Kshitish Ch. Mistri

Normal load moving on magneto-elastic transversely isotropic half-space with irregular and hydrostatic initial stress

The present paper investigates the effect of initial stress, irregularity depth, irregularity factor and magneto-elastic coupling parameter on the dynamic response due to a normal moving load with constant velocity on the free surface of an irregular magneto-elastic transversely isotropic half-space under the state of hydrostatic initial stress. The expressions for normal stress and shear stress are obtained in closed form analytically. The considerable effect of initial stress, irregularity depth, irregularity factor and magneto-elastic coupling parameter on normal stress and shear stress are computed numerically and depicted by means of graphs. Moreover, comparative study highlighting the effect of various types of irregularity viz. rectangular irregularity, parabolic irregularity and no irregularity on the normal stress and shear stress is a key feature of the study.

Propagation of SH-wave in a corrugated viscous sandy layer sandwiched between two elastic half-spaces

Abstract The present paper attempts to investigate the effect of sandiness, corrugated boundary surfaces, heterogeneity, and gravity on phase velocity and attenuation of SH-wave propagating in a viscous sandy layer with corrugated upper and lower boundary surfaces sandwiched between an upper heterogeneous elastic half-space and lower viscoelastic half-space under gravity. Heterogeneity associated with the upper half-space is due to exponentially varying density which is a function of depth; but the rigidity is constant. The closed form of dispersion relation is established and found to be in complex form. Real part and imaginary part of the dispersion relation correspond to dispersion curve and attenuation curve, respectively. One of the salient points of present study is the use of DEBYE asymptotic expansion to establish that the obtained dispersion relation is in well-agreement with the classical Love wave equation in isotropic case. The effect of presence and absence of corrugated boundary surfaces, measured by initial flatness parameter, on dispersion and attenuation curves have been meticulously examined. Moreover, the substantial effect of heterogeneity, sandiness, internal friction, and Biot’s gravity parameter on phase velocity and attenuation coefficient of SH-wave has been studied and demonstrated by means of graphical illustration and numerical computations.

Effect of undulation on SH-wave propagation in corrugated magneto-elastic transversely isotropic layer

ABSTRACT This article delves to study the effect of corrugated boundary surfaces on the propagation of horizontally-polarized shear waves (SH-waves) in a magnetoelastic transversely isotropic layer under a hydrostatic state of stress lying over an elastic half-space under gravity. A dispersion equation has been derived in closed-form and is found to be in good agreement to the classical Love-wave equation. The effect of magnetoelasticity, hydrostatic state of stress, gravity, corrugation, position parameter, and undulation on the phase velocity of the SH-wave has been identified. Numerical computation along with graphical demonstration has been carried out for cadmium, magnesium, and zinc materials of hexagonal symmetry to highlight some significant facts.

Love-Type Wave Propagation in an Irregular Prestressed Composite Sandwiched Layer

AbstractThe present problem analytically investigates the possibility of Love-type wave propagation in a prestressed irregular composite layer lying between an upper prestressed heterogeneous isotropic layer of finite width and a lower prestressed isotropic half-space. The closed-form expression of dispersion relation has been deduced and matched with the classical Love wave equation as a special case of the problem for its authenticity. The effects of size of irregularity, heterogeneity parameter of the uppermost layer, width ratio of layers, and horizontal prestresses, present in each of the media, on the dispersion curve are the prime outcome of the study. A comparative study made between the case in which a composite medium is present as an irregular sandwiched layer and the case in which an isotropic medium is present as an irregular sandwiched layer is one of the major highlights of the problem. Moreover, numerical computations have been carried out and are depicted by means of graphs.

EFFECT OF LOOSE BONDING AND CORRUGATED BOUNDARY SUR-FACE ON PROPAGATION OF RAYLEIGH-TYPE WAVE

THE PROBLEMS CONCERNS TO THE PROPAGATION OF SURFACE WAVE PROPA-GATION THROUGH VARIOUS ANISOTROPIC MEDIUMS WITH INITIAL STRESS AND IRREGULAR BOUNDARIES ARE OF GREAT INTEREST TO SEISMOLOGISTS, DUE TO THEIR APPLICATIONS TOWARDS THE STABILITY OF THE MEDIUM. THE PRESENT PAPER DEALS WITH THE PROPAGATION OF RAYLEIGH-TYPE WAVE IN A CORRU-GATED FIBRE-REINFORCED LAYER LYING OVER AN INITIALLY STRESSED ORTHO-TROPIC HALF-SPACE UNDER GRAVITY. THE UPPER FREE SURFACE IS ASSUMED TO BE CORRUGATED; WHILE THE INTERFACE OF THE LAYER AND HALF-SPACE IS CORRUGATED AS WELL AS LOOSELY BONDED. THE FREQUENCY EQUATION IS DEDUCED IN CLOSED FORM. NUMERICAL COMPUTATION HAS BEEN CARRIED OUT WHICH AIDS TO PLOT THE DIMENSIONLESS PHASE VELOCITY AGAINST DIMENSIONLESS WAVE NUMBER FOR SAKE OF GRAPHICAL DEMONSTRATION. NUMERICAL RESULTS ANALYZE THE INFLUENCE OF CORRUGATION, LOOSE BOND-ING, INITIAL STRESS AND GRAVITY ON THE PHASE VELOCITY OF RAYLEIGH-TYPE WAVE. MOREOVER, THE PRESENCE AND ABSENCE OF CORRUGATION, LOOSE BONDING AND INITIAL STRESS IS ALSO DISCUSSED IN COMPARATIVE MANNER.

Effect of corrugation on the dispersion of Love-type wave in a layer with monoclinic symmetry, overlying an initially stressed transversely isotropic half-space

Purpose The purpose of this paper is to investigate the effect of corrugation, wave number, initial stress and the heterogeneity of the media on the phase velocity of the Love-type wave. Moreover, the paper aims to have a comparative study of the presence and absence of anisotropy, heterogeneity, corrugation and initial stress in the half-space, which serve as a focal theme of the study. Design/methodology/approach The present paper modelled the propagation of the Love-type wave in a corrugated heterogeneous monoclinic layer lying over an initially stressed heterogeneous transversely isotropic half-space. The method of separation of variables is used to procure the dispersion relation. Findings The closed form of dispersion relation is obtained and found to be in well agreement to the classical Love wave equation. Neglecting the corrugation at either of the boundary surfaces, expressions of the phase velocity of the Love-type wave are deduced in closed form as special cases of the problem. It is established through the numerical computation of the obtained relation that the concerned affecting parameters have significant impact on the phase velocity of the Love-type wave. Also, a comparative study shows that the anisotropic case favours more to the phase velocity as comparison to the isotropic case. Originality/value Although many attempts have been made to study the effect of corrugated boundaries on reflection and refraction of seismic waves, but the effect of corrugated boundaries on the dispersion of surface wave (which are dispersive in nature) propagating through mediums pertaining various incredible features still needs to be investigated.