Amares Chattopadhyay

Propagation, reflection and transmission of magnetoelastic shear waves in a self-reinforced medium

Abstract The paper deals with the study of propagation reflection as well as transmission of magnetoelastic shear waves in a self-reinforced medium. The results have been computed taking two self-reinforced media one overlying another and presented graphically to compare with the reinforcement free cases.

Dispersion of horizontally polarized shear waves in an irregular non-homogeneous self-reinforced crustal layer over a semi-infinite self-reinforced medium

The present paper discusses the dispersion equation for horizontally polarized shear waves (SH waves) in a non-homogeneous self-reinforced layer over a semi infinite self-reinforced medium with an irregularity. The dispersion equation has been obtained in closed form. In the isotropic case, when non homogeneity and irregularity are absent, the dispersion equation reduces to standard SH wave equation. The dispersion curves have been presented by means of graphs for different sizes of irregularity and different values of non-homogeneity parameters. The influence of depth of irregularity and non-homogeneity parameters on phase velocity has been studied.

Love type waves in a porous layer with irregular interface

Abstract The dispersion equation is derived relating to the frequency and the phase velocity of propagation of Love waves in a nondissipative liquid filled porous solid underlain by an isotropic and homogeneous half space. The rectangular irregularity in the interface between the upper porous layer and the lower semi-infinite medium with a source in it is studied herein. The modified dispersion equation of Mal and the standard dispersion equation of Love waves are deduced as particular cases. In the present study, the frequency equation is obtained by applying the method of perturbation and the phase velocity curves have been drawn for different irregularities by using the numerical parameteric values as suggested by Biot.

Torsional Surface Waves in a Self-Reinforced Medium over a Heterogeneous Half Space

AbstractThis paper aims to study the dispersion of torsional surface waves in a self-reinforced layer over a half-space with linearly varying rigidity and density. Dispersion equation has been obtained in closed form. Dispersion relation for isotropic layer lying over a heterogeneous half-space has been deduced. As a result, the velocity equation for reinforced layer over a half-space of constant density has also been obtained. It has been observed that for isotropic upper layer over a homogeneous half-space, the velocity of torsional surface waves coincides with that of Love waves. This study shows that the increment in inhomogeneity decreases the phase velocity but the presence of reinforcement increases it significantly. Effects of different inhomogeneity parameters on the phase velocity have been depicted by means of graphs. Dispersion curves have been plotted for both reinforced and reinforcement free cases.

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 a crack due to magnetoelastic shear waves in a self-reinforced medium

This paper investigates the propagation of crack due to horizontally polarized shear waves in a magnetoelastic self-reinforced medium. The methodology includes the Weiner-Hopf technique. The effects of reinforcement and magnetic field on the propagation of the crack have been studied. The stress intensity factor at the crack tip for a concentrated force of a constant intensity has been calculated and depicted by means of graphs for various cases. It is observed that self-reinforcement increases the stress intensity factor whereas magnetoelastic coupling parameter has the reverse impact. It is remarkable to state that the stress intensity factor decreases with the increase in the length of crack. Also, the comparative study has been made through graphs to find the effect of reinforcement over the reinforced-free case on the stress intensity factor. Moreover, some important peculiarities have been observed in graphs.

Effect of Heterogeneity and Reinforcement on Propagation of a Crack due to Shear Waves

This paper investigates the effect of reinforcement and nonhomogeneity on the propagation of cracks caused by horizontally polarized shear waves in a heterogeneous fiber-reinforced medium. The effects of reinforcement and heterogeneity on the propagation of the crack are highlighted in this study. The stress intensity factor at the crack tip for a concentrated force of a constant intensity has been calculated and depicted by means of graphs for various cases. It is observed that fiber reinforcement and heterogeneity parameters decrease the stress intensity factor. Remarkably, the stress intensity factor decreases with the increase in the length and speed of the crack. Also, a comparative study was made for the stress intensity factor in reinforced medium over reinforced-free medium and heterogeneous medium over the homogeneous medium. Moreover, some important peculiarities were observed in graphs.

On the dispersion equation of Love waves in a porous layer

SummaryThe paper is concerned with the propagation of Love waves in a porous layer over an inhomogeneous half-space due to a point source. The dispersion equation for Love waves in a porous layer has been derived. The effects of porosity and inhomogeneity in the half-space have been shown graphically on the dispersion curves. The theory pointed out by Biot for the porous medium has been applied to solve the problem with the help of Greens function technique.

The reflection phenomena of P-waves in a medium of monoclinic type

Abstract In this paper, the reflection of P-waves at free and rigid boundaries in a medium of monoclinic type has been discussed. Rayleigh wave velocity and reflection coefficients have been computed. It has been observed that the Rayleigh wave velocity is significantly affected due to the crystalline nature of the medium. It is also observed that the reflection coefficients of P and SV waves at a free boundary of the crystalline medium is affected significantly when the angle of incidence is between 60 and 88°. The effect of monoclinic medium has been distinctly marked on the graphs.

Seismic Waves in Heterogeneous Crust-Mantle Layers under Initial Stresses

This article investigates the propagations of SH-waves and Rayleigh-type waves in a pre-stressed heterogeneous half-space and also Love-type waves in a pre-stressed heterogeneous layer overlying a pre-stressed heterogeneous half-space. Wave-velocity relations for SH-waves, Rayleigh-type waves, and dispersion equation for Love-type waves are derived. The results reflect that initial stress and inhomogeneity decrease the phase velocity of the SH-waves and Rayleigh-type waves. The phase and damping velocities of Love-type waves decrease with wave number, initial stress of the upper media, and inhomogeneity of the lower media, whereas they increase with initial stress of the lower media and inhomogeneity of the upper media.