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R Kumar

Department of Mathematics, Kurukshetra University, Kurukshetra, Haryana, India

[ 1 ] - Mathematical Modeling for Thermoelastic Double Porous Micro-Beam Resonators

In the present work, the mathematical model of a homogeneous, isotropic thermoelastic double porous micro-beam, based on the Euler-Bernoulli theory is developed in the context of Lord-Shulman [1] theory of thermoelasticity. Laplace transform technique has been used to obtain the expressions for lateral deflection, axial stress, axial displacement, volume fraction field and temperature distribut...

[ 2 ] - Transversely Isotropic Magneto-Visco Thermoelastic Medium with Vacuum and without Energy Dissipation

In the present investigation the disturbances in a homogeneous transversely isotropic magneto-Visco thermoelastic rotating medium with two temperature due to thermomechanical sources has been addressed. The thermoelasticity theories developed by Green-Naghdi (Type II and Type III) both with and without energy dissipation has been applied to the thermomechanical sources. The Laplace and Fourier ...

[ 3 ] - Reflection and Transmission of Plane Waves at Micropolar Piezothermoelastic Solids

The present investigation analysis a problem of r­­­eflection and transmission at an interface of two micropolar orthotropic piezothermoelastic media. The basic equations and constitutive relations for micropolar orthotropic piezothermoelastic media for G-L theory are derived. The expressions for amplitude ratios corresponding to reflected and transmitted waves are derived analytically. The eff...

[ 4 ] - Effects of Hall Current and Rotation in Modified Couple Stress Generalized Thermoelastic Half Space due to Ramp-Type Heating

The objective is to study the deformation in a homogeneous isotropic modified couple stress thermoelastic rotating medium in the presence of Hall current and magnetic field due to a ramp-type thermal source. The generalized theories of thermoelasticity developed by Lord Shulman (L-S, 1967) and Green Lindsay (G-L, 1972) are used to investigate the problem. Laplace and Fourier transform technique...

[ 5 ] - Variational Principle and Plane Wave Propagation in Thermoelastic Medium with Double Porosity Under Lord-Shulman Theory

The present study is concerned with the variational principle and plane wave propagation in double porous thermoelastic infinite medium. Lord-Shulman theory [2] of thermoelasticity with one relaxation time has been used to investigate the problem. It is found that for two dimensional model, there exists four coupled longitudinal waves namely longitudinal wave (P), longitudinal thermal wave (T),...

[ 6 ] - Thermomechanical Response in Thermoelastic Medium with Double Porosity

A dynamic two dimensional problem of thermoelasticity with double porous structure has been considered to investigate the disturbance due to normal force and thermal source. Laplace and Fourier transform technique is applied to the governing equations to solve the problem. The transformed components of stress and temperature distribution are obtained .The resulting expressions are obtained in t...

[ 7 ] - Analysis of Plane Waves in Anisotropic Magneto-Piezothermoelastic Diffusive Body with Fractional Order Derivative

In this paper the propagation of harmonic plane waves in a homogeneous anisotropic magneto-piezothermoelastic diffusive body with fractional order derivative is studied. The governing equations for a homogeneous transversely isotropic body in the context of the theory of thermoelasticity with diffusion given by Sherief et al. [1] are considered as a special case. It is found that three types of...

[ 8 ] - Axisymmetric Problem of Thick Circular Plate with Heat Sources in Modified Couple Stress Theory

The main aim is to study the two dimensional axisymmetric problem of thick circular plate in modified couple stress theory with heat and mass diffusive sources. The thermoelastic theories with mass diffusion developed by Sherief et al. [1] and kumar and Kansal [2] have been used to investigate the problem. Laplace and Hankel transforms technique is applied to obtain the solutions of the governi...

[ 9 ] - Thermomechanical Interactions Due to Hall Current in Transversely Isotropic Thermoelastic with and Without Energy Dissipation with Two Temperatures and Rotation

The present paper is concerned with  the investigation of disturbances in a homogeneous  transversely isotropic thermoelastic rotating  medium with two temperatures, in the presence of the combined effects of   Hall currents and magnetic field due to thermomechanical sources. The formulation is applied to the thermoelasticity theories developed by Green-Naghdi Theories of Type-II and Type-III. ...

[ 10 ] - Response of Two Temperatures on Wave Propagation in Micropolar Thermoelastic Materials with One Relaxation Time Bordered with Layers or Half Spaces of Inviscid Liquid

The present study is concerned with the propagation of Lamb waves in a homogeneous isotropic thermoelastic micropolar solid with two temperatures bordered with layers or half spaces of inviscid liquid subjected to stress free boundary conditions. The generalized theory of thermoelasticity developed by Lord and Shulman has been used to investigate the problem. The secular equations for symmetric...

[ 11 ] - Problem of Rayleigh Wave Propagation in Thermoelastic Diffusion

In this work, the problem of Rayleigh wave propagation is considered in the context of the theory of thermoelastic diffusion. The formulation is applied to a homogeneous isotropic thermoelastic half space with mass diffusion at the stress free, isothermal, isoconcentrated boundary. Using the potential functions and harmonic wave solution, three coupled dilatational waves and a shear wave is obt...

[ 12 ] - Deformation Due to Inclined Loads in Thermoporoelastic Half Space

The present investigation is concerned with the deformation of thermoporoelastic half space with incompressible fluid as a result of inclined load of arbitrary orientation. The inclined load is assumed to be linear combination of normal load and tangential load. The Laplace and Fourier transform technique are used to solve the problem. The concentrated force, uniformly distributed force and a m...

[ 13 ] - Variational Principle, Uniqueness and Reciprocity Theorems in Porous Piezothermoelastic with Mass Diffusion

The basic governing equations in anisotropic elastic material under the effect of porous piezothermoelastic are presented. Biot [1], Lord & Shulman [4] and Sherief et al. [5] theories are used to develop the basic equations for porous piezothermoelastic with mass diffusion material. The variational principle, uniqueness theorem and theorem of reciprocity in this model are established under the ...

[ 14 ] - Reflection and Transmission at the Boundary of Two Couple Stress Generalized Thermoelastic Solids

In this paper the reflection and transmission at a plane interface between two different couple stress generalized thermoelastic solid half spaces in context of Loard-Shulman(LS)[1967] and Green-Lindsay(GL)[1972] theories in welded contact has been investigated. Amplitude ratios of various reflected and transmitted waves are obtained due to incidence of a set of coupled longitudinal waves and c...

[ 15 ] - Wave Propagation at the Boundary Surface of Inviscid Fluid Half-Space and Thermoelastic Diffusion Solid Half-Space with Dual-Phase-Lag Models

The present investigation deals  with the reflection and transmission phenomenon due to incident plane longitudinal wave at a plane interface between inviscid fluid half-space and a thermoelastic diffusion solid half-space with dual-phase-lag heat transfer (DPLT) and dual-phase-lag diffusion (DPLD) models. The theory of thermoelasticity with dual-phase-lag heat transfer developed by Roychoudhar...

[ 16 ] - Wave Propagation in Fibre-Reinforced Transversely Isotropic Thermoelastic Media with Initial Stress at the Boundary Surface

The reflection and transmission of thermoelastic plane waves at an imperfect boundary of two dissimilar fibre-reinforced transversely isotropic thermoelastic solid half-spaces under hydrostatic initial stress has been investigated. The appropriate boundary conditions are applied at the interface to obtain the reflection and transmission coefficients of various reflected and transmitted waves wi...

[ 17 ] - Response of GN Type II and Type III Theories on Reflection and Transmission Coefficients at the Boundary Surface of Micropolar Thermoelastic Media with Two Temperatures

In the present article, the reflection and transmission of plane waves at the boundary of thermally conducting micropolar elastic media with two temperatures is studied. The theory of thermoelasticity with and without energy dissipation is used to investigate the problem. The expressions for amplitudes ratios of reflected and transmitted waves at different angles of incident wave are obtained. ...

[ 18 ] - Wave Propagation at an Interface of Elastic and Microstretch Thermoelastic Solids with Microtemperatures

In the present paper, the problem of reflection and transmission of waves at an interface of elastic and microstretch thermoelastic solids with microtemperatureshas been studied. The amplitude ratios of various reflected and transmitted waves are functions of angle of incidence and frequency of incident wave. The expressions of amplitude ratios have been computed numerically for a particular mo...

[ 19 ] - Axi-Symmetric Deformation Due to Various Sources in Saturated Porous Media with Incompressible Fluid

The general solution of equations of saturated porous media with incompressible fluid for two dimensional axi-symmetric problem is obtained in the transformed domain. The Laplace and Hankel transforms have been used to investigate the problem. As an application of the approach concentrated source and source over circular region have been taken to show the utility of the approach. The transforme...

[ 20 ] - Propagation of Waves at an Interface of Heat Conducting Elastic Solid and Micropolar Fluid Media

The present investigation is concerned with the reflection and transmission coefficients of plane waves at the interface of generalized thermoelastic solid half space and heat conducting micropolar fluid half- space. The amplitude ratios of various reflected and transmitted waves with various angle of incidence have been computed numerically and depicted graphically. Micropolarity and thermal r...

[ 21 ] - Wave Propagation and Fundamental Solution of Initially Stressed Thermoelastic Diffusion with Voids

The present article deals with the study of propagation of plane waves in isotropic generalized thermoelastic diffusion with voids under initial stress. It is found that, for two dimensional model of isotropic generalized thermoelastic diffusion with voids under initial stress, there exists four coupled waves namely, P wave, Mass Diffusion (MD) wave, thermal (T) wave and Volume Fraction (VF) wa...

[ 22 ] - Wave Propagation at the Boundary Surface of Elastic Layer Overlaying a Thermoelastic Without Energy Dissipation Half-space

The present investigation is to study the surface wave propagation at imperfect boundary between an isotropic thermoelastic without energy dissipation half-space and an isotropic elastic layer of finite thickness. The penetration depth of longitudinal, transverse, and thermal waves has been obtained. The secular equation for surface waves in compact form is derived after developing the mathemat...

[ 23 ] - Three-dimensional Free Vibration Analysis of a Transversely Isotropic Thermoelastic Diffusive Cylindrical Panel

The present paper is aimed to study an exact analysis of the free vibrations of a simply supported, homogeneous, transversely isotropic, cylindrical panel based on three-dimensional generalized theories of thermoelastic diffusion. After applying the displacement potential functions in the basic governing equations of generalized thermoelastic diffusion, it is noticed that a purely transverse mo...

[ 24 ] - Wave Propagation in Mixture of Generalized Thermoelastic Solids Half-Space

This paper concentrates on the reflection of plane waves in the mixture of generalized thermo elastic solid half-space. There exists quasi dilatational waves i.e. qP1, qP2, qT and two rotational waves S1, S2 in a two dimensional model of the solid. The boundary conditions are solved to obtain a system of five non-homogeneous equations for amplitude ratios. These amplitude ratios are found to de...

[ 25 ] - Free Vibration Analysis of Micropolar Thermoelastic Cylindrical Curved Plate in Circumferential Direction

The free vibration analysis ofhomogeneous isotropic micropolar thermoelastic cylindrical curved plate in circumferential direction has been investigated in the context of generalized themoelasticity III, recently developed by Green and Naghdi. The model has been simplified using Helmholtz decomposition technique and the resulting equations have been solved using separation of variable method. M...

[ 26 ] - Effect of Rotation and Stiffness on Surface Wave Propagation in a Elastic Layer Lying Over a Generalized Thermodiffusive Elastic Half-Space with Imperfect Boundary

The present investigation is to study the surface waves propagation with imperfect boundary between an isotropic elastic layer of finite thickness and a homogenous isotropic thermodiffusive elastic half- space with rotation in the context of Green-Lindsay (G-L model) theory. The secular equation for surface waves in compact form is derived after developing the mathematical model. The phase velo...

[ 27 ] - Study of Wave Motion in an Anisotropic Fiber-Reinforced Thermoelastic Solid

The present investigation deals with the propagation of waves in the layer of an anisotropic fibre reinforced thermoelastic solid. Secular equations for symmetric and skew-symmetric modes of wave propagation in completely separate terms are derived. The amplitude of displacements and temperature distribution were also obtained. Finally, the numerical solution was carried out for Cobalt material...

[ 28 ] - Analysis of Wave Motion in a Micropolar Transversely Isotropic Medium

The present investigation deals with the propagation of waves in a micropolar transversely isotropic layer. Secular equations for symmetric and skew-symmetric modes of wave propagation in completely separate terms are derived. The amplitudes of displacements and microrotation were also obtained. Finally, the numerical solution was carried out for aluminium epoxy material and the dispersion curv...

[ 29 ] - Wave Propagation in a Layer of Binary Mixture of Elastic Solids

This paper concentrates on the propagation of waves in a layer of binary mixture of elastic solids subjected to stress free boundaries. Secular equations for the layer corresponding to symmetric and antisymmetric wave modes are derived in completely separate terms. The amplitudes of displacement components and specific loss for both symmetric and antisymmetric modes are obtained. The effect of ...

[ 30 ] - 3D Thermoelastic Interactions in an Anisotropic Lastic Slab Due to Prescribed Surface Temparature

The present paper is devoted to the determination of displacement, stresses and temperature from three dimensional anisotropic half spaces due to presence of heat source. The normal mode analysis technique has been used to the basic equations of motion and generalized heat conduction equation proposed by Green-Naghdi model-II [1]. The resulting equation are written in the form of a vector –matr...

[ 31 ] - Damping and Frequency Shift in Microscale Modified Couple Stress Thermoelastic Plate Resonators

In this paper, the vibrations of thin plate in modified couple stress thermoelastic medium by using Kirchhoff- Love plate theory has been investigated. The governing equations of motion and heat conduction equation for Lord Shulman (L-S) [1] theory are written with the help of Kirchhoff- Love plate theory. The thermoelastic damping of micro-beam resonators is analyzed by using the normal mode a...

[ 32 ] - Effects of Viscosity on a Thick Circular Plate in Thermoelastic Diffusion Medium

The problem treated here is to determinethe viscosity effect on stresses, temperature change and chemical potential in a circular plate. The mathematical formulation is applied to two theories of thermoelastic diffusion developed by Sherief et al. [27] with one relaxation time and Kumar and Kansal [9]with two relaxation times. Laplace and Hankel transform techniques are used to obtain the expre...

[ 33 ] - A Problem of Axisymmetric Vibration of Nonlocal Microstretch Thermoelastic Circular Plate with Thermomechanical Sources

In the present manuscript, we investigated a two dimensional axisymmetric problem of nonlocal microstretch thermoelastic circular plate subjected to thermomechanical sources. An eigenvalue approach is proposed to analyze the problem. Laplace and Hankel transforms are used to obtain the transformed solutions for the displacements, microrotation, microstretch, temperature distribution and stresse...

[ 34 ] - Effect of Micropolarity on the Propagation of Shear Waves in a Piezoelectric Layered Structure

This paper studies the propagation of shear waves in a composite structure consisting of a piezoelectric layer perfectly bonded over a micropolar elastic half space. The general dispersion equations for the existence of shear waves are obtained analytically in the closed form. Some particular cases have been discussed and in one special case the relation obtained is in agreement with existing r...

[ 35 ] - Nonlocal Dispersion Analysis of a Fluid – Conveying Thermo Elastic Armchair Single Walled Carbon Nanotube Under Moving Harmonic Excitation

In this work, the nonlocal elastic waves in a fluid conveying armchair thermo elastic single walled carbon nanotube under moving harmonic load is studied using Eringen nonlocal elasticity theory via Euler Bernoulli beam equation. The governing equations that contains partial differential equations for single walled carbon nanotube is derived by considering thermal and Lorenz magnetic force. The...

[ 36 ] - Fundamental Solution and Study of Plane Waves in Bio-Thermoelastic Medium with DPL

The fundamental solution of the system of differential equations in bio-thermoelasticity with dual phase lag (DPL) in case of steady oscillations in terms of elementary function is constructed and basic property is established. The tissue is considered as an isotropic medium and the propagation of plane harmonic waves is studied. The Christoffel equations are obtained and modified with the ther...