DIPS Polytechnic College

India

DIPS Polytechnic College

India

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Kakar R.,DIPS Polytechnic College
20th International Congress on Sound and Vibration 2013, ICSV 2013 | Year: 2013

The effect of magnetic field on torsional waves propagating in non-homogeneous viscoelastic cylindrically aeolotropic material is discussed. The elastic constants and non-homogeneity in viscoelastic medium in terms of density and elastic constant is taken. Bessel functions are taken to solve the problem and frequency equations have been derived in the form of a determinant. Dispersion equation in each case has been derived and the graphs have been plotted showing the effect of Variation of elastic constants and the presence of magnetic field. The obtained dispersion equations are in agreement with the classical result. The numerical calculations have been presented graphically by using MATLAB.


This study is concerned to check the validity and applicability of a five parameter viscoelastic model for harmonic wave propagating in the non-homogeneous viscoelastic rods of varying density. The constitutive relation for five parameter model is first developed and validity of these relations is checked. The non-homogeneous viscoelastic rods are assumed to be initially unstressed and at rest. In this study, it is assumed that density, rigidity and viscosity of the specimen i.e. rod are space dependent. The method of non-linear partial differential equation (Eikonal equation) has been used for finding the dispersion equation of harmonic waves in the rods. A method for treating reflection at the free end of the finite non-homogeneous viscoelastic rod is also presented. All the cases taken in this study are discussed numerically and graphically with MATLAB. © 2013 IAU, Arak Branch.


Kakar R.,DIPS Polytechnic College | Kakar S.,SBBSIET
Multidiscipline Modeling in Materials and Structures | Year: 2014

Purpose - This purpose of this paper is to discuss certain aspects of five-parameter viscoelastic models to study harmonic waves in the non-homogeneous polymer rods of varying density. There are two sections of this paper, in first section, the rheological behaviour of the model is discussed numerically and then it is solved analytically with the help of Friedlander Series using Eikonal equation of optics. In another section, the applicability of the developed model is studied through harmonic wave propagation in polymer non-homogeneous rods. The authors have used linear partial differential equations for finding the dispersion equation of harmonic waves in the polymers. All the cases taken in this study are discussed analytically and numerically with MATLAB. Design/methodology/approach - A five-parameter viscoelastic model constituting of three dash-pots D2(η2), D 2'(η2'), D3(η3) and two springs S1(G1), S2(G2) is considered. Where, G1, G2 are the modulli of elasticity and η2, η2', η3 are the Newtonian viscosity coefficients of the considered model, respectively. The parameters of the model are non-homogeneous in nature, i.e. module of elasticity and viscosity coefficients are space dependent. 1D problem is formed by taking the material in the form of rod of inhomogeneous polymer material by taking one end at x=0. The co-ordinate x is measured positive in the direction of the axis of the filament. Findings - When the density, rigidity and viscosity all are equal for the first material specimen, the sound speed is constant, i.e. non-homogeneous has no effect on speed and phase of the wave is given. So it becomes the case of semi non-homogeneous medium (a medium when characteristics are space dependent while the speed is independent of space variable). The use of five-parameter models is mostly restricted in the field of rock mechanics. Thus, these models can be used in determining the time-dependent behaviour of a polymer medium. Originality/value - The paper is original and it is not published elsewhere. Copyright © 2014 Emerald Group Publishing Limited. All rights reserved.


Kakar R.,DIPS Polytechnic College
Journal of Solid Mechanics | Year: 2012

The propagation of torsional waves in a prestressed fiber-reinforced half-space under the effect of magnetic field and gravity has been discussed. The problem has been solved analytically using Whittaker function to obtain the exact solution frequency equations. Numerical results for stress, gravity and magnetic field are given and illustrated graphically. Comparisons are made with the results predicted by the boundary value condition for rigid boundary and for traction free boundary in the presence and in the absence of the effect of a magnetic field, gravity and stress. It is found that the reinforcement, gravity and magnetic field have great effects on the distribution. © 2012 IAU, Arak Branch.


Kakar R.,DIPS Polytechnic College
Latin American Journal of Solids and Structures | Year: 2013

This study examines the effect of electric and magnetic field on torsional waves in hetrogeneous viscoelastic cylindrically aeolotropic tube subjected to initial compression stresses. A new equation of motion and phase velocity of torsional waves propagating in cylindrically aeolotropic tube subjected to initial compression stresses, nonhomogeneity, electric and magnetic field have been derived. The study reveals that the initial stresses, nonhomogeneity, electric and magnetic field present in the aeolotropic tube of viscoelastic solid have a notable effect on the propagation of torsional waves. The results have been discussed graphically. This investigation is very significant for potential application in various fields of science such as detection of mechanical explosions in the interior of the earth.


Kakar R.,DIPS Polytechnic College | Gupta M.,MM University
Electronic Journal of Geotechnical Engineering | Year: 2014

In this paper we investigate the existence of Love waves in an intermediate heterogeneous layer placed in between homogeneous and inhomogeneous half-spaces. The dispersion relation for propagation of said waves is derived with Green's function method and Fourier transform. As a special case when the intermediate layer and lower half-space are homogeneous, our derived equation is in agreement with the general equation of Love wave. Numerically, it is observed that the velocity of Loves wave increases with the increase of inhomogeneity parameter. © 2014 ejge.


Kakar R.,DIPS Polytechnic College | Kaur K.,DIPS Polytechnic College
20th International Congress on Sound and Vibration 2013, ICSV 2013 | Year: 2013

The aim of this paper is to present a dynamic non-linear viscoelastic model which is useful to explain the essential characteristics of the dynamic soils behavior. The strain dependency and damping capacity of the soil is useful for a reliable prediction of the seismic response. With the help of this model the damping functions in terms of both strain and frequency are obtained. The model validity is checked for constitutive dynamic functions from experimental data.


Kakar R.,DIPS Polytechnic College
Journal of Solid Mechanics | Year: 2013

An approximation technique is considered for computing transmission and reflection coefficients for propagation of an elastic pulse through a planar slab of finite width. The propagation of elastic pulse through a planar slab is derived from first principles using straightforward time-dependent method. The paper ends with calculations of enhancement factor for the elastic plane wave and it is shown that it depends on the velocity ratio of the wave in two different media but not the incident wave form. The result, valid for quite arbitrary incident pulses and quite arbitrary slab inhomogeneities, agrees with that obtained by time-independent methods, but uses more elementary methods. © 2013 IAU, Arak Branch.


Kakar R.,DIPS Polytechnic College
Multidiscipline Modeling in Materials and Structures | Year: 2015

Purpose - The purpose of this paper is to illustrate the propagation of Rayleigh waves in an anisotropic inhomogeneous layer placed over an isotropic gravitational viscoelastic half space of third order. Design/methodology/approach - It is considered that the mass density and the elastic coefficients of the layer are space dependent. Dispersion properties of waves are derived with the simple mathematical techniques. Graphs are plotted between phase velocity 'k' and wave number 'c' for different values of inhomogeneity parameters for a particular model and the effects of inhomogeneity and gravity are studied. Findings - The wave analysis indicates that the phase velocity of Rayleigh waves is affected quite remarkably by the presence of inhomogeneity, gravity and strain rates of strain parameters in the half space. The effects of inhomogeneity and depth on the phase velocity are also shown in corresponding figures. Originality/value - The results presented in this study may be attractive and useful for mathematicians, seismologists and geologists. © 2015 Emerald Group Publishing Limited.


Kakar R.,DIPS Polytechnic College | Kakar S.,SBBSIET
Geomechanics and Engineering | Year: 2014

The effect of various parameters on the propagation of surface waves in electro-magneto thermoelastic orthotropic granular non-homogeneous medium subjected to gravity and initial compression has been studied. All material coefficients are obeyed the same exponent-law dependence on the depth of the granular elastic half space. Some special cases investigated by earlier researchers have also been deduced. Dispersion curves are computed numerically and presented graphically. © 2014 Techno-Press, Ltd.

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