Sumit Vishwakarma - Academia.edu (original) (raw)

Papers by Sumit Vishwakarma

Research paper thumbnail of Torsional wave propagation in Earth’s crustal layer under the influence of imperfect interface

Journal of Vibration and Control, 2012

In this paper, we study the propagation of a torsional surface wave in a homogeneous crustal laye... more In this paper, we study the propagation of a torsional surface wave in a homogeneous crustal layer over an initially stressed mantle with linearly varying directional rigidities, density and initial stress under the effect of an imperfect interface. Twelve different types of imperfect interface have been considered using triangular, rectangular and parabolic shapes. A variable separable technique is adopted for the theoretical derivations and analytical solutions are obtained for the dispersion relation by means of Whittaker function and its derivative. Dispersion equations are in perfect agreement with the standard results when derived for a particular case. The graph is self-explanatory and reveals that the phase velocity of a torsional surface wave depends not only on the wave number, initial stress, inhomogeneity and depth of the irregularity but also on the layer structure.

Research paper thumbnail of Influence of Rigid Boundary and Initial Stress on the Propagation of Love Wave

Applied Mathematics, 2011

In the present paper we study the effect of rigid boundary on the propagation of Love waves in an... more In the present paper we study the effect of rigid boundary on the propagation of Love waves in an inhomogeneous substratum over an initially stressed half space, where the heterogeneity is both in rigidity and density. The dispersion equation of the phase velocity has been derived. It has been found that the phase velocity of Love wave is considerably influenced by the rigid boundary, inhomogeneity and the initial stress present in the half space. The velocity of Love waves have been calculated numerically as a function of KH (where K is a wave number H is a thickness of the layer) and are presented in a number of graphs.

Research paper thumbnail of Mathematical Modeling of G type Seismic Waves in a Homogeneous Layer over a Transversely Isotropic Half-space under Initial Stress

 Abstract—In this paper an attempt has been made to study the propagation of G type seismic wave... more  Abstract—In this paper an attempt has been made to study the propagation of G type seismic waves in homogeneous layer overlying an elastic half space under initial stress. Here we have taken constant rigidity and density in upper layer and variation in elastic modulus in the lower transversely isotropic half space. We have obtained dispersion equations and the displacement of the wave. We have seen that initial stress has dominant effect on the propagation of G type wave. As a particular case dispersion equation coincides with that of Love wave. Dispersion curves are plotted for different variation in inhomogeneity parameters and initial stress parameters. Variation in group velocity against scaled wave number has shown for different values of initial stress parameters. Finally surface plots of group velocity have drawn with respect to wave number and depth parameter different values of initial

Research paper thumbnail of Propagation of Love waves in non-homogeneous substratum over initially stressed heterogeneous half-space

Applied Mathematics and Mechanics, 2013

The present paper deals with the generation of Love waves in a layer of finite thickness over an ... more The present paper deals with the generation of Love waves in a layer of finite thickness over an initially stressed heterogeneous semi-infinite media. The rigidity and density of the layer are functions of temperature, i.e. they are temperature dependent. The lower substratum is an initially stressed medium and its rigidity and density vary linearly with the depth. The frequency relation of Love waves has been acquired in compact form. Numerical calculations are accomplished and a number of graphs for nondimensional phase velocity versus non-dimensional wave number are plotted to display the influence of intrinsic parameters like initial stress and inhomogeneity factors on the generation of Love waves. It is initiated that the non-dimensional phase velocity of Love wave decreases with increase in the non-dimensional wave number and is strongly influenced by the initial stress of the substratum and the inhomogeneity factors of the layer and the substratum. This study may provide effective information in the field of industrial engineering, civil engineering as well as geophysics and seismology.

Research paper thumbnail of Propagation of P- and S-waves in initially stressed gravitating half space

Applied Mathematics and Mechanics, 2013

Research paper thumbnail of Torsional wave propagation in Earth’s crustal layer under the influence of imperfect interface

Journal of Vibration and Control, 2012

In this paper, we study the propagation of a torsional surface wave in a homogeneous crustal laye... more In this paper, we study the propagation of a torsional surface wave in a homogeneous crustal layer over an initially stressed mantle with linearly varying directional rigidities, density and initial stress under the effect of an imperfect interface. Twelve different types of imperfect interface have been considered using triangular, rectangular and parabolic shapes. A variable separable technique is adopted for the theoretical derivations and analytical solutions are obtained for the dispersion relation by means of Whittaker function and its derivative. Dispersion equations are in perfect agreement with the standard results when derived for a particular case. The graph is self-explanatory and reveals that the phase velocity of a torsional surface wave depends not only on the wave number, initial stress, inhomogeneity and depth of the irregularity but also on the layer structure.

Research paper thumbnail of Influence of Rigid Boundary and Initial Stress on the Propagation of Love Wave

Applied Mathematics, 2011

In the present paper we study the effect of rigid boundary on the propagation of Love waves in an... more In the present paper we study the effect of rigid boundary on the propagation of Love waves in an inhomogeneous substratum over an initially stressed half space, where the heterogeneity is both in rigidity and density. The dispersion equation of the phase velocity has been derived. It has been found that the phase velocity of Love wave is considerably influenced by the rigid boundary, inhomogeneity and the initial stress present in the half space. The velocity of Love waves have been calculated numerically as a function of KH (where K is a wave number H is a thickness of the layer) and are presented in a number of graphs.

Research paper thumbnail of Mathematical Modeling of G type Seismic Waves in a Homogeneous Layer over a Transversely Isotropic Half-space under Initial Stress

 Abstract—In this paper an attempt has been made to study the propagation of G type seismic wave... more  Abstract—In this paper an attempt has been made to study the propagation of G type seismic waves in homogeneous layer overlying an elastic half space under initial stress. Here we have taken constant rigidity and density in upper layer and variation in elastic modulus in the lower transversely isotropic half space. We have obtained dispersion equations and the displacement of the wave. We have seen that initial stress has dominant effect on the propagation of G type wave. As a particular case dispersion equation coincides with that of Love wave. Dispersion curves are plotted for different variation in inhomogeneity parameters and initial stress parameters. Variation in group velocity against scaled wave number has shown for different values of initial stress parameters. Finally surface plots of group velocity have drawn with respect to wave number and depth parameter different values of initial

Research paper thumbnail of Propagation of Love waves in non-homogeneous substratum over initially stressed heterogeneous half-space

Applied Mathematics and Mechanics, 2013

The present paper deals with the generation of Love waves in a layer of finite thickness over an ... more The present paper deals with the generation of Love waves in a layer of finite thickness over an initially stressed heterogeneous semi-infinite media. The rigidity and density of the layer are functions of temperature, i.e. they are temperature dependent. The lower substratum is an initially stressed medium and its rigidity and density vary linearly with the depth. The frequency relation of Love waves has been acquired in compact form. Numerical calculations are accomplished and a number of graphs for nondimensional phase velocity versus non-dimensional wave number are plotted to display the influence of intrinsic parameters like initial stress and inhomogeneity factors on the generation of Love waves. It is initiated that the non-dimensional phase velocity of Love wave decreases with increase in the non-dimensional wave number and is strongly influenced by the initial stress of the substratum and the inhomogeneity factors of the layer and the substratum. This study may provide effective information in the field of industrial engineering, civil engineering as well as geophysics and seismology.

Research paper thumbnail of Propagation of P- and S-waves in initially stressed gravitating half space

Applied Mathematics and Mechanics, 2013