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Article
Publication date: 2 October 2018

Gaurav Mittal and Vinayak Kulkarni

The purpose of this paper is to frame a dual-phase-lag model using the fractional theory of thermoelasticity with relaxation time. The generalized Fourier law of heat…

Abstract

Purpose

The purpose of this paper is to frame a dual-phase-lag model using the fractional theory of thermoelasticity with relaxation time. The generalized Fourier law of heat conduction based upon Tzou model that includes temperature gradient, the thermal displacement and two different translations of heat flux vector and temperature gradient has been used to formulate the heat conduction model. The microstructural interactions and corresponding thermal changes have been studied due to the involvement of relaxation time and delay time translations. This results in achieving the finite speed of thermal wave. Classical coupled and generalized thermoelasticity theories are recovered by considering the various special cases for different order of fractional derivatives and two different translations under consideration.

Design/methodology/approach

The work presented in this manuscript proposes a dual-phase-lag mathematical model of a thick circular plate in a finite cylindrical domain subjected to axis-symmetric heat flux. The model has been designed in the context of fractional thermoelasticity by considering two successive terms in Taylor’s series expansion of fractional Fourier law of heat conduction in the two different translations of heat flux vector and temperature gradient. The analytical results have been obtained in Laplace transform domain by transforming the original problem into eigenvalue problem using Hankel and Laplace transforms. The numerical inversions of Laplace transforms have been achieved using the Gaver−Stehfast algorithm, and convergence criterion has been discussed. For illustrative purpose, the dual-phase-lag model proposed in this manuscript has been applied to a periodically varying heat source. The numerical results have been depicted graphically and compared with classical, fractional and generalized thermoelasticity for various fractional orders under consideration.

Findings

The microstructural interactions and corresponding thermal changes have been studied due to the involvement of relaxation time and delay time translations. This results in achieving the finite speed of thermal wave. Classical coupled and generalized thermoelasticity theories are recovered by considering the various special cases for different order of fractional derivatives and two different translations under consideration. This model has been applied to study the thermal effects in a thick circular plate subjected to a periodically varying heat source.

Practical implications

A dual-phase-lag model can effectively be incorporated to study the transient heat conduction problems for an exponentially decaying pulse boundary heat flux and/or for a short-pulse boundary heat flux in long solid tubes and cylinders. This model is also applicable to study the various effects of the thermal lag ratio and the shift time. These dual-phase-lag models are also practically applicable in the problems of modeling of nanoscale heat transport problems of semiconductor devices and accordingly semiconductors can be classified as per their ability of heat conduction.

Originality/value

To the authors’ knowledge, no one has discussed fractional thermoelastic dual-phase-lag problem associated with relaxation time in a finite cylindrical domain for a thick circular plate subjected to an axis-symmetric heat source. This is the latest and novel contribution to the field of thermal mechanics.

Details

Multidiscipline Modeling in Materials and Structures, vol. 14 no. 5
Type: Research Article
ISSN: 1573-6105

Keywords

Article
Publication date: 2 May 2020

Leena Rani and Sushant Shekhar

The two-dimensional deformation of a homogeneous, thermally conducting, monoclinic material has been studied by using Laplace and Fourier transforms technique. A linear…

Abstract

Purpose

The two-dimensional deformation of a homogeneous, thermally conducting, monoclinic material has been studied by using Laplace and Fourier transforms technique. A linear temperature ramping function is used to more realistically model: thermal loading of the half-space surface. The general solution obtained is applied to a specific problem of a half-space subjected to ramp-type heating and loading. The displacements, stresses and temperature distribution so obtained in the physical domain are computed numerically and illustrated graphically. The comparison for Lord-Shulman (L-S), Green and Lindsay (G–L), Green and Naghdi (G–N) and Chandrasekharaiah and Tzou (CTU) theories have been shown graphically to estimate the effect of ramping parameter of heating for an insulated and temperature gradient boundaries.

Design/methodology/approach

The design of the study is eigenvalue approach

Findings

Homogeneous, thermally conducting monoclinic material has been taken under consideration to study the effect of linear temperature ramping parameter on temperature and normal displacement field. It is observed that magnitude of field quantities is large near the point of application of source for the non-dimensional values of time in all the four models. The numerical values for the field quantities are computed graphically for a wide range of values of finite pulse rise-time in the two situations t0 < t, t0 > t for generalized thermoelasticity theories.

Originality/value

(1) Governing equations for homogeneous, t0 thermally conducting, monoclinic material are described and solved. (2) Eigen value approach is used to solve the problem. (3) The effect of ramping parameter of heating has been studied for various models of the thermoelasticity to show the comparision between them.

Details

Multidiscipline Modeling in Materials and Structures, vol. 16 no. 6
Type: Research Article
ISSN: 1573-6105

Keywords

Article
Publication date: 15 November 2011

Rajneesh Kumar and Rajeev Kumar

The purpose of this paper is to study the wave propagation in transversely isotropic generalized thermoelastic half‐space with voids under initial stress.

Abstract

Purpose

The purpose of this paper is to study the wave propagation in transversely isotropic generalized thermoelastic half‐space with voids under initial stress.

Design/methodology/approach

The authors analyze the wave propagation and reflection of plane waves incident at the stress free, thermally insulated or isothermal surface of a homogeneous, transversely isotropic generalized thermoelastic half‐space with voids. The graphical representation is given for amplitude ratios of various reflected waves to that of incident waves for different direction of propagation. The phase velocities and attenuation coefficients of plane waves are also computed and presented graphically for various incident angles.

Findings

The phase velocities and attenuation coefficients of these plane waves are computed along various direction of wave propagation and the reflection characteristics of these waves, stress free, thermally insulated or isothermal boundary conditions are considered. The amplitude ratios of various reflected waves to that of incident waves have been obtained numerically.

Originality/value

Wave propagation in an elastic medium is of great practical importance. Since valuable organic and inorganic deposits beneath the earth surface are difficult to detect by drilling randomly, wave propagation is the simplest and most economic technique and does not require any drilling through the earth. Almost all the oil companies rely on seismic interpretation for selecting the sites for exploratory oil wells because seismic wave methods have higher accuracy, higher resolution and are more economical, compared to drilling, which is expensive and time consuming. The study described in this paper would be very useful for those involved in signal processing, sound system and wireless communication.

Details

Multidiscipline Modeling in Materials and Structures, vol. 7 no. 4
Type: Research Article
ISSN: 1573-6105

Keywords

Article
Publication date: 28 September 2012

Kunal Sharma

The present investigation aims to examine the reflection of plane waves from a free surface of a thermodiffusive elastic half space with void.

Abstract

Purpose

The present investigation aims to examine the reflection of plane waves from a free surface of a thermodiffusive elastic half space with void.

Design/methodology/approach

Generalized theory of thermoelasticity developed by Lord‐Shulma was used to investigate the problem. The amplitude ratios of various reflected waves are obtained in a closed form. The dependence of these amplitude ratios with an angle of propagation as well as other material parameter are shown graphically.

Findings

Effects of void and diffusion are observed on these amplitude ratios and have been found to be significant.

Originality/value

It is found that there exist four longitudinal waves (namely P‐wave, thermal wave (T‐wave), mass diffusion wave (MD‐wave), volume fraction wave (VF‐wave, carrying a change in void volume fraction) and a transverse SV wave). Some special cases of interest are also deduced from the present investigation.

Details

Multidiscipline Modeling in Materials and Structures, vol. 8 no. 3
Type: Research Article
ISSN: 1573-6105

Keywords

Article
Publication date: 23 November 2018

Tarun Kansal

The purpose of this paper to construct the fundamental solution of partial differential equations in the generalized theory of thermoelastic diffusion materials with…

Abstract

Purpose

The purpose of this paper to construct the fundamental solution of partial differential equations in the generalized theory of thermoelastic diffusion materials with double porosity.

Design/methodology/approach

The paper deals with the study of pseudo oscillations in the generalized theory of thermoelastic diffusion materials with double porosity.

Findings

The paper finds the fundamental solution of partial differential equations in terms of elementary functions.

Originality/value

Assuming the displacement vector, volume fraction fields, temperature change and chemical potential functions in terms of oscillation frequency in the governing equations, pseudo oscillations have been studied and finally the fundamental solution of partial differential equations in case of pseudo oscillations in terms of elementary functions has been constructed.

Details

Multidiscipline Modeling in Materials and Structures, vol. 15 no. 2
Type: Research Article
ISSN: 1573-6105

Keywords

Article
Publication date: 9 August 2013

Rajneesh Kumar and Rajeev Kumar

The purpose of this research is to study the reflection and transmission of elastic waves at the interface of an elastic half‐space and initially stressed thermoelastic…

Abstract

Purpose

The purpose of this research is to study the reflection and transmission of elastic waves at the interface of an elastic half‐space and initially stressed thermoelastic diffusion with voids half‐space.

Design/methodology/approach

Two‐dimensional model has been considered of an isotropic elastic half‐space (Medium I) lying over a homogeneous isotropic generalized initially stressed thermoelastic diffusion with voids half‐space (Medium II). There exist two waves, P‐wave and SV‐wave, in isotropic elastic half‐space and four quasi‐longitudinal waves, namely, quasi‐longitudinal wave (QP‐mode), quasi‐longitudinal mass diffusive wave (QMD‐mode), quasi‐longitudinal thermal wave (QPT‐mode) and quasi‐longitudinal volume fractional wave (QPV‐mode), and one quasi‐transverse wave (QSV‐mode) exists in initially stressed thermoelastic diffusion with voids half‐space.

Findings

The energy ratios of these waves are computed along various directions of incident wave, and it is found that the sum of all energy ratios is exactly unity at each value of incident angle. The amplitude ratios of various waves have been obtained numerically.

Originality/value

Reflection and transmission of an elastic medium is of great practical importance. Since valuable organic and inorganic deposits beneath the earth surface are difficult to detect by drilling randomly, wave propagation is the simplest and most economic technique for these and does not require any drilling through the earth. Almost all the oil companies rely on seismic interpretation for selecting the sites for exploratory oil wells because seismic wave methods have higher accuracy, have higher resolution and are more economical, as compared to drilling which is expansive and time consuming.

Details

Multidiscipline Modeling in Materials and Structures, vol. 9 no. 2
Type: Research Article
ISSN: 1573-6105

Keywords

Article
Publication date: 28 September 2012

Rajneesh Kumar and Rajeev Kumar

The purpose of this research is to study the reflection and refraction of elastic waves at the interface of an elastic half‐space and initially stressed thermoelastic with…

Abstract

Purpose

The purpose of this research is to study the reflection and refraction of elastic waves at the interface of an elastic half‐space and initially stressed thermoelastic with voids half‐space.

Design/methodology/approach

A two‐dimensional model was considered of an isotropic elastic half‐space (medium I) lying over a homogeneous isotropic generalized initially stressed thermoelastic with voids half‐space(medium II). There exist two waves, P‐wave and SV‐wave in isotropic elastic half‐space and three quasi‐longitudinal waves namely, quasi‐longitudinal wave (QP‐mode), quasi‐longitudinal thermal wave (QPT‐mode), quasi‐longitudinal volume fractional wave (QPV‐mode) and one quasi‐transverse wave (QSV‐mode) exists in initially stressed thermoelastic with voids half‐space.

Findings

The energy ratios of these waves are computed along various directions of incident wave, and it is found that the sum of all energy ratios is exactly unity at each value of incident angle. The amplitude ratios of various waves were obtained numerically.

Originality/value

Reflection and refraction of an elastic medium is of great practical importance. Since valuable organic and inorganic deposits beneath the earth surface are difficult to detect by drilling randomly, wave propagation is the simplest and most economic technique to these and does not require any drilling through the earth. Almost all the oil companies rely on seismic interpretation for selecting the sites for exploratory oil wells because seismic wave methods have higher accuracy, higher resolution and more economical, as compared to drilling which is expansive and time consuming.

Details

Multidiscipline Modeling in Materials and Structures, vol. 8 no. 3
Type: Research Article
ISSN: 1573-6105

Keywords

Article
Publication date: 8 August 2016

Mohamed Ibrahim A Othman and Mohamed I. M. Hilal

The purpose of this paper is to investigate the influence of the gravity and the magnetic fields on the plane waves in a homogenous, linear and isotropic thermoelastic…

81

Abstract

Purpose

The purpose of this paper is to investigate the influence of the gravity and the magnetic fields on the plane waves in a homogenous, linear and isotropic thermoelastic medium subjected to the laser pulse heating.

Design/methodology/approach

The problem has been solved analytically and numerically by using the normal mode analysis.

Findings

Numerical results for the temperature, the displacement components, the stress components and the volume fraction were presented graphically and analyzed the results. The graphical results indicate that the effect of gravity and magnetic fields are observable physical effects on the porous thermoelastic material heated by a laser pulse. Comparisons are made with the results in the absence and presence of the gravity and the magnetic fields, also at various times.

Originality/value

In the present work, the authors shall formulate a 2-D problem for the propagation of plane waves on the porous thermoelastic material influenced by the gravity and the magnetic fields subjected to a laser pulse heating act as a thermal shock. A comparison is also made between the two types II and III of Green-Naghdi theory in the absence and the presence of the gravity and the magnetic fields. Such problems are very important in many dynamical systems.

Details

Multidiscipline Modeling in Materials and Structures, vol. 12 no. 2
Type: Research Article
ISSN: 1573-6105

Keywords

Article
Publication date: 4 November 2014

Rajneesh Kumar and Vandana Gupta

The purpose of this paper is to depict the effect of thermal and diffusion phase-lags on plane waves propagating in thermoelastic diffusion medium with different material…

Abstract

Purpose

The purpose of this paper is to depict the effect of thermal and diffusion phase-lags on plane waves propagating in thermoelastic diffusion medium with different material symmetry. A generalized form of mass diffusion equation is introduced instead of classical Fick's diffusion theory by using two diffusion phase-lags, one phase-lag of diffusing mass flux vector, represents the delayed time required for the diffusion of the mass flux and the other phase-lag of chemical potential, represents the delayed time required for the establishment of the potential gradient. The basic equations for the anisotropic thermoelastic diffusion medium in the context of dual-phase-lag heat transfer (DPLT) and dual-phase-lag diffusion (DPLD) models are presented. The governing equations for transversely isotropic and isotropic case are also reduced. The different characteristics of waves like phase velocity, attenuation coefficient, specific loss and penetration depth are computed numerically. Numerically computed results are depicted graphically for anisotropic, transversely isotropic and isotropic medium. The effect of diffusion and thermal phase-lags are shown on the different characteristic of waves. Some particular cases of result are also deduced from the present investigation.

Design/methodology/approach

The governing equations of thermoelastic diffusion are presented using DPLT model and a new model of DPLD. Effect of phase-lags of thermal and diffusion is presented on different characteristic of waves.

Findings

The effect of diffusion and thermal phase-lags on the different characteristic of waves is appreciable. Also the use of diffusion phase-lags in the equation of mass diffusion gives a more realistic model of thermoelastic diffusion media as it allows a delayed response between the relative mass flux vector and the potential gradient.

Originality/value

Introduction of a new model of DPLD in the equation of mass diffusion.

Details

Multidiscipline Modeling in Materials and Structures, vol. 10 no. 4
Type: Research Article
ISSN: 1573-6105

Keywords

Article
Publication date: 18 May 2021

Shishir Gupta, Rishi Dwivedi, Smita and Rachaita Dutta

The purpose of study to this article is to analyze the Rayleigh wave propagation in an isotropic dry sandy thermoelastic half-space. Various wave characteristics, i.e wave…

Abstract

Purpose

The purpose of study to this article is to analyze the Rayleigh wave propagation in an isotropic dry sandy thermoelastic half-space. Various wave characteristics, i.e wave velocity, penetration depth and temperature have been derived and represented graphically. The generalized secular equation and classical dispersion equation of Rayleigh wave is obtained in a compact form.

Design/methodology/approach

The present article deals with the propagation of Rayleigh surface wave in a homogeneous, dry sandy thermoelastic half-space. The dispersion equation for the proposed model is derived in closed form and computed analytically. The velocity of Rayleigh surface wave is discussed through graphs. Phase velocity and penetration depth of generated quasi P, quasi SH wave, and thermal mode wave is computed mathematically and analyzed graphically. To illustrate the analytical developments, some particular cases are deliberated, which agrees with the classical equation of Rayleigh waves.

Findings

The dispersion equation of Rayleigh waves in the presence of thermal conductivity for a dry sandy thermoelastic medium has been derived. The dry sandiness parameter plays an effective role in thermoelastic media, especially with respect to the reference temperature for η = 0.6,0.8,1. The significant difference in η changes a lot in thermal parameters that are obvious from graphs. The penetration depth and phase velocity for generated quasi-wave is deduced due to the propagation of Rayleigh wave. The generalized secular equation and classical dispersion equation of Rayleigh wave is obtained in a compact form.

Originality/value

Rayleigh surface wave propagation in dry sandy thermoelastic medium has not been attempted so far. In the present investigation, the propagation of Rayleigh waves in dry sandy thermoelastic half-space has been considered. This study will find its applications in the design of surface acoustic wave devices, earthquake engineering structural mechanics and damages in the characterization of materials.

Details

Engineering Computations, vol. 38 no. 8
Type: Research Article
ISSN: 0264-4401

Keywords

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