/non-rotating half-space with and without the effect of the decay parameter can be obtained due to the unified thermoelasticity theory. The present medium is subjected to a time-dependent thermal shock taking into account that the magnitude of the thermal shock wave is not totally fixed but decaying over time. A special case of a thermal shock waveform with constant magnitude may be considered. The field quantities such as temperature, displacements, and stresses of the present problem are analytically obtained. Some plots of these field variables are presented in two- and three-dimensional illustrations in the context of refined theories.

Effect of Hydrostatic Initial Stress on a Rotating Half-Space in the Context of a Two-Relaxation Power-Law Model

The simple and refined Lord–Shulman theories, the simple and refined Green–Lindsay theories as well as the coupled thermoelasticity theory were all employed to investigate the deformation of a rotating thermoelastic half-space. The present medium is subjected to initial pressure, bounded by hydrostatic initial stress and rotation. A unified heat conduction equation is presented. The normal mode strategy is applied to get all analytical expressions of temperature, stresses, and displacements. Some outcomes are tabulated to validate the present refined theories with the simple and classical thermoelasticity theories. The effect of hydrostatic initial stress was investigated on all field quantities of the rotating thermoelastic half-space with and without initial pressure. Two- and three-dimensional plots are illustrated in the context of refined theories to discuss the behaviors of all variables through the coordinate axes. Some particular cases of special interest have been deduced from the present investigation.