Santanu Manna

The generalized continuous wavelet transform associated with the fractional Fourier transform

The main objective of this paper is to study the fractional Fourier transform (FrFT) and the generalized continuous wavelet transform and some of their basic properties. Applications of the FrFT in solving generalized nth-order linear nonhomogeneous ordinary differential equations and a generalized wave equation are given. The generalized continuous wavelet transform, and its inversion formula, and the Parseval relation are also studied using the fractional Fourier transform.

Love wave propagation in a piezoelectric layer overlying in an inhomogeneous elastic half-space

The present paper is devoted to study the propagation of Love wave in a piezoelectric layer overlying an inhomogeneous half-space. This paper deals with two different piezoelectric layers, one is an electrically open and another is an electrically short circuit. As mathematical tools, the method of separation of variables and Whittaker’s function are applied to obtain the dispersion equation of Love wave. In a particular case the dispersion equation reduces to the classical equation of Love wave when the layer is not piezoelectric and half-space is homogeneous. The numerical values of the dimensionless phase velocities are calculated and presented graphically to illustrate the effects of inhomogeneity, piezoelectricity and dielectric constants. It is observed that the phase velocities decrease with the increase of inhomogeneity parameters and electricity constant. It is also found that the phase velocity increases with the increases of the dielectric constant. Graphical user interface software has been developed by using MATLAB software to generalize the effect of various 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.

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.

Propagation of a torsional surface wave in a non-homogeneous anisotropic layer over a heterogeneous half-space

This paper aims to study the dispersion of torsional surface waves in a non-homogeneous anisotropic layer over heterogeneous half-space. We consider the inhomogeneity varies exponentially with depth in the layer and in half-space three types of heterogeneities, namely, quadratic, hyperbolic and exponential are assumed. The dispersion equation has been deducted for each case in a closed form by means of variable separable method. It has been observed that for homogeneous isotropic upper layer over a homogeneous half-space, the velocity of torsional surface waves coincides with that of Love waves. Dispersion curves are plotted for different variation in inhomogeneity parameters. The effects of the medium characteristics on the propagation of torsional surface waves are discussed.

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.

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.

Influence of Initial Stress and Inhomogeneity on Propagation of Torsional Type Surface Wave in a Crustal Layer

AbstractThis article explores the propagation of torsional type surface waves in an initially stressed inhomogeneous layer of finite thickness lying over an inhomogeneous half-space. Inhomogeneity in this layer is caused by hyperbolic variation in directional rigidities, density, and initial stress. Inhomogeneity in the half-space is caused by linear variation in rigidity and density. The inhomogeneity parameter and the initial stress play major roles in the propagation of torsional type surface waves. This research derives the dispersion relation of the phase velocity in a concrete form using separation of variables and numerically calculates the velocities of torsional type waves as a function of dimensionless wave number.

Influence of initial stress and gravity on torsional surface wave in heterogeneous medium

The present paper investigates the effect of gravity and initial stress on the propagation of torsional surface waves in heterogeneous medium. The dispersion equation has been obtained for rigid and traction free boundaries in terms of Whittaker function. The present study reveals that torsional surface waves can propagate in both the cases. In this paper, we assume the expansion of Whittaker function up to linear term. It is observed that, in presence of initial stress and gravity for both rigid and traction free boundary, the phase velocity of torsional surface waves increases with the growth of rigidity. In both the cases, it has also been noticed that as the gravity increases, the phase velocity of the torsional surface waves decreases in presence of heterogeneity and initial stress. It is concluded that in presence of traction free boundary, the phase velocity of the torsional surface waves is more than the rigid boundary.