# Baljeet SinghPost Graduate Government College, Sector 11, Chandigarh, India · Department of Mathematics

Baljeet Singh

PhD

## About

168

Publications

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2,281

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Citations since 2016

Introduction

Elasticity theory and wave propagation

Additional affiliations

Education

July 1990 - August 1997

## Publications

Publications (168)

In this paper, the propagation of a Rayleigh-type wave is explored in a half-space of an incompressible nematic elastomer with a uniform director aligned orthogonal to the surface. The nematic elastomer is idealized so as to fit within the framework of linear viscoelasticity theory. The governing equations of nematic elastomers are subjected to the...

In this paper, the homogeneous plane wave characteristics are explored in an elastic solid by considering the effects of static and dynamic flexoelectricity, micro-inertia, and strain gradient elasticity. The plane wave solutions of the governing field equations suggest the propagation of two coupled longitudinal waves and two coupled transverse wa...

Purpose
The purpose of this paper is to analyze the propagation characteristics of the Rayleigh-type surface wave in a thermally conducting mixture of an elastic solid and a Newtonian fluid by applying the mixture theory.
Design/methodology/approach
The governing equations are formulated in context of both Green–Lindsay (G-L) and Lord–Shulman (L-S...

The properties of Rayleigh-type surface wave in a linear, homogeneous and transversely isotropic nonlocal micropolar piezoelectric solid half-space are explored. Dispersion relations for Rayleigh-type surface wave are derived for both charge free and electrically shorted cases. Using an algorithm of iteration method in MATLAB software, the wave spe...

In this paper, we investigate a problem on reflection and transmission of plane-waves at an interface between two dissimilar half-spaces of a transversely isotropic micropolar piezoelectric material. The entire model is assumed to rotate with a uniform angular velocity. The governing equations of rotating and transversely isotropic micropolar piezo...

The size-dependent theoretical modeling of coupled phenomena between deformation and mass diffusion is of current interest in the fields of nanomechanics and nanotechnology. The theory of nonlocal elasticity is applied to study the propagation of plane waves in a linear and isotropic diffusive elastic material. The governing equations of motion are...

In this paper, the nonlocal non-Fick diffusion elasticity theory is applied to study the propagation of Rayleigh-type surface waves along the stress-free surface of an isotropic diffusive elastic half-space. The equations governing the motion in an isotropic nonlocal non-Fick diffusion elastic medium are specialized for a plane. The appropriate sur...

In this paper, the nonlocal elasticity theory is applied to study the propagation of plane wave and Rayleigh-type surface wave in an incompressible, rotating and transversely isotropic material. The governing equations of motion for an incompressible, rotating, transversely isotropic and nonlocal elastic medium are specialized for a plane. The medi...

The characteristic equations of Rayleigh waves in monoclinic materials have already been derived by various prominent researchers. This paper revisits all these studies with special attention on numerical solutions of the characteristic equation. In this work, the propagation of a Rayleigh surface wave in a rotating monoclinic half-plane is studied...

Linear theory of micropolar elasticity has potential applications in exploration of materials made from bar-like molecules with micro-rotational effects. This theory is employed to investigate the Rayleigh surface waves in an incompressible micropolar solid half-space whose surface is subjected to the Tiersten’s impedance boundary conditions. An im...

This paper presents a study on plane waves propagating in a micropolar piezoelectric material with transverse isotropy. The plane wave solutions of the governing field equations suggest that there exists three coupled plane waves propagating in a micropolar piezoelectric medium. Reflection of a plane wave incident at a non-free surface of a micropo...

Lord–Shulman theory of generalized thermoelasticity is employed to derive the governing equations of generalized thermo-microstretch elasticity with diffusion. The governing equations are specialized in x-y plane and solved for plane wave solutions. It is found that there exist six plane waves propagating with distinct speeds in a thermo-microstret...

In this paper, we specialize the governing equations of microstructured flexoelectric solids in a plane and solve for possible plane wave propagation. It is shown that there exist two plane waves, namely quasi-P and quasi-SV waves, in a microstructured flexoelectric solid half-space.
A numerical example is considered to plot the speeds of quasi-P a...

In the present work, we consider a problem of reflection and transmission of plane waves at an interface between two different isotropic dielectric half-spaces by considering the effects of flexoelectricity, micro-inertia and strain gradient elasticity. The plane wave solutions of the governing field equations for such a medium shows the existence...

This paper investigates the propagation of theremoelastic waves in a homogeneous, linear and isotropic porous solid. For physical and mathematical simplicity, a one-dimensional solid bar is used to explain the concept of heat transfer caused by motion. Solution of governing equations shows that the transfer of heat in a one-dimensional porous rod i...

Taking into consideration the effects of micro-inertia, flexoelectricity, and non-uniform strain, the field equations of isotropic dielectrics with centrosymmetric microstructures are specialized for a plane. Plane-wave solutions of these two-dimensional (2D) governing equations suggest the possibility of two plane waves propagating in a flexoelect...

A phenomenon of reflection of plane waves from a thermally insulated surface of a solid half-space is studied in context of Lord-Shulman theory of generalized thermo-viscoelasticity with voids. The governing equations of generalized thermo-viscoelastic medium with voids are specialized in x–z plane. The plane wave solution of these equations shows...

The present paper is concerned with plane and surface wave solutions of the governing equation for an incompressible, homogeneous, transversely isotropic and rotating thermoelastic medium in the context of the Green–Naghdi theory. The velocity equation for homogeneous plane waves is obtained which indicates the existence of two coupled plane shear...

In the present paper, the governing equations for two-temperature generalized porothermoelasticity are formulated in accordance with Green and Naghdi theory of thermoelasticity without energy dissipation. Two-dimensional plane wave solution of these governing equations indicates the existence of one shear vertical and four coupled longitudinal wave...

In this paper, the Rayleigh wave propagation is investigated in rotating half-space of incompressible monoclinic elastic materials which are subjected to the impedance boundary conditions. In particular, the explicit secular equation of the Rayleigh wave is obtained. The main objective of this paper is to illustrate the dependence of dimensionless...

The governing equations of an initially stressed, rotating and transversely isotropic thermoelastic solid permeated with magnetic field are solved for surface wave solutions. The appropriate particular solutions in the half-space satisfy the required boundary conditions at a thermally insulated stress free surface. A velocity equation is obtained f...

In this paper, a problem on reflection and transmission of plane waves at an imperfect interface between two dissimilar monoclinic elastic half-spaces is studied. The boundary conditions at imperfect interface are satisfied by appropriate particular solutions in the half-spaces to obtain a non-homogeneous system of four equations in amplitude ratio...

In the present paper, the governing equations of isotropic linear incompressible microstretch solid are solved for plane wave solutions in x-z plane (i) when the displacement vector) ,0, (= 3 1 u u u and the microrotation vector ,0) (0, = 2 φ φ and, (ii) when the displacement vector ,0) (0, = 2 u u and the microrotation vector) ,0, (= 3 1 φ φ φ. It...

In the present paper, the governing equations of transversely isotropic dual-phase-lag thermoelasticity are solved for the surface wave solutions. The particular solutions satisfy the boundary conditions at a thermally insulated /isothermal stress free surface of a half-space to obtain the frequency equation of the Rayleigh wave. The frequency equa...

The propagation of Rayleigh type surface waves in a rotating elastic half-space of orthotropic type is studied under impedance boundary conditions. The secular equation is obtained explicitly using traditional methodology. A program in MATLAB software is developed to obtain the numerical values of the nondimensional speed of Rayleigh wave. The spee...

The present paper deals with the propagation of surface waves in an isotropic and homogeneous nonlocal generalized thermoelastic solid half-space with voids. The dispersion relations for Rayleigh-type surface wave are derived for both thermally insulated and isothermal boundaries. The non-dimensional wave speed of Rayleigh-type surface wave is comp...

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 thermoel...

The governing equations for a homogeneous and isotropic thermoelastic medium are formulated in the context of coupled thermoelasticity, Lord and Shulman theory of generalized thermoelasticity with one relaxation time, Green and Lindsay theory of generalized thermoelasticity with two relaxation times, Green and Nagdhi theory of thermoelasticity with...

The governing equations of two-temperature generalized magneto-thermoelasticity with hydrostatic initial stress are specialized in two dimensions and are solved for surface wave solutions. The appropriate solutions in a half-space are obtained which satisfy relevant radiation condition and boundary conditions at thermally insulated as well as iso-t...

In the present paper, we consider a problem of reflection and transmission of plane waves at an interface between two different transversely isotropic micropolar piezoelectric half-spaces. The plane wave solution of governing equations for micropolar piezoelectric medium indicates the propagation of three coupled plane waves. An incident plane wave...

The current work analyzes the transmission behavior of plane harmonic waves in an isotropic medium. The observation is made for homogeneous type solid in the context of generalized dual phase lag model of thermoelasticity. Concept micro-temperature, where the microelements have different temperatures has also been considered. The basic focus of the...

In this paper, the governing equations of linear, isotropic, homogeneous and generalized micropolar thermoelasticity are specialized in a plane. The governing equations are solved for plane harmonic wave solutions. Two separate velocity equations are obtained which indicate the existence of four plane waves with distinct speeds. A problem on reflec...

Sinha and Sinha (J. Phys. Earth, 22, 237-244, 1974) studied a problem on the reflection of thermoelastic waves at a stress free thermally insulated solid half-space in context of the Lord and Shulman theory of generalized thermoelastcity. He showed the existence of three plane waves (two longitudinal waves and a shear wave) in a homogeneous, linear...

Within the framework of the quasi-electrostatic approximation, the theory of the superposition of infinitesimal deformations and electric fields on a finite deformation with an underlying electric field is employed to examine the problem of the reflection of small amplitude homogeneous electroelastic plane waves from the boundary of an incompressib...

A problem of reflection and transmission of elastic waves at an interface between an elastic solid half-space and a micropolar piezoelectric solid half-space is considered. Both the half-spaces are assumed to be transversely isotropic. For an incident wave from transversely isotropic elastic solid half-space, two reflected waves in transversely iso...

In this paper, the governing equations of a linear, homogeneous and transversely isotropic rotating micropolar piezoelectric medium are solved for surface wave solutions. The appropriate solutions satisfying the radiation conditions are obtained in a half-space. These solutions are applied to suitable boundary conditions at the free surface of the...

A phenomenon of reflection of plane waves from a thermally insulated surface of a solid half-space is studied in context of Lord-Shulman theory of generalized thermo-viscoelasti-city with voids. The governing equations of generalized thermo-viscoelastic medium with voids are specialized in x-z plane. The plane wave solution of these equations shows...

In the present paper, a problem on the Rayleigh type surface wave at a traction free surface of a generalized porothermoelastic solid half-space is considered. The governing equations of generalized porothermoelastcity are specialized for x1 − x2 plane. The surface wave solutions in x1 − x2 plane are obtained which satisfy the required radiation co...

The present work is supposed to analyze the propagation of plane harmonic waves in a homogeneous isotropic medium in the context of generalized dual phase lag model of thermoelasticity. The concept micro-temperature where the microelements have different temperatures is considered. Further, the medium is set on rotation with some specific rotating...

In the present paper, the Rayleigh wave at a stress free thermally insulated surface of a generalized porothermoelastic solid half-space is considered. The governing equations of generalized porothermoelasticity are solved for general surface wave solution. The particular solutions satisfying the required radiation conditions are obtained. These so...

Background
The theory of microstretch elastic bodies was first developed by Eringen (1971, 1990, 1999, 2004). This theory was developed by extending the theory of micropolar elastcity. Each material point in this theory has three deformable directors. Methods
The governing equations of a transversely isotropic microstretch material are specialized...

In this paper, the governing equations of an incompressible rotating orthotropic elastic medium are formulated and are solved to obtain Rayleigh surface wave solutions in a particular half-space. The surface of half-space is subjected to impedance boundary conditions, in which normal and tangential stresses are proportional to frequency times norma...

The governing equations of transversely isotropic dual-phase-lag two-temperature ther-moelasticity are solved for the surface wave solutions. The particular solutions in the half-space satisfy the' boundary conditions at a thermally insulated /isothermal stress-free surface of a half-space to obtain the frequency equation of the Rayleigh wave for t...

In this article, the governing equations of micropolar thermoelasticity with diffusion are formulated in the context of Lord–Shulman theory of generalized thermoelasticity. The plane wave solutions of these equations indicate the existence of six plane waves, namely, coupled longitudinal displacement (CLD) wave, coupled thermal wave, coupled mass d...

The paper is concerned with the propagation of plane waves in a transversely isotropic two temperature generalized thermoelastic solid half-space with voids and rotation. The governing equations are modified in the context of Lord and Shulman theory of generalized thermoelasticity and solved to show the existence of four plane waves in the x – z pl...

The governing equations for a rotating monoclinic magnetothermoelastic medium are formulated in the context of the Lord–Shulman theory and are solved to yield the velocity equation that points to the existence of three quasiplane waves. Some particular cases are obtained, i.e., waves in the absence of anisotropy, rotation, and thermal and magnetic...

In the present paper, the governing equations of generalized thermo-magneto-electro-elastic solid are formulated in one-dimension. The time-harmonic plane wave solution of these equations leads to a velocity equation, which shows the existence of two plane waves namely longitudinal and thermal waves. A particular example of LiNbO 3 is taken for num...

The present paper is concerned with the propagation of plane waves in a rotating, transversely isotropic, two-temperature generalized thermoelastic solid half-space without energy dissipation. The governing equations are solved to show the existence of three plane waves in the x-z plane. The reflection of these plane waves from a thermally insulate...

The linear governing equations of a micropolar thermoelastic medium without energy dissipation are solved for surface wave solutions. The appropriate solutions satisfying the radiation conditions are applied to the required boundary conditions at the free surface of the half-space of the medium. A frequency equation is obtained for Rayleigh wave in...

In the present paper, the equation of motion for an incompressible transversely isotropic fibre-reinforced elastic solid is derived in terms of a scalar function. The general solution of the equation of motion is obtained, which satisfies the required radiation condition. The appropriate impedance boundary conditions are also satisfied by the solut...

In this paper, the governing equations of micropolar thermoelasticity with diffusion are formulated in context of Lord-Shulman theory of generalized thermoelasticity. The plane wave solutions of these equations indicate the existence of six plane waves. The speed of these plane waves are computed for a particular material and plotted against the di...

In the present paper, the Rayleigh wave in a generalized thermoelastic solid half-space is considered with impedance boundary conditions. The governing equations of homogeneous and isotropic generalized thermoelastcity are solved for general surface wave solutions. The general solutions in the half-space satisfy the required radiation conditions. T...

In the present paper, the equations of motion and heat conduction equation of an incompressible transversely isotropic thermoelastic solid are formulated in view of Lord and Shulman theory on generalized thermoelastcity. The equations of motion and heat conduction equation reduce to two coupled equations in temperature and a scalar function dependi...

The linear governing equations of a transversely isotropic microstretch elastic solid medium are formulated and solved for surface wave solutions. The appropriate solutions satisfying the radiation conditions are applied to the required boundary conditions at the free surface of the half-space of the medium. A frequency equation is obtained for Ray...

The phenomena of reflection and refraction of elastic waves due to incident plane
wave at an interface between two dissimilar incompressible transversely isotropic
fibre-reinforced elastic half-spaces has been investigated. The expressions of the
reflection and refraction coefficients corresponding to the reflected and refracted
waves are derived b...

In the present paper, the propagation of plane waves in an isotropic two-temperature generalized thermoelastic solid half-space with diffusion is studied. The governing equations are modified with the use of Lord and Shulman theory of generalized thermoelasticity and are solved for plane wave solutions, which show the existence of four plane waves...

In this paper the equations governing small amplitude motions in a rotating transversely isotropic initially stressed elastic solid are derived, both for compressible and incompressible linearly elastic materials. The equations are first applied to study the effects of initial stress and rotation on the speed of homogeneous plane waves propagating...

A thermal shock problem of rotating generalized thermoelastic half-space with diffusion is considered. The governing equations of the model are reduced in xy-plane in terms of non-dimensional quantities. The corresponding finite element equations are obtained, the solutions of
which are subjected to required initial and boundary conditions. Using f...

The basic equations for the wave on the surface of an initially stressed transversely isotropic dual-phase-lag thermoelastic body subjected to the action of a magnetic field were solved. Particular solutions were applied to the thermally insulated free surface of a half-space to obtain the frequency equation for the Rayleigh wave. This equation was...

The governing equations of rotating thermoelastic solid with diffusion are solved in context of Green-Naghdi theory (Type II) to show the numerical existence of four coupled plane waves. The required boundary conditions at stress free and thermally insulated surface of the model are satisfied to obtain the reflection coefficients of various reflect...

The Rayleigh surface wave is studied at a stress-free thermally insulated surface of an isotropic, linear, and homogeneous thermoelastic solid half-space with microtemperatures. The governing equations of the thermoelastic medium with microtemperatures are solved for surface wave solutions. The particular solutions in the half-space are applied to...

Green-Naghdi's theory of generalized thermoelasticity is applied to study the reflection of P and SV waves from the free surface of a magneto-thermoelastic solid half-space. The boundary conditions are satisfied by appropriate potential functions to obtain a system of four non-homogeneous equations in reflection coefficients. The reflection coeffic...

In the present paper, the governing equations of transversely isotropic dual-phase-lag thermoelasticity are solved for the surface wave solutions. The particular solutions satisfy the boundary conditions at a thermally insulated /isothermal stress free surface of a half-space to obtain the frequency equation of the Rayleigh wave. The frequency equa...

The influence of rotation, magnetic field, voids and initial stress on the reflection of P waves in thermoelasticity without energy dissipation are studied. The basic governing equations for isotropic and homogeneous thermoelastic half-space with voids, rotation, are based on Green and Naghdi (GN) theory under the effect of initial stress, where th...

The present paper is concerned with the propagation of plane waves in a transversely isotropic dual-phase-lag generalized thermoelastic solid half-space. The governing equations are solved in x–z plane to show the existence of three plane waves. Reflection of these plane waves from thermally insulated as well as isothermal stress-free surfaces is s...

Purpose
The purpose of this paper is to compute the phase velocities and attenuation coefficients of coupled longitudinal waves in a generalized thermoporoelastic model and to observe the effect of porosity, frequency and thermal parameters on the phase velocities and attenuation coefficients on these waves graphically.
Design/methodology/approach...

Reflection of plane waves is studied at a free surface of a perfectly conducting transversely isotropic elastic solid half-space with initial stress. The governing equations are solved to obtain the velocity equation which indicates the existence of two quasi planar waves in the medium. Reflection coefficients and energy ratios for reflected qP and...

The governing equations of an initially stressed rotating piezoelectric
medium are solved for surface wave solutions. The appropriate solutions
in the half-space of the medium satisfy the required boundary conditions
to obtain the frequency equation of Rayleigh wave for charge free as
well as electrically shorted cases. The non-dimensional speed of...

Elastic/piezoelectric and piezoelectric/piezoelectric interfaces are considered for SH wave propagation. The boundary conditions at the interfaces are satisfied to obtain the amplitude and energy ratios for the incidence of SH wave. These amplitude and energy ratios are computed numerically for particular model of interfaces, i.e., for Steel/PZT4 a...

The Green and Naghdi theory of thermoelasticity is applied to study plane-wave propagation in an elastic solid with thermo-diffusion. The governing equations of an elastic solid with generalized thermo-diffusion are solved to show the existence of three coupled longitudinal waves and a shear vertical (SV) wave in a two-dimensional model of the soli...

A problem on Rayleigh wave in a rotating half-space of an orthotropic micropolar material is considered. The governing equations are solved for surface wave solutions in the half space of the material. These solutions satisfy the boundary conditions at free surface of the half-space to obtain the frequency equation of the Rayleigh wave. For numeric...

The Rayleigh surface wave is
studied at a stress-free thermally insulated surface of an
isotropic, linear, and homogeneous two-temperature thermoelastic
solid half-space in the context of Lord and Shulman theory of
generalized thermoelasticity. The governing equations of
a two-temperature generalized thermoelastic medium are solved for
surface wave...

In this paper, the equations of motion for an incompressible rotating orthotropic elastic solid are solved in two-dimension. The velocity equation of the homogeneous plane wave and the secular equation for the Rayleigh surface wave are obtained. The non-dimensional speeds of the homogeneous plane wave and the Rayleigh surface wave are computed nume...

In the present paper, the reflection of plane waves from a free surface of a generalized porothermoelastic solid half-space is studied. The appropriate solutions in the generalized porothermoelastic solid half-space are obtained which satisfy the required boundary conditions at the free surface of the half-space to obtain the relations between the...

In this paper, Rayleigh surface wave is studied at a stress free thermally insulated surface of a two-temperature thermoelastic solid half-space in absence of energy dissipation. The governing equations of two-temperature generalized thermoelastic medium without energy dissipation are solved for surface wave solutions. The appropriate particular so...

In the present paper, a problem is studied on the reflection of plane waves from stress-free surface of a rotating and electrically conducting fibre-reinforced elastic solid half-space with magnetic field. The governing equations are solved to obtain the velocity equation which indicates the existence of two quasi-plane waves in the medium. The clo...

The governing equations of generalizedmagneto- thermoelas- ticity with
hydrostatic initial stress and rotation are solved for surface wave
solutions. The particular solutions are applied to the boundary con-
ditions at a free surface of a half-space to obtain the frequency
equation of Rayleigh wave. For numerical purpose, the frequency equation
is...

The governing equations of a model of rotating generalized thermoelastic diffusion in an isotropic medium with temperature-dependent mechanical properties are formulated in context of Lord-Shulman theory of generalized thermoelasticity. The modulus of elasticity is taken as a linear function of reference temperature. The solution of the governing e...

The governing equations for a transversely isotropic rotating magnetothermoelastic medium are solved, giving a cubic velocity equation, which is indicative of three plane waves. Some limiting cases are considered: in the absence of anisotropy, rotation, and thermal and magnetic effects. The effects of the anisotropy, rotation, thermal and magnetic...

Reflection of Plane Waves in a Rotating Transversly Isotropic Magneto-Thermoelastic Solid Half-Space
The governing equations of a rotating transversely isotropic magneto-thermoelastic medium are solved to obtain the velocity equation, which indicates the existence of three quasi plane waves. Reflection of these plane waves from a stress-free therma...

The present paper is concerned with the propagation of plane waves in an isotropic generalized thermoelastic solid half-space with two temperatures. The governing equations are modified in the context of the Lord-Shulman theory of generalized thermoelasticity and are solved to show the existence of three plane waves, namely, P, thermal, and SV wave...

The present paper is concerned with the propagation of plane waves in a transversely isotropic generalized thermoelastic solid half-space with two temperatures. The governing equations are modified in the context of Lord and Shulman’s theory of generalized thermoelasticity and are solved to show the existence of three plane waves in the x-z plane....

In this paper, the problem of wave propagation in a thermoelastic solid half-space with voids and rotation is considered in context of the Green-Naghdi theory of thermoelasticity. The basic governing equations for an isotropic and homogeneous thermoelastic half-space are formulated and solved analytically. The solution of the governing equations in...

A solution of the field equations governing small motions of a micropolar viscoelastic solid half-space with stretch is employed
to study the reflection and transmission at the interface between a liquid and a micropolar viscoelastic solid with stretch.
The amplitude ratios for various reflected and refracted waves are computed and depicted graphic...

This paper is concerned with the propagation of plane waves in a transversely isotropic generalized thermoelastic solid half-space with diffusion. The governing equations are modified in the context of the Lord and Shulman theory of generalized thermoelasticity and are solved to show the existence of four plane waves in the xz plane. Reflection of...

The governing equations of an initially stressed rotating orthotropic dissipative medium are solved analytically to obtain the velocity equation which indicates the existence of two quasi-planar waves. The appropriate particular solutions in the half-space satisfy the required boundary conditions at the stress-free surface to obtain the expressions...

The present paper is concerned with the propagation of plane waves in an isotropic two-temperature generalized thermoelastic solid half-space in context of Green and Naghdi theory of type II (without energy dissipation). The governing equations in x-z plane are solved to show the existence of three coupled plane waves. The reflection of plane waves...

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