• Geomechanics and Engineering
• /
• 제32권5호
• /
• pp.475-482
• /
• 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
• /
• 제77권4호
• /
• pp.473-479
• /
• 2021

The propagation of plane waves in a linear, homogeneous and isotropic nonlocal generalized thermoelastic solid medium is considered in the framework of Lord and Shulman generalization. The governing field equations are formulated and specialized in a plane. Plane wave solutions of governing equations show that there exists three plane waves, namely, P, thermal and SV waves which propagate with distinct speeds. Reflection of P and SV waves from thermally insulated or isothermal boundary of a half-space is considered. The relevant boundary conditions are applied at stress free boundary and a non-homogeneous system of three equations in reflection coefficients is obtained. For incidence of both P and SV waves, the expressions for energy ratios of reflected P, thermal and SV waves are also obtained. The speeds and energy ratios of reflected waves are computed for relevant physical constants of a thermoelastic material. The speeds of plane waves are plotted against nonlocal parameter and frequency. The energy ratios of reflected waves are also plotted against the angle of incidence of P wave at a thermally insulated stress-free surface. The effect of nonlocal parameter is shown graphically on the speeds and energy ratios of reflected waves.

• Earthquakes and Structures
• /
• 제9권3호
• /
• pp.577-601
• /
• 2015

The thermomagnetic effect on plane wave propagation at the liquid-solid interface with nonclassical thermoelasticity is investigated. It is assumed that liquid-solid half-space is under initial stress. Numerical computations are performed for the developed amplitude ratios of P, SV and thermal waves under Cattaneo-Lord-Shulman theory, Green-Lindsay theory and classical thermoelasticity. The system of developed equations is solved by the application of the MATLAB software at different angles of incidence for Green and Lindsay model. The effect of initial stress and magnetic field in the lower half-space are discussed and comparison is made in LS, GL and CT models of thermoelasticity. In the absence of magnetic field, the obtained results are in agreement with the same results obtained by the relevant authors. This study would be useful for magneto-thermoelastic acoustic device field.

• Steel and Composite Structures
• /
• 제25권2호
• /
• pp.177-186
• /
• 2017

In this work, the model of magneto-thermoelasticity based on memory-dependent derivative (MDD) is applied to a one-dimensional thermal shock problem for a functionally graded half-space whose surface is assumed to be traction free and subjected to an arbitrary thermal loading. The $Lam{\acute{e}}^{\prime}s$ modulii are taken as functions of the vertical distance from the surface of thermoelastic perfect conducting medium in the presence of a uniform magnetic field. Laplace transform and the perturbation techniques are used to derive the solution in the Laplace transform domain. A numerical method is employed for the inversion of the Laplace transforms. The effects of the time-delay on the temperature, stress and displacement distribution for different linear forms of Kernel functions are discussed. Numerical results are represented graphically and discussed.

• Interaction and multiscale mechanics
• /
• 제3권2호
• /
• pp.145-156
• /
• 2010

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.

• Structural Engineering and Mechanics
• /
• 제66권1호
• /
• pp.113-124
• /
• 2018

In the present paper, we have considered a layered medium of two semi-infinite nonlocal elastic solids with intermediate transversely isotropic magnetothermoelastic solid. The intermediate slab is of uniform thickness with the effects of two temperature, rotation and Hall current and with and without energy dissipation. A plane longitudinal or transverse wave propagating through one of the nonlocal elastic solid half spaces, is made incident upon transversely isotropic slab and it results into various reflected and refracted waves. The amplitude ratios of various reflected and refracted waves are obtained by using appropriate boundary conditions. The effect of nonlocal parameter on the variation of various amplitude ratios with angle of incidence are depicted graphically. Some cases of interest are also deduced.

• Geomechanics and Engineering
• /
• 제23권3호
• /
• pp.217-225
• /
• 2020

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.

• Structural Engineering and Mechanics
• /
• 제34권3호
• /
• pp.285-300
• /
• 2010

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.

• Steel and Composite Structures
• /
• 제22권2호
• /
• pp.369-386
• /
• 2016

In this work, the two-dimensional generalized magneto-thermoelastic problem of a fiber-reinforced anisotropic material is investigated under Green and Naghdi theory of type III. The solution will be obtained for a certain model when the half space subjected to ramp-type heating and traction free surface. Laplace and exponential Fourier transform techniques are used to obtain the analytical solutions in the transformed domain by the eigenvalue approach. The inverses of Fourier transforms are obtained analytically. The results have been verified numerically and are represented graphically. Comparisons are made with the results predicted by the presence and absence of reinforcement and magnetic field.

• Structural Engineering and Mechanics
• /
• 제57권2호
• /
• pp.201-220
• /
• 2016

A general model of equations of the two-temperature theory of generalized thermoelasticity is applied to study the wave propagation in a fiber-reinforced magneto-thermoelastic medium in the context of the three-phase-lag model and Green-Naghdi theory without energy dissipation. The material is a homogeneous isotropic elastic half-space. The exact expression of the displacement components, force stresses, thermodynamic temperature and conductive temperature is obtained by using normal mode analysis. The variations of the considered variables with the horizontal distance are illustrated graphically. Comparisons are made with the results of the two theories in the absence and presence of a magnetic field as well as a two-temperature parameter. A comparison is also made between the results of the two theories in the absence and presence of reinforcement.