Pato Kumari

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.

Modeling of magnetoelastic shear waves due to point source in a viscoelastic crustal layer over an inhomogeneous viscoelastic half space

In the present study, propagation of magnetoelastic shear wave due to a momentary point source in a viscoelastic crustal layer over inhomogeneous viscoelastic half space has been discussed. Green’s function technique and Fourier transform along with method of successive approximation are used to find the closed-form solutions for displacement and generalized shear wave period equation. Attenuation of the resultant shear wave is computed and effects of magnetic field, width of the layer, complex wave number, viscosity, and inhomogeneity parameters are distinctly marked on dissipation curves using two-dimensional and surface plots. It is found that effect of layer’s magnetoelastic coupling parameter on attenuation pattern of shear wave is just the reverse of half space magnetoelastic coupling parameter. Similarly, internal friction of layer has somewhat different effect on shear wave angular frequency than lower half space viscosity. Certain published results are also derived as special cases to the present study.

Reflection and refraction at the interface between distinct generally anisotropic half spaces for three-dimensional plane quasi-P waves

In this paper, reflection and refraction phenomena are studied for a three-dimensional plane quasi-P wave incident at the interface between distinct triclinic half spaces. A method has been developed to find the analytical expressions of all the phase velocities of reflected and transmitted quasi-P (qP), quasi-SV (qSV), and quasi-SH (qSH) waves. Closed form expressions for the amplitude ratios of reflection and transmission coefficients of qP, qSV, and qSH waves are also obtained. These expressions are computed numerically for a given set of data and the velocity distributions and variation of reflection and transmission coefficients with polar and azimuthal angle of incidence are shown graphically using two-dimensional single and double axes graphs. Surface plots of velocity variations of different reflected and transmitted waves are drawn to analyze the combined effect of incident polar and azimuthal angle on velocity distribution. Numerical results presented indicate that anisotropy effects on the reflection and transmission coefficients are significantly different in the three-dimensional case compared to the two-dimensional case. Certain published work has been derived as special cases to illustrate the present technique. Software in MATLAB has been designed to analyze the reflection/transmission phenomena with present geometry in simpler elastic media, such as monoclinic, transversely isotropic, isotropic, etc.

Reflection/refraction pattern of quasi-(P/SV) waves in dissimilar monoclinic media separated with finite isotropic layer

This paper concentrates on the study of reflection and refraction of incident quasi (P/SV) waves in dissimilar monoclinic media separated by an isotropic layer of finite thickness. It is shown that incident quasi waves at lower interface generates two reflected quasi waves and two transmitted purely longitudinal and transversal waves; these transmitted waves further give rise to reflected and transmitted waves at the upper interface. A closed form solution for velocity profile and reflection/transmission coefficients for all reflected/refracted waves are obtained along with numerical simulation showing the effect of incident angle, layer width, elastic coefficients and the nature of the incident quasi (P/SV) wave. Findings of the present problem show that reflection and refraction of quasi waves at layered interface sandwiched between different monoclinic media may be useful in signal processing, sound system and wireless communication, piezoelectric sensors, and motion detectors, in addition to improving surface acoustic wave devices and defense equipment.

Torsional Wave in a Viscoelastic Layer over a Viscoelastic Substratum of Voigt Types

This article explores the dissipation and dispersion of torsional wave resulting from imperfection in elasticity in terms of internal friction, layer width between dissimilar homogeneous viscoelastic isotropic medium having Voigt-type viscosity. The closed forms solutions for the displacement in the upper layer and lower half space are obtained separately. The generalized torsional wave period equation is obtained and the angular frequency has been plotted against wave number for different values of relevant parametric variation and certain particular cases have been deduced. Dissipation and dispersion are analysed using two and three dimensional plots along with filled contour plots.

Dynamic response of normal moving load on a transversely isotropic piezoelectric half-space with parabolic irregularity

Abstract Due to unique electro-mechanical behavior, piezoelectric devices are being used in important sensors (mostly based on surface acoustic waves) and other devices of vital importance and therefore exposed to dynamic loading. These devices often work in geological conditions possessing irregular free surface and subject to external moving load. Present study contributes a theoretical framework to study the stresses produced on such devices due to moving load exerted by operating environment or other situational scenario. In present manuscript, authors have investigated the dynamic response of normal moving load in a piezoelectric transversely isotropic half-space with parabolic irregularity. Closed form solutions for the normal stress, shear stress, and dielectric displacement for both the cases of electrically open and electrically short circuit have been found analytically. This study examines in detail the effect of frictional coefficients, depth of the parabolic irregularity, irregularity parameter, and ground depth on dielectric displacement and magnitude of resultant stresses. Many particular cases have been investigated and compared with numerical simulation along with graphical demonstration of observed results.

Torsional surface wave propagation in viscoelastic isotropic layer sandwiched between inhomogeneous half spaces

Present work deals with torsional surface wave propagation in a viscoelastic isotropic layer with Voigt type viscosity sandwiched between inhomogeneous half spaces. Exponential variation in rigidity and density is taken in the upper half space, whereas inhomogeneities in the lower half space associated with rigidity and density are assumed to follow linear variation. Displacement components in the viscoelastic layer, upper and lower half spaces are found in closed form and used to derive the dispersion and absorption relations for torsional wave under the assumed geometry in terms of generalized implicit function. The effects of inhomogeneity, viscosity parameters and dimensionless wave number have been explored in numerical section and explained by suitable graphs.