• Structural Engineering and Mechanics
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• v.63 no.1
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• pp.89-102
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• 2017

In this work, we present a theoretical framework to study the thermovisco-elastic responses of homogeneous, isotropic and perfectly conducting medium subjected to inclined load. Based on recently developed generalized thermoelasticity theory with fractional order strain, the two-dimensional governing equations are obtained in the context of generalized magnetothermo-viscoelasticity theory without energy dissipation. The Kelvin-Voigt model of linear viscoelasticity is employed to describe the viscoelastic nature of the material. The resulting formulation of the field equations is solved analytically in the Laplace and Fourier transform domain. On the application of inclined load at the surface of half-space, the analytical expressions for the normal displacement, strain, temperature, normal stress and tangential stress are derived in the joint-transformed domain. To restore the fields in physical domain, an appropriate numerical algorithm is used for the inversion of the Laplace and Fourier transforms. Finally, we have demonstrated the effect of magnetic field, viscosity, mechanical relaxation time, fractional order parameter and time on the physical fields in graphical form for copper material. Some special cases have also been deduced from the present investigation.

• Structural Engineering and Mechanics
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• v.90 no.2
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• pp.209-218
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• 2024

The present paper is focused on the study of the propagation of plane waves in thermoelastic media under a modified Green-Lindsay (MG-L) model having the influence of non-local and two temperature. The problem is formulated for the considered model in dimensionless form and is explained by using the reflection phenomenon. The plane wave solution of these equations indicates the existence of three waves namely Longitudinal waves (LD-Wave), Thermal waves (T-wave), and Shear waves (SV-wave) from a stress-free surface. The variation of amplitude ratios is computed analytically and depicted graphically against the angle of incidence to elaborate the impact of non-local, two temperature, and different theories of thermoelasticity. Some particular cases of interest are also deduced from the present investigation. The present study finds applications in a wide range of problems in engineering and sciences, control theory, vibration mechanics, and continuum mechanics.

• 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.20 no.5
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• pp.1103-1117
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• 2016

The present investigation is to study the plane problem in initially stressed thermoelastic half-space with voids due to thermal source. Lord-Shulman (Lord and Shulman 1967) theory of thermoelasticity with one relaxation time has been used to investigate the problem. A particular type of thermal source has been taken as an application of the approach. Finite element technique has been used to solve the problem. The components of displacement, stress, temperature change and volume fraction field are computed numerically. The resulting quantities are depicted graphically for different values of initial stress parameter. The relaxation time and the initial stress parameter have a significant effect on all distributions.

• Steel and Composite Structures
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• v.35 no.3
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• pp.343-351
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• 2020

The present research deals with the multi-dual-phase-lags thermoelasticity theory for thermoelastic behavior of transversely isotropic thermoelastic thin circular plate The Laplace and Hankel transform techniques have been used to find the solution of the problem. The displacement components, stress components, and conductive temperature distribution are computed in the transformed domain with the radial distance and further determined in the physical domain using numerical inversion techniques. The effect of rotation and two temperature are depicted graphically on the resulting quantities.

• Computers and Concrete
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• v.25 no.5
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• pp.471-478
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• 2020

In this work, the analytical solution for the stresses in piezo-thermo-elastic homogeneous, transversely isotropic material under the effect of the rotation has investigated. The thermoelasticity theory has used to study the problem. The material subjected to boundary conditions. Finally, the numerical solution has carried out piezo - thermo-elastic material under the effect of rotation, to illustrate the analytical development. The corresponding simulated results of various physical quantities such as the displacements and the stresses, the temperature and the electrical displacement have presented graphically.

• Steel and Composite Structures
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• v.27 no.4
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• pp.439-451
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• 2018

In the present investigation, a plane P (longitudinal) wave is made incident upon a transversely isotropic magnetothermoelastic solid slab of uniform thickness, interposed between two different semi-infinite viscoelastic solids. The transversely isotropic magnetothermoelastic sandwiched layer is homogeneous with combined effects of two temperature, rotation and Hall current in the context of GN Type-II and Type-III (1993) theory of thermoelasticity. The amplitude ratios of various reflected and refracted waves are obtained by using appropriate boundary conditions. The effect of energy dissipation on various amplitude ratios of longitudinal wave with angle of incidence are depicted graphically. Some cases of interest are also deduced from the present investigation.

• Geomechanics and Engineering
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• v.21 no.1
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• pp.1-9
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• 2020

In this article, an analytical solution for the effect of the rotation on thermo-viscoelastic non-homogeneous medium with a spherical cavity subjected to periodic loading is studied. The distribution of displacements, temperature, redial stress, and hoop stress in non-homogeneous medium, in the context of generalized thermo-viscoelasticity using the GL theory, is discussed and obtained. The results are displayed graphically to illustrate the effect of the rotation. Comparisons with the previous work in the absence of rotation and viscosity are made.

• 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.

• Steel and Composite Structures
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• v.42 no.6
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• pp.723-732
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• 2022

The present research is concerned to study the effect of fractional parameter and rotation on the propagation of Rayleigh waves in an orthotropic magneto-thermoelastic media with three-phase-lags in the context of fractional order theory of generalized thermoelasticity with combined effect of rotation and hall current. The secular equations of Rayleigh waves are derived by using the appropriate boundary conditions. The wave properties such as phase velocity, attenuation coefficient are computed numerically and the numerical simulated results are presented through graphs to show the effect on all the components. Some special cases are also discussed in the present investigation.