• Advances in materials Research
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• v.8 no.2
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• pp.83-102
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• 2019

The present research deals with the time harmonic deformation in transversely isotropic magneto thermoelastic solid with two temperature (2T), rotation and without energy dissipation due to inclined load. Lord-Shulman theory has been formulated for this mathematical model. The entire thermo-elastic medium is rotating with a uniform angular velocity. The Fourier transform techniques have been used to find the solution to the problem. The displacement components, stress components and conductive temperature distribution with the horizontal distance are computed in the transformed domain and further calculated in the physical domain using numerical inversion techniques. The effect of time harmonic source and rotation is depicted graphically on the resulting quantities.

• Structural Engineering and Mechanics
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• v.70 no.2
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• pp.245-255
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• 2019

In present research, we have considered transversely isotropic magneto thermoelastic solid with two temperature and without energy dissipation due to inclined load. The mathematical model has been formulated using Lord-Shulman theory. The Laplace and Fourier transform techniques have been used to find the solution to the problem. The displacement components, stress components and conductive temperature distribution with the horizontal distance are computed in the transformed domain and further calculated in the physical domain using numerical inversion techniques. The effect of rotation and angle of inclination of inclined load is depicted graphically on the resulting quantities.

• Steel and Composite Structures
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• v.38 no.4
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• pp.355-363
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• 2021

The present paper attempts to investigate the propagation of plane waves in an isotropic elastic medium under the effect of initial stress and temperature-dependent properties. The modulus of elasticity is taken as a linear function of the reference temperature. The formulation is applied under the thermoelasticity theory with dual-phase-lag; the normal mode analysis is used to obtain the expressions for the displacement components, the temperature, the stress, and the strain components. Numerical results for the field quantities are given in the physical domain and illustrated graphically. Comparisons are made with the results predicted by different theories (Lord-Shulman theory, the classical coupled theory of thermoelasticity and the dual-phase-lag model) in the absence and presence of the initial stress as well as the case where the modulus of elasticity is independent of temperature.

• Geomechanics and Engineering
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• v.28 no.4
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• pp.347-358
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• 2022

The main concern of this article is to discuss the problem of a two-temperature fiber-reinforced micropolar thermoelastic medium with voids under the effect rotation, mechanical force in the context four different theories with memory-dependent derivative (MDD) and variable thermal conductivity. The three-phase-lag model (3PHL), dual-phase-lag model (DPL), Green-Naghdi theory (G-N II, G-N III), coupled theory, and the Lord-Shulman theory (L-S) are employed to solve the present problem. Analytical expressions of the physical quantities are obtained by using Laplace-Fourier transforms technique. Numerical results are shown graphically and the results obtained are analyzed. The most significant points are highlighted.

• Structural Engineering and Mechanics
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• v.82 no.4
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• pp.469-476
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• 2022

A mathematical model of Lord-Shulman photo-thermal theorem induced by pulse heat flux is presented to study the propagations waves for plasma, thermal and elastic in two-dimensional semiconductor materials. The medium is assumed initially quiescent. By using Laplace-Fourier transforms with the eigenvalue method, the variables are obtained analytically. A semiconductor medium such as silicon is investigated. The displacements, stresses, the carrier density and temperature distributions are calculated numerically and clarified graphically. The outcomes show that thermal relaxation time has varying degrees of effects on the studying fields.

• Structural Engineering and Mechanics
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• v.89 no.4
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• pp.375-381
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• 2024

In this paper, Eringen's nonlocal thermoelasticity is constructed to study wave propagation in a rotating two-temperature thermoelastic half-space. The problem is applied in the context of the dual-phase-lag (Dual) model, coupled theory (CD), and Lord-Shulman (L-S) theory. Using suitable non-dimensional fields, the harmonic wave analysis is used to solve the problem. Comparisons are carried with the numerical values predicted in the absence and presence of the gravity field, a nonlocal parameter as well as rotation. The present study is valuable for the analysis of nonlocal thermoelastic problems under the influence of the gravity field, mechanical force, and rotation.

• Coupled systems mechanics
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• v.13 no.3
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• pp.231-245
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• 2024

In the present work, a microelogated thermoelastic model based on Lord-Shulman (1967) and Green-Lindsay (1972) theories of thermoelasticity has been constructed. The governing equations for the simulated model are converted into two-dimensional case and made dimensionless for further simplification. Laplace and Hankel transforms followed by eigen value approach has been employed to solve the problem. The use of eigen value approach hasthe advantage of finding the solution of governing equationsin matrix form notations. This approach is straight forward and convenient for numerical computation and avoids the complicate nature of the problem. The components of displacement,stress and temperature distribution are obtained in the transformed domain. Numerical inversion techniques have been used to invert the resulting quantities in the physical domain. Graphical representation of the resulting quantities for describing the effect of microelongation are presented. A special case is also deduced from the present investigation. The problem find application in many engineering problems like thick-walled pressure vesselsuch as a nuclear containment vessel, a cylindricalroller etc.

• Structural Engineering and Mechanics
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• v.60 no.3
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• pp.529-545
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• 2016

In this article, the generalized coupled non-Fickian diffusion-thermoelasticity analysis is carried out using an analytical method. The transient behaviors of field variables, including mass concentration, temperature and displacement are studied in a strip, which is subjected to shock loading. The governing equations are derived using generalized coupled non-Fickian diffusion-thermoelasticity theory, which is based on Lord-Shulman theory of coupled thermoelasticity. The governing equations are transferred to the frequency domain using Laplace transform technique and then the field variables are obtained in analytical forms using the presented method. The field variables are eventually determined in time domain by employing the Talbot technique. The dynamic behaviors of mass concentration, temperature and displacement are studied in details. It is concluded that the presented analytical method has a high capability for simulating the wave propagation with finite speed in mass concentration field as well as for tracking thermoelastic waves. Furthermore, the obtained results are more realistic than that of others.

• Structural Engineering and Mechanics
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• v.78 no.1
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• pp.23-30
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• 2021

In this paper, we established the generalized thermoelasticity phenomenon in an isotropic elastic medium considering the electromagnetic field, rotation and two-temperature. Three theories of generalized thermoelasticity have been applied: Lord-Shulman (one relaxation time), Green-Lindsay (two relaxation times), as well as the coupled theory. We discussed some particular cases in the context of the wave propagation phenomenon in thermoelasticity. From solving the fundamental equations, we arrived that there are three waves: P-, T- and SV-waves that we calculated their velocities. The boundary conditions for mechanical stress and Maxwell's stress and thermal insulated or isothermal have been applied to determine the amplitudes ratios (reflection coefficients) for P-, T - and SV waves. Some utilitarian aspects are obtained from the reflection coefficients, presented graphically, and the new conclusions have been presented. Comparisons are made for the results predicted by different theories (CT, LS, GL) in the absence and presence of the electro-magnetic field, rotation, as well as two-temperature on the reflection of generalized thermoelastic waves. The results obtained concluded that the external parameters as the angle of incidence, electromagnetic field, rotation as well as the theories parameters have strong effect on the phenomenon.

• Structural Engineering and Mechanics
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• v.72 no.4
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• pp.455-468
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• 2019

The present article is aimed at studying the reflection phenomena of plane waves in a homogeneous, orthotropic, initially stressed magneto-thermoelastic rotating medium with diffusion. The enuciation is applied to generalized thermoelasticity based on Lord-Shulman theory. There exist four coupled waves, namely, quasi-longitudinal P-wave (qP), quasi-longitudinal thermal wave (qT), quasi-longitudinal mass diffusive wave (qMD) and quasi-transverse wave (qSV) in the medium. The amplitude and energy ratios for these reflected waves are derived and the numerical computations have been carried out with the help of MATLAB programming. The effects of rotation, initial stress, magnetic and diffusion parameters on the amplitude ratios are depicted graphically. The expressions of energy ratios have also been obtained in explicit form and are shown graphically as functions of angle of incidence. It has been verified that during reflection phenomena, the sum of energy ratios is equal to unity at each angle of incidence. Effect of anisotropy is also depicted on velocities of various reflected waves.