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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

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Article
Publication date: 15 September 2017

Vijay Chawla, Sanjeev Ahuja and Varsha Rani

The purpose of this paper is to study the fundamental solution in transversely isotropic micropolar thermoelastic media. With this objective, the two-dimensional general…

Abstract

Purpose

The purpose of this paper is to study the fundamental solution in transversely isotropic micropolar thermoelastic media. With this objective, the two-dimensional general solution in transversely isotropic thermoelastic media is derived.

Design/methodology/approach

On the basis of the general solution, the fundamental solution for a steady point heat source on the surface of a semi-infinite transversely isotropic micropolar thermoelastic material is constructed by six newly introduced harmonic functions.

Findings

The components of displacement, stress, temperature distribution and couple stress are expressed in terms of elementary functions. From the present investigation, a special case of interest is also deduced and compared with the previous results obtained.

Practical implications

Fundamental solutions can be used to construct many analytical solutions of practical problems when boundary conditions are imposed. They are essential in the boundary element method as well as the study of cracks, defects and inclusions.

Originality/value

Fundamental solutions for a steady point heat source acting on the surface of a micropolar thermoelastic material is obtained by seven newly introduced harmonic functions. From the present investigation, some special cases of interest are also deduced.

Details

Multidiscipline Modeling in Materials and Structures, vol. 13 no. 3
Type: Research Article
ISSN: 1573-6105

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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. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 6 April 2020

Sunita Deswal, Devender Sheoran and Kapil Kumar Kalkal

The purpose of this paper is to establish a model of two-dimensional half-space problem of linear, isotropic, homogeneous, initially stressed, rotating thermoelastic

Abstract

Purpose

The purpose of this paper is to establish a model of two-dimensional half-space problem of linear, isotropic, homogeneous, initially stressed, rotating thermoelastic medium with microtemperatures. The expressions for different physical variables such as displacement distribution, stress distribution, temperature field and microtemperatures are obtained in the physical domain.

Design/methodology/approach

Normal mode analysis technique is adopted to procure the exact solution of the problem.

Findings

Numerical computations have been carried out with the help of MATLAB programming, and the results are illustrated graphically. Comparisons are made to show the effects of rotation, time and microtemperatures on the resulting quantities. The graphical results indicate that the effects of rotation, microtemperatures and time are very pronounced on the field variables.

Originality/value

In the present work, we have investigated the effects of rotation, time and microtemperature in an initially stressed thermoelastic medium. Although various investigations do exist to observe the disturbances in a thermoelastic medium under the effects of different parameters, the work in its present form, i.e. the disturbances in a thermoelastic medium in the presence of angular velocity, initial stress and microtemperature have not been studied till now. The present work is useful and valuable for analysis of problems involving coupled thermal shock, rotation parameter, microtemperatures and elastic deformation.

Details

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

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Article
Publication date: 9 November 2015

Rajneesh Kumar and Vandana Gupta

– The purpose of this paper is to study the propagation of Rayleigh waves in thermoelastic medium with mass diffusion.

Abstract

Purpose

The purpose of this paper is to study the propagation of Rayleigh waves in thermoelastic medium with mass diffusion.

Design/methodology/approach

The field equations for the linear theory of homogeneous isotropic thermoelastic diffusion medium are taken into consideration by using dual-phase-lag heat transfer (DPLT) and dual-phase-lag diffusion (DPLD) models. Using the potential functions and harmonic wave solution, three coupled dilatational waves and a shear wave is obtained. After developing mathematical formulation, the dispersion equation is obtained, which results to be complex and irrational. This equation is converted into a polynomial form of higher degree.

Findings

From the polynomial equation, Rayleigh wave root is found. The secular equation is resolved into a polynomial form to find the roots and therefore to find the existence and propagation of Rayleigh wave. The existence of Rayleigh wave in the assumed model depends on the values of various parameters involved in the secular equation. These roots are resolved for phase velocity and attenuation of the inhomogeneous propagation of Rayleigh wave. Behavior of particle motion of these waves inside and at the surface of the thermoelastic medium with mass diffusion is studied. Particular cases of the interest are also deduced from the present investigation.

Originality/value

Governing equations corresponding to DPLT and DPLD models of thermoelastic diffusion are formulated to study the wave propagation and their dependence on various material parameters. In this paper effects of thermal and diffusion phase lags on the phase velocity, attenuation and on particle paths are observed and depicted graphically.

Details

Multidiscipline Modeling in Materials and Structures, vol. 11 no. 4
Type: Research Article
ISSN: 1573-6105

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Article
Publication date: 11 January 2018

Mohamed I.A. Othman, S.M. Abo-Dahab and Haneen A. Alosaimi

The purpose of this paper is to study a model of the equations of a two-dimensional problem in a half space, whose surface in a free micropolar thermoelastic medium…

Abstract

Purpose

The purpose of this paper is to study a model of the equations of a two-dimensional problem in a half space, whose surface in a free micropolar thermoelastic medium possesses cubic symmetry as a result of inclined load. The problem is formulated in the context of Green-Naghdi theory of type II (G-N II) (without energy dissipation) and of type III (G-N III) (with energy dissipation) under the effect of magnetic field.

Design/methodology/approach

The normal mode analysis is used to obtain the exact expressions of the physical quantities.

Findings

The numerical results are given and presented graphically when the inclined load and magnetic field are applied. Comparisons are made with the results predicted by G-N theory of both types II and III in the presence and absence of the magnetic field and for different values of the angle of inclination.

Originality/value

In the present work, the authors study the influence of inclined load and magnetic field in a micropolar thermoelastic medium in the context of the G-N theory of both types II and III. Numerical results for the field quantities are obtained and represented graphically.

Details

Multidiscipline Modeling in Materials and Structures, vol. 14 no. 2
Type: Research Article
ISSN: 1573-6105

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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

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Article
Publication date: 9 December 2020

Rajesh Kumar, Seema Thakran, Ankush Gunghas and Kapil Kumar Kalkal

The purpose of this study is to analyze the two-dimensional disturbances in a nonlocal, functionally graded, isotropic thermoelastic medium under the purview of the…

Abstract

Purpose

The purpose of this study is to analyze the two-dimensional disturbances in a nonlocal, functionally graded, isotropic thermoelastic medium under the purview of the Green–Lindsay model of generalized thermoelasticity. The formulation is subjected to a mechanical load. All the thermomechanical properties of the solid are assumed to vary exponentially with the position.

Design/methodology/approach

Normal mode technique is proposed to obtain the exact expressions for the displacement components, stresses and temperature field.

Findings

Numerical computations have been carried out with the help of MATLAB software and the results are illustrated graphically. These are also calculated numerically for a magnesium crystal-like material and illustrated through graphs. Theoretical and numerical results demonstrate that the nonlocality and nonhomogeneity parameters have significant effects on the considered physical fields.

Originality/value

Influences of nonlocality and nonhomogeneity on the physical quantities are carefully analyzed for isothermal and insulated boundaries. The present work is useful and valuable for analysis of problems involving mechanical shock, nonlocal parameter, functionally graded materials and elastic deformation.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 19 November 2020

Sunita Deswal, Ravinder Poonia and Kapil Kumar Kalkal

The present investigation is concerned with the two-dimensional deformations in an inhomogeneous fiber-reinforced thermoelastic medium under the influence of gravity in…

Abstract

Purpose

The present investigation is concerned with the two-dimensional deformations in an inhomogeneous fiber-reinforced thermoelastic medium under the influence of gravity in the context of Green–Lindsay theory.

Design/methodology/approach

Material properties are supposed to be graded in x-direction, and normal mode technique is adopted to obtain the exact expressions for the temperature field, displacement components and stresses.

Findings

Numerical computations have been carried out with the help of MATLAB software, and the results are depicted graphically to observe the disturbances induced in the considered medium. Comparisons made within the theory of the physical quantities are shown in figures to highlight the effects of fiber reinforcement, inhomogeneity parameter, gravity and time.

Originality/value

In the present work, we have investigated the effects of fiber reinforcement, inhomogeneity parameter, gravity and time in an inhomogeneous, fiber-reinforced thermoelastic medium under the influence of gravity. Although various investigations do exist to observe the disturbances in a thermoelastic medium under the effects of different parameters, the work in its present form i.e. thermally induced vibrations in an inhomogeneous fiber-reinforced thermoelastic material with gravity has not been studied till now. The present work is useful and valuable for analysis of problems involving thermal shock, gravity parameter, fiber reinforcement, inhomogeneous and elastic deformation.

Details

Multidiscipline Modeling in Materials and Structures, vol. 17 no. 2
Type: Research Article
ISSN: 1573-6105

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Article
Publication date: 11 September 2019

Baljeet Singh and Himanshu Singla

The purpose of this paper is to study the effects of rotation, voids and diffusion on characteristics of plane waves in a thermoelastic material.

Abstract

Purpose

The purpose of this paper is to study the effects of rotation, voids and diffusion on characteristics of plane waves in a thermoelastic material.

Design/methodology/approach

Lord and Shulman generalization of linear thermoelasticity is used to study the plane waves in a rotating thermoelastic material with voids and diffusion. The thermoelastic solid is rotating with a uniform angular velocity. The problem is specialized in two dimensions to study wave propagation. The plane harmonic solutions of governing field equations in a plane are obtained.

Findings

A velocity equation is obtained which indicates the propagation of five coupled plane waves in the medium. Reflection of an incident plane wave from stress-free surface of a half-space is also considered to obtain the amplitude ratios of various reflected waves. A numerical example is considered to illustrate graphically the effects of rotation, frequency, void and diffusion parameters on speeds and amplitude ratios of plane waves.

Originality/value

The present problem covers the combined effects of rotation, voids and diffusion on characteristics of plane waves in linear thermoelastic material in the context of Lord and Shulman (1967) and Aouadi (2010) theories, which are not studied in literature yet.

Details

Multidiscipline Modeling in Materials and Structures, vol. 16 no. 1
Type: Research Article
ISSN: 1573-6105

Keywords

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