• Geomechanics and Engineering
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• v.32 no.5
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• pp.475-482
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• 2023

This paper studies the effect of the relaxation time on a two-dimensional thermoelastic medium which has a doubly porous structure in the presence of diffusion and gravity. The normal mode analysis is used to obtain the analytic expressions of the physical quantities, which we take the solution form in the exponential image. We have discussed a homogeneous thermoelastic half-space with double porosity with the effect of diffusion and gravity. The equations of generalized thermoelastic material with double porosity structure with one relaxation time have been developed. Moreover, the expressions of many physical quantities are explained. The general solutions, under specific boundary conditions of the problem, were found in some detail. In addition, numerical results are computed.

• Structural Engineering and Mechanics
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• v.51 no.4
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• pp.651-662
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• 2014

The main goal of this study is to extend the domain of influence result to cover the micropolar thermoelastic diffusion. So, we prove that for a finite time t>0 the displacement field $u_i$, the microrotation vector ${\varphi}_i$, the temperature ${\theta}$ and the chemical potential P generate no disturbance outside a bounded domain $B_t$.

• Structural Engineering and Mechanics
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• v.90 no.3
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• pp.263-272
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• 2024

This research deals with the study of two-dimensional deformation in transversely isotropic thermoelastic diffusion medium. This investigation integrates the effect of diffusion and thermal effects in transversely isotropic thermoelastic solids under inclined load. Inclined load is taken as linear combination of normal load and tangential load. Laplace and Fourier transformation techniques are employed to transform the physical domain and then transformed solutions are inverted with the aid of numerical inversion techniques. Concentrated and distributed load are considered to exemplify its utility. Graphical representation of variation in displacement, stresses, temperature and concentration distribution with distance is depicted by taking inclination at different angles. Some particular cases are studied.

• Structural Engineering and Mechanics
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• v.28 no.1
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• pp.19-38
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• 2008

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.

• Coupled systems mechanics
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• v.8 no.1
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• pp.39-53
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• 2019

Here in this investigation, a two-dimensional thermoelastic problem of thick circular plate of finite thickness under fractional order theory of thermoelastic diffusion has been considered in frequency domain. The effect of frequency in the axisymmetric thick circular plate has been depicted. The upper and lower surfaces of the thick plate are traction free and subjected to an axisymmetric heat supply. The solution is found by using Hankel transform techniques. The analytical expressions of displacements, stresses and chemical potential, temperature change and mass concentration are computed in transformed domain. Numerical inversion technique has been applied to obtain the results in the physical domain. Numerically simulated results are depicted graphically. The effect frequency has been shown on the various components.

• Steel and Composite Structures
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• v.34 no.2
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• pp.309-319
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• 2020

The objective is to study the deformation in a homogeneous isotropic modified couple stress thermoelastic medium with mass diffusion and with two temperatures due to a thermal source and mechanical force. Laplace and Fourier transform techniques are applied to obtain the solutions of the governing equations. The displacements, stress components, conductive temperature, mass concentration and couple stress are obtained in the transformed domain. Numerical inversion technique has been used to obtain the solutions in the physical domain. Isothermal boundary and insulated boundaryconditions are used to investigate the problem. Some special cases of interest are also deduced.

• Structural Engineering and Mechanics
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• v.75 no.2
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• pp.133-144
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• 2020

This investigation is to study the effect of gravitational field and diffusion on a microstretch thermoelastic medium heating by a non-Gaussian laser beam. The problem was studied in the context of the dual-phase-lag model. The normal mode analysis is used to solve the problem to obtain the exact expressions for the non-dimensional displacement components, the micro-rotation, the stresses, and the temperature distribution. The effect of time parameter, heat flux parameter and gravity response of three theories of thermoelasticity i.e. dual-phase-lag model (DPL), Lord and Shulman theory (L-S) and coupled theory (CT) on these quantities have been depicted graphically for a particular model.

• Steel and Composite Structures
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• v.36 no.6
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• pp.617-629
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• 2020

The purpose of this paper is to depict the effect of rotation and initial stress on a magneto-thermoelastic medium with diffusion. The problem discussed within memory-dependent derivative in the context of the three-phase-lag model (3PHL), Green-Naghdi theory of type III (G-N III) and Lord and Shulman theory (L-S). Analytical expressions of the considered variables are obtained by using Laplace-Fourier transforms technique. Numerical results for the field quantities given in the physical domain and illustrated graphically in the absence and presence of a magnetic field, initial stress as well as the rotation. The differences in variable thermal conductivity are also presented at different parameter of thermal conductivity. The numerical results of the field variables are presented graphically to discuss the effect of various parameters of interest. Some special cases are also deduced from the present investigation.

• Laser Solutions
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• v.4 no.3
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• pp.40-44
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• 2001

Microbump formation during CO$_2$ laser texturing of glass substrates is examined in this paper. Experimental results show that different bump shapes (dome-shaped, with a central dimple, and with a peripheral rim) are generated depending on the laser fluence. A theoretical model for the process is suggested based on thermoelastic behavior but limited only to the dome-shaped bump. The dimensions (maximum height and base area) of the bump shows a logarithmic dependence on laser fluence as expected from the theory. Numerical computation reveals that the effect of thermal diffusion is not negligible for relatively long laser pulses.

• Coupled systems mechanics
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• v.10 no.1
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• pp.21-38
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• 2021

This work is an attempt to design a dynamic model for a non local bio-thermoelastic medium with diffusion. The system of governing equations are formulated in terms of displacement vector field, chemical potential and the tissue temperature in the context of non local dual phase lag (NL DPL) theories of heat conduction and mass diffusion. Based on this considered model, we study the fundamental solution and propagation of plane harmonic waves in tissues. In order to analyze the behavior of the NL DPL model, we construct basic theorem in the terms of elementary function which determine the existence of three longitudinal and one transverse wave. The effects of various parameters on the characteristics of waves i.e., phase velocity and attenuation coefficients are elaborated by plotting various figures of physical quantities in the later part of the paper.