Sudarshan Dhua

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.

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.

Quasi-P and quasi-S waves in a self–reinforced medium under initial stresses and under gravity

The present paper is concerned with the propagation of plane waves in self–reinforced media. The velocities of quasi-P and quasi-S waves in an unbounded self–reinforced medium under initial stresses and under gravity field have been derived. Also the reflection coefficients and the partition of energy of reflected quasi-P and quasi-SV waves due to incident quasi-P and quasi-SV waves have been obtained under the influence of initial stress and gravity field. It has been noticed that the velocities, reflection coefficients and energy coefficients not only depend on the initial stress and gravity but also on the direction of propagation. The results are in agreement with the classical case in the absence of initial stresses and gravity. In presence of initial stresses and gravity field, the velocities, reflection coefficients and energy coefficients of quasi-P and quasi-S waves are calculated numerically and are presented by means of graphs.

Propagation of torsional wave in a composite layer overlying an anisotropic heterogeneous half-space with initial stress

In this paper we have discussed the propagation of torsional wave in a composite layer overlying an anisotropic heterogeneous half space with initial stress. The method of separation of variables is applied to find the dispersion equation. Numerical results analyzing the dispersion equation are discussed and presented by means of graphs. The effect of reinforcement, inhomogeneity parameter and the initial stress on the propagation of torsional surface wave is the main objective in our study. It has been observed that the directional rigidities of the half space have a favoring effect on the phase velocity, whereas the density and initial stress parameter in the half-space have the adverse effect on the velocity of torsional surface wave. It is remarkable to quote that reinforcement prevails in the medium, the phase velocity increases significantly.

Reflection and Refraction for Three-Dimensional Plane Waves at the Interface between Distinct Anisotropic Half-Spaces under Initial Stresses

AbstractThis paper deals with the reflection and refraction (transmission) phenomena that result from a three-dimensional plane-wave incident at the plane interface between two distinct triclinic media under the influence of initial stresses. Analytical expressions of all the phase velocities of reflected and transmitted quasi-compressional qP and quasi-shear waves qS1 and qS2 (or qSV and qSH) under initial stresses were obtained. Closed-form expressions for the amplitude ratios or reflection and refraction coefficients of the three quasi-waves were derived for suitable boundary conditions. It has been shown that reflection and transmission coefficients depend on the angle of incidence, the material constants, and the initial stresses present in the media. For numerical discussion, the variations of reflection and transmission coefficients with the initial stresses and angle of incidence are presented by means of graphs using mathematical software. Some particular remarkable cases are also considered.

Propagation of surface wave in a fluid layer overlying a slightly compressible, finitely deformed elastic medium

In this paper the dispersion relation of surface wave for a fluid layer overlying a slightly compressible, finitely deformed half-space is discussed. It has been observed that as the wave number tends to zero the dispersion relation transformed to the speed equation of surface waves. For graphical representation we have considered Neo-Hookean form of strain energy function. Phase speed curves have been plotted and different discussions have been made.

Reflection of Three-Dimensional Plane Waves in a Self-Reinforced Medium under Initial Stresses

AbstractThe present paper deals with the reflection of three-dimensional plane waves at a traction-free boundary of a self-reinforced medium under initial stresses. The analytical expressions of all three phase velocities of quasi-compressional (qP), quasi-shear (qS1 and qS2) waves in three dimensions under initial stresses have been obtained. The closed form expressions for the amplitude ratios of reflection coefficients of the three quasi waves in a self-reinforced medium in terms of the phase velocity, propagation vector, initial stresses, and the stiffness coefficients of the medium have also been obtained. The variations of reflected coefficients with the angle of incidence have been carried out numerically, and the results are given in the form of graphs.

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.

Wave propagation in heterogeneous layers of the Earth

Abstract This paper represents the analytical and numerical study of the propagation of horizontally polarized shear wave in two inhomogeneous layers lying over an isotropic homogeneous semi-infinite elastic medium. The inhomogeneity of the upper layer is caused by the exponential variation of rigidity and density with the depth, whereas the second layer exhibits inhomogeneity due to quadratic variation in rigidity of the medium. The dispersion relation has been obtained in closed form using Debye asymptotic expansion which is the major highlight of this study. The comparative study and some important peculiarities have been revealed by means of graphical illustrations.

Effects of Anisotropy, Initial Stress, Heterogeneity, and Gravity on Torsional Wave Propagation

AbstractThe present paper provides the results of a study of the propagation of torsional surface waves in an initially stressed self-reinforced layer lying over a dry sandy Gibson half-space in the presence of initial stress and gravity. The closed-form dispersion relation was obtained analytically. The influences of initial stress, reinforcement, inhomogeneity, gravity, and sandy parameter on the torsional wave were investigated by plotting the dispersion curves. It was observed that the rigidities, initial stress, and sandy parameter of the half-space have a favoring effect on the phase velocity, whereas gravity has the reverse effect on the velocity of the torsional surface wave. It also was noted that as reinforcement increased in the medium, the phase velocity also increased significantly.