Shishir Gupta

Torsional surface waves in nonhomogeneous and anisotropic medium

The paper discusses the possibility of propagation of torsional surface waves in (i) a nonhomogeneous elastic medium with polynomial variation of rigidity and density, (ii) exponential variation of rigidity with constant density, and (iii) exponential variation of both rigidity and density. It is also shown that homogeneous isotropic and anisotropic media will not allow torsional surface waves to propagate but some types of inhomogeneity in the rigidity and density in the medium allow such propagation. It is also observed that in certain types of nonhomogeneity there may be two torsional wavefronts.

Propagation of Torsional Surface Waves in Dry Sandy Medium under Gravity

This paper studies the possibility of propagation of torsional surface waves in a gravitating earth with a dry sandy medium. The mathematical analysis of the problem has been dealt with in the Whittaker function. Assuming the expansion of the Whittaker function to linear terms, it is concluded that the gravity field will always allow torsional waves to propagate. The expansion of the Whittaker function to quadratic terms shows that two such wave fronts may exist. Finally, it is concluded that the sandy medium without support of a gravity field cannot allow the propagation of torsional surface waves, whereas the presence of a gravity field always supports the propagation of torsional surface waves regardless of whether the medium is elastic or dry sandy.

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 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.

Behavior of Rayleigh surface waves in an anisotropic media lying over a prestressed orthotropic half-space

ABSTRACT The present paper discusses the propagation of Rayleigh waves in an anisotropic layer with finite thickness lying over a prestressed orthotropic half-space. An anisotropic media and orthotropic media are supposed for the upper layer and lower half-space, respectively. Dispersion equation and displacement components are computed in a compact form considering the case that the displacement and stress are continuous at the interface and stress vanishes on a free surface. Graphs are sketched to represent the effect of density, initial stress and height of the layer on wave velocity. The graphs are also configured to exhibit the mode of propagation of Rayleigh waves. This paper is an attempt to explain the nature of Rayleigh waves mathematically.

A comparative analysis (real-time data and theoretical results) for propagation of SH waves in a viscoelastic model influenced by a point source

The propagation of SH waves in a heterogeneous viscoelastic layer lying over a heterogeneous viscoelastic half space from a point source is examined analytically. The significance of the heterogeneity of hyperbolic and exponential variations associated with rigidity, viscosity, and density is investigated mathematically. A dispersion equation and displacement components are computed in a compact form, considering the case that displacement and stress are continuous at the interface and stress vanishes on a free surface. The acquired dispersion equation signifies the relation between phase velocity and dimensionless wavenumber. The dispersion equation is highly influenced by heterogeneous parameters of both the layer and the half space. The dispersion equation is reduced to the classical equation of the Love wave after eliminating all the heterogeneous parameters, in agreement with pre-established results. The analysis uses the technique of Fourier transformation and Green’s function. The wavenumber is supposed to be complex, as the frequency is fixed in the viscoelastic model. Graphs are presented to demonstrate the effect of heterogeneous parameters on phase and damping velocity with respect to wavenumber.

Study of the surface wave vibrations in a functionally graded material layered structure: a WKB method

In this paper, a theoretical investigation is described of the propagation behaviour of Love-type waves in a functionally graded material layered structure. The Wentzel–Kramers–Brillouin (WKB) method was applied to obtain the analytical solution for the functionally graded material layer. The study was carried out to investigate the transference of Love-type waves in a functionally graded material layer bounded by a viscous fluid layer and a highly anisotropic half-space. Two cases were studied, one in which the material property variation of the functionally graded material layer was arbitrary and one in which the material property variation was taken as exponential. A variable separation method was employed to obtain the displacement components in both the viscous liquid and the highly anisotropic medium. Profound effects of material gradient coefficient, viscous coefficient, liquid mass density, initial stress parameter and wavelength on real and imaginary components of phase velocities were established. Some numerical calculations were also made. The considered model facilitates a theoretical foundation and practical application for the development of surface acoustic wave devices.

Effect of dry sandiness parameter and initial stress on the scattering of plane SH wave

The present paper is incorporated into a mathematical model of transmission and reflection of shear waves through the initially stressed dry sandy medium sandwiched between two initially stressed distinct orthotropic half-spaces. The formulae of transmission and reflection coefficients have been deduced for the propagation of SH waves in the described model subjected to certain boundary conditions applying Snell’s law and Cramer’s method. These coefficients are observed as a function of wave number, phase velocity, initial stress, rigidity, and dry sandiness coefficients. The concepts of energy partition, phase shift, conservation of energy, critical angle, and slowness section are introduced. Graphical approach has been carried out to accomplish a relation between reflection/refraction coefficient, phase shift, and energy ratio with an angle of incidence and wave number on the propagation of shear wave. The study reveals that sandiness parameter, initial stress, and wave number have a cogent respond to the scattering of shear wave that has been illustrated graphically.

The study of reflection/transmission phenomena in a corrugated interface between two magnetoelastic transversely isotropic media

In this paper, an integrated approach has been carried out with an intent to study the reflection and transmission phenomena of plane SH-type wave on a corrugated interface separating two magnetoelastic transversely isotropic half-space. Closed form expressions for reflection and transmission coefficients have been derived for both plane and corrugated surface. Rayleigh’s method of approximation have been incorporated to deduce equations for the first- and second-order approximation of corrugation. Analytical solutions for both the half-spaces have been worked out. All possible cases have been apprehended specially for anisotropic and an isotropic medium. The effects of magnetoelastic coupling parameter, angle at which the wave crosses the magnetic field, corrugation amplitude, frequency factor and wave number have been explained by collaborating with graphical analysis.

SH-wave in a multilayered orthotropic crust under initial stress: A finite difference approach

The present work examines the finite difference modeling of SH-wave in a multilayered orthotropic crust to perceive the stability criterion and dispersion equation. The dispersion equation, for the case when layers underlying the earth or along its surface, is obtained in a standard form. This paper actually assigns to apply the finite difference method in seismic wave propagation. The phase and group velocity are retrieved utilizing the techniques of finite difference method. For the occurrence of SH-wave propagation, stability conditions are constituted applying the technique of finite difference method in time and space. The graphs are produced to comprehend the concepts of dispersion equation, group velocity, and phase velocity.