• Steel and Composite Structures
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• v.32 no.6
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• pp.779-793
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• 2019

The purpose of this research paper is to depict the thermomechanical interactions in transversely isotropic magneto thermoelastic solid with two temperatures and without energy dissipation in generalized LS theories of thermoelasticity. The Laplace and Fourier transform techniques have been used to find the solution of 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 numerically. The effect of two temperature and relaxation time are depicted graphically on the resulting quantities.

• Structural Engineering and Mechanics
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• v.56 no.4
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• pp.649-665
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• 2015

The present paper attempts to investigate the propagation of plane waves in generalized piezo-thermoelastic medium under the effect of rotation. The normal mode analysis is used to obtain the expressions for the displacement components, the temperature, the stress and the strain components. Comparisons are made with the results predicted by different theories (Coupled theory, Lord-Schulman, Green-Lindsay) in the absence and presence of rotation.

• Structural Engineering and Mechanics
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• v.81 no.1
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• pp.29-37
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• 2022

The present paper deals with the application of one dimensional piezoelectric materials in particular piezo-thermoelastic nanobeam. The generalized piezo-thermo-elastic theory with two temperature and Euler Bernoulli theory with small scale effects using nonlocal Eringen's theory have been used to form the mathematical model. The ends of nanobeam are considered to be simply supported and at a constant temperature. The mathematical model so formed is solved to obtain the non-dimensional expressions for lateral deflection, electric potential, thermal moment, thermoelastic damping and frequency shift. Effect of frequency and nonlocal parameter on the lateral deflection, electric potential, thermal moment with generalized piezothermoelastic theory are represented graphically using the MATLAB software. Comparisons are made with the different theories of thermoelasticity.

• 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.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.

• Steel and Composite Structures
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• v.24 no.3
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• pp.297-307
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• 2017

A unified mathematical model of phase-lag Green-Naghdi magneto-thermoelasticty theories based on fractional derivative heat transfer for perfectly conducting media in the presence of a constant magnetic field is given. The GN theories as well as the theories of coupled and of generalized magneto-thermoelasticity with thermal relaxation follow as limit cases. The resulting nondimensional coupled equations together with the Laplace transforms techniques are applied to a half space, which is assumed to be traction free and subjected to a thermal shock that is a function of time. The inverse transforms are obtained by using a numerical method based on Fourier expansion techniques. The predictions of the theory are discussed and compared with those for the generalized theory of magneto-thermoelasticity with one relaxation time. The effects of Alfven velocity and the fractional order parameter on copper-like material are discussed in different types of GN theories.

• Structural Engineering and Mechanics
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• v.34 no.3
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• pp.285-300
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• 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.

• Structural Engineering and Mechanics
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• v.87 no.5
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• pp.475-485
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• 2023

The present study deals with wave propagation in a modified couple-stress generalized thermoelastic solid under the effect of gravity and magnetic field. The problem is solved by a refined microtemperatures multi-phase-lags thermoelastic theory. The Fourier series and Laplace transforms will be used to obtain the general solution for any set of boundary conditions. Some comparisons have been shown in figures to estimate the effects of the gravity field, the magnetic field, and different theories of thermoelasticity in the presence of the hall current effect on all the physical quantities. Some particular cases of special interest have been deduced from the present investigation.

• Structural Engineering and Mechanics
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• v.57 no.2
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• pp.201-220
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• 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.

• Smart Structures and Systems
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• v.18 no.4
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• pp.707-731
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• 2016

A unified mathematical model of the equations of generalized magneto-thermoelasticty based on fractional derivative heat transfer for isotropic perfect conducting media is given. Some essential theorems on the linear coupled and generalized theories of thermoelasticity e.g., the Lord- Shulman (LS) theory, Green-Lindsay (GL) theory and the coupled theory (CTE) as well as dual-phase-lag (DPL) heat conduction law are established. Laplace transform techniques are used. The method of the matrix exponential which constitutes the basis of the state-space approach of modern theory is applied to the non-dimensional equations. The resulting formulation is applied to a variety of one-dimensional problems. The solutions to a thermal shock problem and to a problem of a layer media are obtained in the present of a transverse uniform magnetic field. According to the numerical results and its graphs, conclusion about the new model has been constructed. The effects of the fractional derivative parameter on thermoelastic fields for different theories are discussed.