Self-reinforced Medium Research Articles

Analytical solution for diffraction of magnetoelastic plane waves by a rigid strip in self-reinforced medium: a contour integration method

This study analytically addresses the diffraction of magnetoelastic plane waves by a rigid strip in a self-reinforced infinite elastic medium. Formulation of the studied model includes mixed type boundary value problem and has been solved by the method of integral equation. The expressions of vertical diffracted displacement and normal stress are established in the closed form by employing the contour integration technique. For the sake of validation, the deduced expressions of vertical diffracted displacement and normal stress are reduced to the special cases, such as without magnetoelastic coupling as well as anisotropy and matched with the pre-established results. The diffraction patterns for the vertical displacement component in the considered material medium are calculated numerically, and its dependence on various affecting parameters viz. magnetoelastic coupling parameter, phase velocity, wave number of the propagating magnetoelastic plane wave, and distance has been depicted graphically for self-reinforced and isotropic materials. Moreover, the influence of anisotropy of the infinite medium has been portrayed remarkably by the comparative study.

Initial stress and heterogeneity effects on torsional waves in dry sand half-space between reinforced half-space and poroelastic medium

PurposeThe purpose of this paper is to investigate the effect of initial stress and heterogeneity on the propagation of torsional waves in dissipative medium. The problem consists of dry sand poroelastic half-space embedded between heterogeneous self-reinforced half-space and poroelastic medium. The frequency equation is derived in the framework of Biot's theory with some variants.Design/methodology/approachTorsional wave propagation in dry sand poroelastic half-space embedded between self-reinforced half-space and poroelastic medium. All the constituents here are assumed to be dissipative, heterogeneous and initial stressed.FindingsPhase velocity and attenuation are computed against wavenumber for various values of self-reinforcement parameter, inhomogeneity parameter and initial stress. Particular cases are discussed in absence of dissipation. The numerical results are presented graphically.Originality/valueInitial stress and heterogeneity effects on torsional waves in dry sand half-space between reinforced half-space and poroelastic medium are investigated. The frequency equation is derived, and which intern gives the phase velocity and attenuation coefficient for various values of initial stress, self-reinforcement parameter and heterogeneity parameter. From the numerical results, it is clear that as wavenumber varies phase velocity and attenuation are periodic in nature for all the cases. Particular cases are discussed in absence of dissipation. This kind of analysis can be extended to any elastic solid by taking magnetic, thermo and piezoelectric effects into account.

Shear wave propagation in magneto poroelastic medium sandwiched between self-reinforced poroelastic medium and poroelastic half space

PurposeThe purpose of this paper is to investigate the effect of reinforcement, inhomogeneity and initial stress on the propagation of shear waves. The problem consists of magneto poroelastic medium sandwiched between self-reinforced medium and poroelastic half space. Using Biot’s theory of wave propagation, the frequency equation is obtained.Design/methodology/approachShear wave propagation in magneto poroelastic medium embedded between a self-reinforced medium and poroelastic half space is investigated. This particular setup is quite possible in the Earth crust. All the three media are assumed to be inhomogeneous under initial stress. The significant effects of initial stress and inhomogeneity parameters of individual media have been studied.FindingsPhase velocity is computed against wavenumber for various values of self-reinforcement, heterogeneity parameter and initial stress. Classical elasticity results are deduced as a particular case of the present study. Also in the absence of inhomogeneity and initial stress, frequency equation is discussed. Graphical representation is made to exhibit the results.Originality/valueShear wave propagation in magneto poroelastic medium embedded between a self-reinforced medium, and poroelastic half space are investigated in presence of initial stress, and inhomogeneity parameter. For heterogeneous poroelastic half space, the Whittaker’s solution is obtained. From the numerical results, it is observed that heterogeneity parameter, inhomogeneity parameter and reinforcement parameter have significant influences on the wave characteristics. In addition, frequency equation is discussed in absence of inhomogeneity and initial stress. For the validation purpose, numerical results are also computed for a particular case.

Scattering of waves at the interface of two distinct anisotropic media

The present paper aims to study the reflection/transmission of two-dimensional plane elastic waves (quasi-longitudinal displacement waves) at the interface between a self-reinforced half-space and an orthotropic micropolar elastic solid half-space. Three kinds of coupled elastic waves are reflected in the orthotropic micropolar half-space, and two types of waves are transmitted in the self-reinforced medium. The phase velocities obtained in closed form depend upon the angle of propagation and material parameters. The boundary conditions at the interface of the two media are solved, and reflection/transmission coefficients are obtained using Cramer’s rule. Numerical examples are given, and dependence of the reflection/transmission coefficients on the incident angle has been shown graphically. Also, the comparisons between anisotropic and isotropic cases have been marked distinctly. The obtained results may be utilised for the interpretation and analysis of geophysical data.

Effect of Anisotropy, Earth Magnetism and Irregular Boundary on Polarized Shear wave propagation

A mathematical model is considered to investigate the behaviour of horizontally polarized shear waves (SH waves) in an irregular, heterogeneous, magnetoelastic self-reinforced medium sandwiched between two heterogeneous half- spaces. Heterogeneity in the upper half-space is due to linear variation of elastic parameters whereas quadratic variation has been considered for lower half-space. Heterogeneity in the layer is caused due to exponential variation of the parameters. The irregularity is taken in the form of rectangle. Dispersion equation for propagation of SH-waves has been obtained. Whittaker's function and the method of separation of variable are used to solve the problem.

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.

Effect of Heterogeneity, Irregularity, and Reinforcement on the Stress Produced by a Moving Load on a Self-Reinforced Composite Half-Space

AbstractThe present study deals with the stress produced in an irregular heterogeneous self-reinforced composite half-space due to a load acting as a shearing force and moving along the free surface. The expression of shear stress produced in this case was obtained in closed form. The effect of heterogeneity, reinforcement, maximum depth of irregularity, and the irregularity factor on shear stress is the highlight of the study. In addition, the effect of different shapes of irregularity on shear stress is discussed through the irregularity factor. Moreover, a comparison is made for three different cases of irregularity, namely, rectangular, parabolic, and no irregularity. As a special case of the problem, the stress produced because of a moving load acting as a shearing force in an isotropic half-space with and without heterogeneity and irregularity is discussed. A comparative study of a self-reinforced composite medium and an isotropic medium in the present context of the problem was performed using grap...

Torsional wave propagation in a self-reinforced medium sandwiched between a rigid layer and a viscoelastic half space under gravity

The present paper constitutes the study of torsional surface wave propagation in a self-reinforced layer resting over a gravitating viscoelastic half space. The layer has an inhomogeneity of linear type associated with the rigidity and density of the medium. Dispersion equation has been obtained in the terms of HypergeometricU and LaguerreL function. The dispersion equation reduces to a classical form when the inhomogeneity of the layer, gravity and viscosity of the half space vanishes. The influence of various parameters has been depicted by means of graphs for both reinforced and reinforcement free medium.

Propagation of a crack due to magnetoelastic shear waves in a self-reinforced medium

This paper investigates the propagation of crack due to horizontally polarized shear waves in a magnetoelastic self-reinforced medium. The methodology includes the Weiner-Hopf technique. The effects of reinforcement and magnetic field on the propagation of the crack have been studied. 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 self-reinforcement increases the stress intensity factor whereas magnetoelastic coupling parameter has the reverse impact. It is remarkable to state that the stress intensity factor decreases with the increase in the length of crack. Also, the comparative study has been made through graphs to find the effect of reinforcement over the reinforced-free case on the stress intensity factor. Moreover, some important peculiarities have been observed in graphs.

Dispersion of horizontally polarized shear waves in an irregular non-homogeneous self-reinforced crustal layer over a semi-infinite self-reinforced medium

The present paper discusses the dispersion equation for horizontally polarized shear waves (SH waves) in a non-homogeneous self-reinforced layer over a semi infinite self-reinforced medium with an irregularity. The dispersion equation has been obtained in closed form. In the isotropic case, when non homogeneity and irregularity are absent, the dispersion equation reduces to standard SH wave equation. The dispersion curves have been presented by means of graphs for different sizes of irregularity and different values of non-homogeneity parameters. The influence of depth of irregularity and non-homogeneity parameters on phase velocity has been studied.

The dispersion of shear wave in multilayered magnetoelastic self-reinforced media

In this paper, we study the propagation of shear waves in a magnetoelastic self-reinforced medium using finite difference technique. Dispersion equation has been deduced for the case when ( n − 1) layers lie over a half space. It is observed that the obtained dispersion equation is in assertion with the classical Love wave equation for both the cases when a single and double layer lies over a half space. The stability condition for the used finite difference scheme and the expression for the phase and group velocity have been derived. The dispersion curve for different values of magnetoelastic coupling parameter, phase and group velocity variation for different values of stability ratio has been depicted by means of graphs.

Torsional Waves in Self-Reinforced Medium

The present paper discusses the frequency equation for torsional waves in a self-reinforced medium. It can be seen that the phase velocity of torsional waves in a self-reinforced rod of circular cross section is influenced by the reinforced parameters. Numerical computation shows that the presence of the reinforcement parameter increases the phase velocity significantly. It has been observed that the velocity of torsional waves coincides with the shear wave velocity when the reinforcement parameters are zero.

Propagation, reflection and transmission of magnetoelastic shear waves in a self-reinforced medium

The paper deals with the study of propagation reflection as well as transmission of magnetoelastic shear waves in a self-reinforced medium. The results have been computed taking two self-reinforced media one overlying another and presented graphically to compare with the reinforcement free cases.