Santimoy Kundu

PROPAGATION OF LOVE WAVE IN FIBER-REINFORCED MEDIUM OVER A NONHOMOGENEOUS HALF-SPACE

The present paper is devoted to study the Love wave propagation in a fiber-reinforced medium laying over a nonhomogeneous half-space. The upper layer is assumed as reinforced medium and we have taken exponential variation in both rigidity and density of lower half-space. As Mathematical tools the techniques of separation of variables and Whittaker function are applied to obtain the dispersion equation of Love wave in the assumed media. The dispersion equation has been investigated for three different cases. In a special case when both the media are homogeneous our computed equation coincides with the classical equation of Love wave. For graphical representation, we used MATLAB software to study the effects of reinforced parameters and inhomogeneity parameters. It has been observed that the phase velocity increases with the decreases of nondimensional wave number. We have also seen that the phase velocity decreases with the increase of reinforced parameters and inhomogeneity parameters. The results may be useful to understand the nature of seismic wave propagation in fiber reinforced medium.

Effect of Reinforcement and Inhomogeneity on the Propagation of Love Waves

AbstractThe aim of this paper is to investigate the propagation of Love waves in an anisotropic fiber-reinforced layer over an elastic inhomogeneous stratum. The inhomogeneity of the half-space has been taken as a linear variation of rigidity and density. The equations of motion have been formulated separately for layer and half-space under suitable boundary conditions. The frequency relation of phase velocity has been deduced in compact form using separation of variables by means of the Whittaker function. Some particular cases have also been investigated. As a special case when both the layer and half-space are homogeneous, the computed frequency relation coincides with the general equation of the Love wave. Numerical calculations of frequency relation have been performed for different values of parameters and plotted graphically to study the effect of different factors. The wave velocity is strongly influenced by the reinforcement and inhomogeneity parameters.

Propagation of Love-Type Wave in Porous Medium over an Orthotropic Semi-Infinite Medium with Rectangular Irregularity

Propagation of Love-type wave in an initially stressed porous medium over a semi-infinite orthotropic medium with the irregular interface has been studied. The method of separation of variables has been adopted to get the dispersion relation of Love-type wave. The irregularity is assumed to be rectangular at the interface of the layer and half-space. Finally, the dispersion relation of Love wave has been obtained in classical form. The presence of porosity, irregularity, and initial stress in the dispersion equation approves the significant effect of these parameters in the propagation of Love-type waves in porous medium bounded below by an orthotropic half-space. The scientific effect of porosity, irregularity, and initial stress in the phase velocity of the Love-type wave propagation has been studied and shown graphically.

Analysis of dispersion and absorption characteristics of shear waves in sinusoidally corrugated elastic medium with void pores

This theoretical work reports the dispersion and absorption characteristics of horizontally polarized shear wave (SH-wave) in a corrugated medium with void pores sandwiched between two dissimilar half-spaces. The dispersion and absorption equations have been derived in a closed form using the method of separation of variables. It has been established that there are two different kinds of wavefronts propagating in the proposed media. One of the wavefronts depends on the modulus of rigidity of elastic matrix of the medium and satisfies the dispersion equation of SH-waves. The second wavefront depends on the changes in volume fraction of the pores. Numerical computation of the obtained relations has been performed and the results are depicted graphically. The influence of corrugation, sandiness on the phase velocity and the damped velocity of SH-wave has been studied extensively.

Study of Rayleigh type surface wave in the initial stressed irregular bottom of ocean due to point source

Abstract Rayleigh type surface wave propagation in the irregular bottom of ocean model which is the interface of homogeneous liquid layer over laying an irregular boundary of homogeneous orthotropic half space under initial stresses has been discussed in this paper. Three different dispersion equations are obtained in the form of simple equation using and not using Perturbation technique. Some special cases have been considered. The effect of irregularity, initial stressed, point source, and depth of liquid layer on the propagation of Rayleigh waves has been analyzed and results of numerical discussion have been presented graphically for three different dispersion equations. Mainly the graphs are shown the variation of phase velocity with wave number in different cases.

Study of torsional wave in a poroelastic medium sandwiched between a layer and a half-space of heterogeneous dry sandy media

Abstract In this article, the propagation of torsional surface wave in an anisotropic poroelastic layer of finite thickness sandwiched between two heterogeneous dry sandy media is investigated. The first uppermost dry sandy medium is considered as a layer of finite thickness and the second one is considered as a lower half-space. The heterogeneities in both dry sandy media are assumed to arise due to quadratic variations in elastic moduli and mass densities. Whittaker’s functions and variable separable techniques have been taken into the application to calculate the interior deformations inside the assumed model; consequently, we obtain a closed form dispersion relation for the torsional wave using effective boundary conditions. Moreover, casewise dispersion equations for some particular aspects of the problem have been studied, which serve as the focal theme of the study. Some significant observations have been made by detailed numerical calculations and graphical visuals related to the effects of tensile and compressive initial stresses, sandy parameters, heterogeneity parameters, porosity parameter, and thickness ratio parameter on the phase velocity of the torsional wave.

Surface Wave Propagation in Inhomogeneous Liquid Layer over a Heterogeneous Anisotropic Elastic Half Space

The effect of the inhomogeneity and homogeneity on the dispersion of the Rayleigh-type surface waves in an inhomogeneous liquid layer over a heterogeneous transversely isotopic elastic half space has been discussed. The frequency equation is obtained. The dispersion curve of variation of phase velocity with the wave number is observed and depicted graphically. Also various particular cases have been considered.

Shear waves in magneto-elastic transversely isotropic (MTI) layer bonded between two heterogeneous elastic media

ABSTRACT This paper studies shear wave propagation in magneto-elastic transversely isotropic material, sandwiched between a layer and a half-space of heterogeneous elastic materials. Elastic constants of the layer and half-space are assumed to vary in a parabolic form with depth. Whittaker’s functions and variable separable techniques have been employed to calculate the interior deformations; consequently, we obtain a general dispersion relation for shear wave. Effects of various affecting parameters on phase velocity of shear wave are considered through some numerical examples. In addition, a comparative study has been carried out for three examples of sandwiched layer, namely Beryl, Magnesium and isotropic.

Love wave propagation in a heterogeneous orthotropic layer under initial stress lying over an inhomogeneous half-space

The present research work elucidates the characteristics of Love waves propagating through a prestressed non-homogeneous orthotropic medium overlying a heterogeneous half-space. It has been considered here that the properties of the layer vary in the direction of thickness with the help of suitable boundary conditions. The dispersion relation has been obtained by variable separable method. A special case has been undertaken in which due to homogeneity of half-space and layer, the dispersion relation satisfies the classical equation of Love waves. To show the nature of Love waves, dispersion curves have been plotted by taking variation in initial stress and inhomogeneities of layer and half-space. This problem may find its applications in various geophysical prospects.

Effect of surface wave propagation in a four-layered oceanic crust model

Dispersion of Rayleigh type surface wave propagation has been discussed in four-layered oceanic crust. It includes a sandy layer over a crystalline elastic half-space and over it there are two more layers—on the top inhomogeneous liquid layer and under it a liquid-saturated porous layer. Frequency equation is obtained in the form of determinant. The effects of the width of different layers as well as the inhomogeneity of liquid layer, sandiness of sandy layer on surface waves are depicted and shown graphically by considering all possible case of the particular model. Some special cases have been deduced, few special cases give the dispersion equation of Scholte wave and Stoneley wave, some of which have already been discussed elsewhere.