Value Of Inhomogeneity Parameter Research Articles

Thermal stress analysis of functionally graded annular fin

Thermal stress distributions in an annular fin with rectangular profile made of functionally graded material (FGM) are considered. The material properties of annular fin are assumed to be graded along the fin radius as a power-law function while the Poisson’s ratio is taken to be constant. The governing equations are solved analytically for specific value of inhomogeneity parameter of thermal conductivity and all numerical values of inhomogeneity parameters of modulus of elasticity and linear thermal expansion coefficient. The effect of the inhomogeneity parameters on temperature distribution and thermal stresses are presented in graphical form. The formulation is validated with benchmark results in the literature. It is also shown that functionally graded annular fin is subject to lower stresses, although it has higher tip temperature than the homogeneous one.

Shear wave propagation in viscoelastic heterogeneous layers lying over an initially stressed half-space

ABSTRACTThe role of the present article is to study the propagation of horizontally polarized shear waves in vertically heterogeneous viscoelastic double layers lying over a homogeneous half-space under initial stress. Both linear and exponential variations have been considered in the inhomogeneity associated to rigidity, internal friction, and density of the media. The dispersion equation of shear waves has been obtained in closed form. The dimensionless phase and damping velocities have been plotted against dimensionless wave number for different values of inhomogeneity parameters separately. Also, surface plots of phase velocity against dimensionless wave number and inhomogeneity parameters have been given.

Propagation of SH waves in a visco-elastic layer overlying an inhomogeneous isotropic half-space

This paper is concerned with the propagation of SH-waves in an inhomogeneous viscoelastic layer overlying an inhomogeneous isotropic half-space. For the study of viscoelastic layer Kelvin–Voigt type model has been considered. The exponential type inhomogeneity is considered in viscoelastic layer with different parameters for viscoelastic part and for density of medium whereas for the half-space, it is quadratic type with single inhomogeneity parameter for rigidity and density. The solutions are obtained analytically for both the layer and half-space. Dispersion relation is obtained and subjected to continuity conditions at interfaces of viscoelastic layer and half-space and the upper boundary of layer as free surface. The effects of the inhomogeneity parameter are studied for both viscoelastic layer and inhomogeneous isotropic half-space. The numerical results are shown by plotting the graph between phase velocity and wave number for different values of inhomogeneity parameter and for the variation of depth of the layer.

Propagation of shear waves in viscoelastic heterogeneous layer overlying an initially stressed half space

The present paper is concerned with the propagation of shear waves in an isotropic, viscoelastic, heterogeneous layer lying over a homogeneous half space under initial stress. For the layer the inhomogeneity associated to rigidity, internal friction and density is assumed to be linear function of depth. The dispersion equation of shear waves has been obtained in closed form. The dimensionless phase velocity and damping velocity have been plotted against dimensionless wave number for different values of inhomogeneity parameter and initial stress. The effects of inhomogeneity and initial stress have been shown in the dispersion curves.

Analysis of gravity and non-homogeneity on Rayleigh wave in anisotropic elastic-viscoelastic half space of higher order

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.

Propagation of SH-type waves in inhomogeneous anisotropic layer overlying an anisotropic viscoelastic half-space

An analysis has been carried out for the propagation of SH-type waves in inhomogeneous anisotropic layer overlying anisotropic viscoelastic half-space of higher order. The dispersion relation is obtained under certain boundary conditions. The effects of inhomogeneity in elastic coefficients and density for the layer are studied. The numerical results are discussed through figures for a particular model by plotting the graph between phase velocity and wave number for different values of inhomogeneity parameters and thickness of layer. Keywords : SH-type waves, Anisotropic layer, Inhomogeneity, Viscoelastic coefficient, Phase velocity.

Propagation of Love waves in a heterogeneous medium over an inhomogeneous half-space under the effect of point source

The present paper deals with the effect of point source on the propagation of Love wave in a heterogeneous layer and inhomogeneous half-space. The upper heterogeneous layer is caused by consideration of exponential variation in rigidity and density. Also in half-space inhomogeneity parameters associated to rigidity, internal friction and density are assumed to be functions of depth. The dispersion equation of Love wave has been obtained by using Green’s function technique. As a special case when the upper layer and lower half-space are homogeneous, our computed equation coincides with the general equation of Love wave. The propagation of Love waves are influenced by inhomogeneity parameters. The dimensionless phase velocity has been plotted against the dimensionless wave number for different values of inhomogeneity parameters. We have observed that the velocity of wave increases with the increase of inhomogeneity parameters.

Propagation of G-type seismic waves in heterogeneous layer lying over an initially stressed heterogeneous half-space

The aim of present paper is to investigate the propagation of G-type seismic waves in a heterogeneous layer overlying a heterogeneous half-space under initial stress. Exponential variations in rigidity and density have been taken in the upper layer. In the lower half-space both rigidity and density are varying with depth. Dispersion equation has been obtained in closed form. Dispersion equation in case of homogeneous media coincides with the general equation of Love wave. Curves are plotted for different values of inhomogeneity parameters and initial stress parameter. We have seen that the phase velocity decreases with the increase of inhomogeneity parameters. It is observed that initial stress has dominant effect on the propagation of G-type wave. Variation in group velocity has shown for different values of initial stress parameter. We have also drawn surface plots of group velocity with respect to wave number and depth parameter for different values of initial stress parameter.

Torsional wave propagation in non‐homogeneous layer between non‐homogeneous half‐spaces

SUMMARYThe study of surface wave in a layered medium has their possible application in geophysical prospecting. In the present work, dispersion equation for torsional wave in an inhomogeneous isotropic layer between inhomogeneous isotropic half‐spaces has been derived. Two cases are discussed separately for torsional wave propagation in inhomogeneous layer between homogeneous and non‐homogeneous half‐spaces, respectively. Further, two possible modes for torsional wave propagation are obtained in case of inhomogeneous layer sandwiched between non‐homogeneous half‐spaces. Closed form solutions for displacement in the layer and half‐spaces are obtained in each case. The study reveals that the layer width, layer inhomogeneity, frequency of inhomogeneity, as well as inhomogeneity in the half‐space has significant effect on the propagation of torsional surface waves. Displacement and implicit dispersion equation for torsional wave velocities are expressed in terms of Heun functions and their derivatives. Effects of inhomogeneity on torsional wave velocity are also discussed graphically by plotting the dimensionless phase velocity against dimensionless and scaled wave number for different values of inhomogeneity parameter. Copyright © 2012 John Wiley & Sons, Ltd.

Effect of point source and heterogeneity on the propagation of SH-Waves in a viscoelastic layer over a viscoelastic half space

The present paper is concerned with the propagation of shear waves in a homogeneous viscoelastic isotropic layer lying over a semi-infinite heterogeneous viscoelastic isotropic half-space due to point source. The inhomogeneity parameters associated to rigidity, internal friction and density are assumed to be functions of depth. The dispersion equation of shear waves has been obtained using Green’s function technique. The dimensionless angular frequency has been plotted against dimensionless wave number for different values of inhomogeneity parameters. The effects of inhomogeneity have been shown in the dispersion curves. graphical user interface (GUI) software in MATLAB has been developed to show the effect of various inhomogeneity parameters on angular frequency. The topic can be of interest for geophysical applications in propagation of shear waves on the Earth’s crust.

Propagation of torsional waves in an inhomogeneous layer over an inhomogeneous half-space

The present paper is concerned with the study of propagation of torsional waves in an inhomogeneous isotropic layer whose material properties vary harmonically with a space variable, lying over a semi-infinite inhomogeneous isotropic half-space. The closed form solutions for the displacement in the layer and half-space are obtained separately. The dimensionless phase velocity has been plotted against dimensionless wave number and scaled wave number for different values of inhomogeneity parameters. The effects of inhomogeneity have been shown in the dispersion curves using 2D and 3D plot.

Electromagnetoelastic behaviors of functionally graded piezoelectric

Analytical studies on electromagnetoelastic behaviors are presented for the functionally graded piezoelectric material (FGPM) solid cylinder and sphere placed in a uniform magnetic field and subjected to the external pressure and electric loading. When the mechanical, electric and magnetic properties of the material obey an identical power law in the radial direction, the exact displacements, stresses, electric potentials and perturbations of magnetic field vector in the FGPM solid cylinder and sphere are obtained by using the infinitesimal theory of electromagnetoelasticity. Numerical examples also show the significant influence of material inhomogeneity. It is interesting to note that selecting a specific value of inhomogeneity parameter can optimize the electromagnetoelastic responses, which will be of particular importance in modern engineering designs.

Classical Hall transition and magnetoresistance in strongly inhomogeneous planar systems

The magneto-transport properties of planar and layered strongly inhomogeneous two-phase systems are investigated, using the explicit expressions for the effective conductivities and resistivities obtained by the exact dual transformation, connecting effective conductivities of in-plane isotropic two-phase systems with and without magnetic field. These expressions allow to describe the effective resistivity of various inhomogeneous media at arbitrary concentrations x and magnetic fields H. The corresponding plots of the x-dependence of the Hall constant R H ( x , H ) and the magnetoresistance R ( x , H ) are constructed for various values of magnetic field at some values of inhomogeneity parameters. These plots for strongly inhomogeneous systems at high magnetic fields show a sharp transition between partial Hall resistivities (or Hall conductivities) with different dependencies of R H on the phase concentrations. It is shown that there is a strong correlation between large linear magnetoresistance effect and this sharp Hall transition. Both these effects are a consequence of the exact duality symmetry. A possible physical explanation of these effects and their correlation is proposed.

Large linear magnetoresistivity in strongly inhomogeneous planar and layered systems

Explicit expressions for magnetoresistance R of planar and layered strongly inhomogeneous two-phase systems are obtained, using exact dual transformation, connecting effective conductivities of in-plane isotropic two-phase systems with and without magnetic field. These expressions allow to describe the magnetoresistance of various inhomogeneous media at arbitrary concentrations x and magnetic fields H. All expressions show large linear magnetoresistance effect with different dependencies on the phase concentrations. The corresponding plots of the x- and H-dependencies of R ( x , H ) are represented for various values, respectively, of magnetic field and concentrations at some values of inhomogeneity parameter. The obtained results show a remarkable similarity with the existing experimental data on linear magnetoresistance in silver chalcogenides Ag 2 + δ Se . A possible physical explanation of this similarity is proposed. It is shown that the random, stripe type, structures of inhomogeneities are the most suitable for a fabrication of magnetic sensors and a storage of information at room temperatures.