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1
Content available remote Micropolar curved rods. 2-D, high order, Timoshenko’s and Euler-Bernoulli models
100%
Zozulya V. V.
Curved and Layered Structures
|
2017
|
tom 4
|
nr 1
104-118
EN
New models for micropolar plane curved rods have been developed. 2-D theory is developed from general 2-D equations of linear micropolar elasticity using a special curvilinear system of coordinates related to the middle line of the rod and special hypothesis based on assumptions that take into account the fact that the rod is thin.High order theory is based on the expansion of the equations of the theory of elasticity into Fourier series in terms of Legendre polynomials. First stress and strain tensors,vectors of displacements and rotation and body force shave been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate.Thereby all equations of elasticity including Hooke’s law have been transformed to the corresponding equations for Fourier coefficients. Then in the same way as in the theory of elasticity, system of differential equations in term of displacements and boundary conditions for Fourier coefficients have been obtained. The Timoshenko’s and Euler-Bernoulli theories are based on the classical hypothesis and 2-D equations of linear micropolar elasticity in a special curvilinear system. The obtained equations can be used to calculate stress-strain and to model thin walled structures in macro, micro and nano scale when taking in to account micropolar couple stress and rotation effects.
2
Interaction due to thermodiffusive and mechanical sources in micropolar elastic medium
88%
Kumar R. , Kaushal S. , Miglani A.
Journal of Technical Physics
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2009
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tom Vol. 50, no 4
317-342
EN
In this present paper, first the equations of generalized micropolar thermodiffusive medium, based on the theory of Lord and Shulman with one relaxation time are derived and then, deformation in a micropolar thermoelastic diffusive medium has been studied due to various sources. Laplace and Fourier transforms are used to solve the problem. The application of concentrated normal force, thermal point source and chemical potential point source has been considered to show the utility of the solution obtained. The transformed components of stress, temperature distribution and chemical potential are inverted numerically using a numerical inversion technique. The effect of micropolarity and diffusion on these quantities are presented graphically in order to illustrate and compare the analytical results. Some special cases of micropolarity and diffusion are also deduced.
3
Content available remote Reflection of PlaneWaves at Micropolar Piezothermoelastic Half-space
88%
Kumar R. , Sharma N. , Lata P. , Marin M.
Computational Methods in Science and Technology
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2018
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tom Vol. 24, No. 2
113--124
EN
A problem of reflection at a free surface of micropolar orthotropic piezothermoelastic medium is discussed in the present paper. It is found that there exist five type plane waves in micropolar orthotropic piezothermoelastic medium, namely quasi longitudinal displacement wave (quasi LD wave), quasi thermal wave (quasi T wave), quasi CD-I, quasi CD-II wave and electric potential wave (PE wave). The amplitude ratios corresponding to reflected waves are obtained numerically. The effect of angle of incidence and thermopiezoelectric interactions on the reflected waves are studied for a specific model. Some particular cases of interest are also discussed.
4
Content available Study of axi-symmetric vibrations in a micropolar transversely isotropic layer
75%
Gupta R. R. , Gupta R. R.
International Journal of Applied Mechanics and Engineering
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2019
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tom Vol. 24, no. 2
259--268
EN
The present investigation deals with the propagation of circular crested Lamb waves in a homogeneous micropolar transversely isotropic medium. Secular equations for symmetric and skew-symmetric modes of wave propagation in completely separate terms are derived. The amplitudes of displacements and microrotation are computed numerically for magnesium as a material and the dispersion curves, amplitudes of displacements and microrotation for symmetric and skew-symmetric wave modes are presented graphically to evince the effect of anisotropy. Some special cases of interest are also deduced.
5
Content available remote Elastodynamic response of various sources in micropolar thermodiffusive elastic medium
75%
Kumar R. , Kaushal S. , Miglani A.
International Journal of Applied Mechanics and Engineering
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2010
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tom Vol. 15, no 1
63-98
EN
A general solution to the field equations of a micropolar thermodiffusive elastic solid are obtained in the transformed form, using the Laplace and Fourier transform techniques. The deformation due to various sources has been investigated. As an application, concentrated and distributed sources are taken to show the utility of the approach. The transformed solutions are inverted using a numerical inversion technique to invert the Laplace and Fourier transforms. The components of stress, temperature distribution and chemical potential distribution are obtained numerically and discussed graphically to depict the effects of micropolarity and diffusion.
6
Content available Investigation of waves generated in transversely isotropic micropolar generalized thermoelastic half space under temperature dependent properties
75%
Gupta R. R. , Gupta R. R.
International Journal of Applied Mechanics and Engineering
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2019
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tom Vol. 24, no. 4
53--65
EN
The present study deals with the propagation of waves in a transversely isotropic micropolar generalized thermoelastic material possessing temperature dependent elastic properties. After developing the solution for LS, GL and CT theory, the phase velocities and attenuation quality factor have been obtained. The expressions for amplitudes of stresses, displacements, microratation and temperature distribution have been derived and computed numerically. The numerically evaluated results have been plotted graphically. Some particular cases of interest have also been obtained.
7
Content available remote Deformation due to time harwortic source in orthotropic micropolar viscoelastic medium
75%
Kumar R. , Choudhary S.
International Journal of Applied Mechanics and Engineering
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2005
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tom Vol. 10, no 4
617-629
EN
The present study is concerned with the plane strain problem in a homogeneous orthotropic micropolar viscoelastic solid. The disturbance due to a time harmonic uniformly distributed source is investigated by employing the eigen-value approach. The integral transforms have been inverted by using a numerical technique to obtain the component of displacement, force stress and couple stress in the physical domain. The results of these quantities are given and illustrated graphically.
8
Content available Study of circular crested waves in a micropolar porous medium possessing cubic symmetry
75%
Kumar R. , Panchal M.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2011
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tom Vol. 59, nr 1
103-110
EN
The paper is concerned with the propagation of circular crested Lamb waves in a homogeneous micpropolar porous medium possessing cubic symmetry. The frequency equations, connecting the phase velocity with wave number and other material parameters, for symmetric as well as antisymmetric modes of wave propagation are derived. The amplitudes of displacement components, microrotation and volume fraction field are computed numerically. The numerical results obtained have been illustrated graphically to understand the behavior of phase velocity and attenuation coefficient versus wave number of a wave.
9
Content available remote Propagation of waves in a micropolar transversely isotropic generalized thermoelastic half-space
75%
Kumar R. , Gupta R. R.
International Journal of Applied Mechanics and Engineering
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2011
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tom Vol. 16, no 3
671-681
EN
Rayleigh waves in a half-space exhibiting microplar transversely isotropic generalized thermoelastic properties based on the Lord-Shulman (L-S), Green and Lindsay (G-L) and Coupled thermoelasticty (C-T) theories are discussed. The phase velocity and attenuation coefficient in the previous three different theories have been obtained. A comparison is carried out of phase velocity, attenuation coefficient and specific loss as calculated from the different theories of generalized thermoelasticity along with the comparison of anisotropy. The amplitudes of displacements, microrotation, stresses and temperature distribution are also obtained. The results obtained and the conclusions drawn are discussed numerically and illustrated graphically. Relevant results of previous investigations are deduced as special cases.
10
Content available remote Thermal Instability in a Rotating Micropolar Viscoelastic Fluid Layer Under the Effect of Electric Field
75%
Othman M. I. A. , Zaki S. A.
Mechanics and Mechanical Engineering
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2008
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tom Vol. 12, nr 2
171-184
EN
The problem of onset of convective instability in a dielectric micropolar viscoelastic fluid (Walters' liquid B') heated from below confined between two horizontal plates under the simultaneous action of the rotation of the system, vertical temperature gradient, one relaxation time and vertical electric field is considered. Linear stability theory is used to derive an eigenvalue of twelve order, and an exact eigenvalue equation for a neutral instability is obtained. Under somewhat artificial boundary conditions, this equation can be solved exactly to yield the eigenvalue relationship from which various critical values are determined in detail. Critical Rayleigh heat numbers and wave number for the onset of instability are presented graphically as a function of rotation at a certain value of the Prandtl number, for various values of the relaxation time, the Rayleigh electric number, the elastic parameter and micropolar parameters.
11
Content available remote Analysis of micropolar porous thermoelastic circular plate by eigenvalue approach
75%
Kumar R. , Miglani A. , Rani R.
Archives of Mechanics
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2016
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tom Vol. 68, nr 6
423--439
EN
The present paper examined a two-dimensional axi-symmetric problem of thick circular plate in a micropolar porous thermoelastic medium due to thermomechanical sources. An eigenvalue approach has been employed after applying the Laplace and Hankel transforms to investigate the problem. The expressions of displacements, stresses, microrotation, volume fraction field and temperature distribution are obtained in the transformed domain. A numerical inversion technique has been used to obtain the resulting quantities in the physical domain. The numerical simulated resulting quantities are shown graphically to depict the effects of thermal forces and porosity. Particular cases of interest are also studied and presented.
12
Content available Surface wave characteristics in a micropolar transversely isotropic halfspace underlying an inviscid liquid layer
75%
Gupta R. R. , Gupta R. R.
International Journal of Applied Mechanics and Engineering
|
2014
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tom Vol. 19, no. 1
49--60
EN
The present investigation deals with the propagation of waves in a micropolar transversely isotropic half space with an overlying inviscid fluid layer. Effects of fluid loading and anisotropy on the phase velocity, attenuation coefficient, specific loss and relative frequency shift. Finally, a numerical solution was carried out for aluminium epoxy material and the computer simulated results for the phase velocity, attenuation coefficient, specific loss and relative frequency shift are presented graphically. A particular case for the propagation of Rayleigh waves in a micropolar transversely isotropic half-space is deduced and dispersion curves are plotted for the same as functions of the wave number. An amplitude of displacements and microrotation together with the path of surface particles are also calculated for the propagation of Rayleigh waves in the latter case.
13
Content available remote Elastodynamics of time harmonic inclined load in micropolar thermoelastic medium possessing cubic symmetry
75%
Kumar R. , Ailawalia P.
International Journal of Applied Mechanics and Engineering
|
2007
|
tom Vol. 12, no 3
629-644
EN
The analytic expressions for the displacements, microrotation, stresses and temperature distribution on the free surface of a micropolar thermoelastic medium possessing cubic symmetry as a result of time harmonic inclined load have been obtained. The inclined load is assumed to be a linear combination of a normal load and a tangential load. The Fourierer transform has been employed to solve the problem. The variations of the displacements, microrotation, stresses and temperature distribution with the horizontal distance have been shown graphically.
14
Content available remote Axi-symmetric problem in a micropolar generalized thermoelastic half-space
75%
Kumar R. , Deswal S.
International Journal of Applied Mechanics and Engineering
|
2007
|
tom Vol. 12, no 2
413-429
EN
The disturbance due to mechanical and thermal sources in a homogeneous isotropic micropolar generalized thermoelastic half space is investigated by the use of Laplace-Hankel transform techniques. The integral transforms are inverted by using a numerical technique. The displacement components, temperature field, normal and tangential stresses are obtained in the physical domain for Lord-Shulman (L-S), Green-Lindsay (G-L) and Green-Naghdi (G-N) theońes of micropolar generalized thermoelasticity and are shown graphically for magnesium crystal like material.
15
Content available Refined multi-phase-lags theory and Thomson effect on a micropolar thermoelastic medium with voids
75%
Alharbi A. M. , Abd-Elaziz E. M. , Othman M. I. A.
Archives of Thermodynamics
|
2021
|
tom Vol. 42, no 3
279--309
EN
The problem considered is that of an isotropic, micropolar thermoelastic medium with voids subjected to the Thomson effect. The solution to the problem is presented in the context of the refined multiphase-lags theory of thermoelasticity. The normal mode analysis was used to obtain the analytical expressions of the considered variables. The nondimensional displacement, temperature, microrotation, the change in the volume fraction field and stress of the material are obtained and illustrated graphically. The variations of these quantities have been depicted graphically in the refined-phase-lag theory, Green and Naghdi theory of type II, Lord and Shulman theory and a coupled theory. The effects of the Thomson parameter and phase lag parameters on a homogeneous, isotropic, micropolar thermoelastic material with voids are revealed and discussed. Some particular cases of interest are deduced from the present investigation.
16
Content available remote Effects of viscosity with moving load at micropolar boundary surface
75%
Kumar R. , Ailawalia P.
International Journal of Applied Mechanics and Engineering
|
2005
|
tom Vol. 10, no 1
95-108
EN
The steady state response at viscous fluid/micropolar elastic solid interface to a moving point load has been studied for subsonic, supersonic and transonic load velocities. The Fourier transform has been used to solve the problem. The displacement, microrotation and stress components for a micropolar elastic solid so obtained in the physical domain are computed numerically by using the numerical inversion technique. Viscosity and micropolarity effects on the resulting expressions have been presented graphically for a specific material.
17
Content available Wave propagation in a micropolar transversely isotropic generalized thermoelastic half-space
75%
Gupta R. R.
International Journal of Applied Mechanics and Engineering
|
2014
|
tom Vol. 19, no. 2
247--257
EN
Rayleigh waves in a half-space exhibiting microplar transversely isotropic generalized thermoelastic properties based on the Lord-Shulman (L-S), Green and Lindsay (G-L) and Coupled thermoelasticty (C-T) theories are discussed. The phase velocity and attenuation coefficient in the previous three different theories have been obtained. A comparison is carried out of the phase velocity, attenuation coefficient and specific loss as calculated from the different theories of generalized thermoelasticity along with the comparison of anisotropy. The amplitudes of displacements, microrotation, stresses and temperature distribution were also obtained. The results obtained and the conclusions drawn are discussed numerically and illustrated graphically. Relevant results of previous investigations are deduced as special cases.
18
Content available On wave propagation in a random micropolar generalized thermoelastic medium
63%
Mitra M. , Bhattacharyya R. K.
Archives of Thermodynamics
|
2017
|
tom Vol. 38, no. 2
21--60
EN
This paper endeavours to study aspects of wave propagation in a random generalized-thermal micropolar elastic medium. The smooth perturbation technique conformable to stochastic differential equations has been employed. Six different types of waves propagate in the random medium. The dispersion equations have been derived. The effects due to random variations of micropolar elastic and generalized thermal parameters have been computed. Randomness causes change of phase speed and attenuation of waves. Attenuation coefficients for high frequency waves have been computed. Second moment properties have been briefly discussed with application to wave propagation in the random micropolar elastic medium. Integrals involving correlation functions have been transformed to radial forms. A special type of generalized thermo-mechanical auto-correlation functions has been used to approximately compute effects of random variations of parameters. Uncoupled problem has been briefly outlined.
19
Content available remote The effect of heat laser pulse on generalized thermoelasticity for micropolar medium
63%
Othman M. I. A. , Marin M.
Mechanics and Mechanical Engineering
|
2017
|
tom Vol. 21, nr 4
797--811
EN
We introduced the coupled theory, Lord-Schulman theory with one relaxation time and Green-Lindsay theory with two relaxation times to study the influence of thermal loading due to laser pulse on generalized micropolar thermoelasticity. The bounding plane surface is heated by a non-Gaussian laser beam with the pulse duration of 8 ps. The methodology applied here is the use of normal mode analysis to solve the problem of thermal loading due to laser pulse to obtain the exact expressions for the displacement components, force stresses, temperature, couple stresses and microrotation. The distributions of the considered variables are illustrated graphically. Comparisons are made with the results predicted by three theories in the presence of laser pulse and for different values of time.
20
Content available remote Inclined Load in Micropolar Thermoelastic Medium Possesing Cubic Symmetry with One Relaxation Time
63%
Kumar R. , Ailawalia P.
Mechanics and Mechanical Engineering
|
2007
|
tom Vol. 11, nr 1
129-157
EN
The analytic expressions for the displacements, microrotation, stresses and temperature distribution on the free surface of micropolar thermoelastic medium possessing cubic symmetry as a result of inclined load have been obtained. The inclined load is assumed to be a linear combination of a normal load and a tangential load. The Laplace and Fourier transforms have been employed to solve the problem. A special case of moving inclined load has been deduced by making the appropriate changes. The variations of the displacements, microrotation, stresses and temperature distribution with the horizontal distance have been shown graphically for both the problems.
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