Effect of point source and heterogeneity on the propagation of SH-Waves in a viscoelastic layer over a viscoelastic half space (original) (raw)
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SH-waves in viscoelastic heterogeneous layer over half-space with self-weight
2013
The effect of gravity, heterogeneity and internal friction on propagation of SH-waves (horizontally polarised shear waves) in viscoelastic layer over a half-space has been studied. Using the method of separation of variables, dispersion equation has been obtained and used to recover the damped velocity of SH-waves. Both the real and imaginary parts of dispersion equation are in well agreement with the classical Love wave equation. It has been observed that heterogeneity of the medium affects the velocity profile of SH-wave significantly. Some other peculiarities have been observed and discussed in our study.
G-Type Seismic Wave in Magnetoelastic Monoclinic Layer
Applied Mathematics, 2011
This paper deals with the study of propagation of G type waves along the plane surface at the interface of two different types of media. The upper medium is taken as monoclinic magnetoelastic layer whereas the lower half-space is inhomogeneous isotropic. Dispersion equation and condition for maximum energy flow near the surface are obtained in compact form. The dispersion equation is in assertion with the classical Love-type wave equation for the isotropic case. Effect of magnetic field and inhomogeneity on phase velocity and variation of group velocity with scaled wave number has been depicted by means of graphs. It is observed that inhomogenetity decreases phase velocity and the magnetic field has the favouring effect. A comparative study for the case of isotropic layer and monoclinic layer over the same isotropic inhomogeneous half space has been made through graphs.
Acta Mechanica, 2017
This paper presents an outcome of the broader effect to assess the importance of magnetoelasticity, compressive and tensile initial stress in soil dynamics. Haskell's matrix technique is employed to investigate the SH-wave propagation in a multilayered magnetoelastic orthotropic (MMO) medium. The dispersion relation for the total (n − 1) layers lying over a half-space is obtained in a closed form. Special cases are derived for both the single and double layers, and the obtained relations are found to be in good agreement with the Classical Love wave equation. Based on the finite difference technique, a stability analysis is performed to reduce the escalation of errors to make it stable and convergent. The expression for the phase and group velocities is attained by this technique when the SH-wave propagates across the MMO medium. Numerical computations and graphical exhibition have been carried out to show the effects of different values of the magnetoelastic coupling parameter, compressive and tensile initial stresses and courant number on the phase and group velocities.
Applied …, 2011
This paper investigates the propagation of horizontally polarised shear waves due to a point source in a magnetoelastic self-reinforced layer lying over a heterogeneous self-reinforced half-space. The heterogeneity is caused by consideration of quadratic variation in rigidity. The methodology employed combines an efficient derivation for Green's functions based on algebraic transformations with the perturbation approach. Dispersion equation has been obtained in the closed form. The dispersion curves are compared for different values of magnetoelastic coupling parameters and inhomogeneity parameters. Also, the comparative study is being made through graphs to find the effect of reinforcement over the reinforced-free case on the phase velocity. It is observed that the dispersion equation is in assertion with the classical Love-type wave equation in the absence of reinforcement, magnetic field and heterogeneity. Moreover, some important peculiarities have been observed in graphs.
Applied Mathematics and Computation, 2019
The present paper deals with the Shear wave propagation in a multilayered magnetoelastic anisotropic monoclinic medium with finite difference modeling to comprehend the stability criteria, phase velocity, and group velocity. Utilizing Maxwell's fundamental theory of magnetoelasticity, the problem has been constructed. Haskell's matrix technique has been utilized to obtain the frequency equation. Stability analysis has been conducted based on the finite difference technique to reduce the soaring error values and control its stability. Numerical evaluation as well as graphical representation, have been employed to enlighten the effects of different values of courant number and magnetoelasticity on the phase and group velocities.
Seismic wave in magnetoelastic irregular anisotropic layer
Proceedings of the 6th Wseas International Conference on Computer Engineering and Applications and Proceedings of the 2012 American Conference on Applied Mathematics, 2012
This paper aims to study the propagation of horizontally polarized shear wave (SH wave) in a magnetoelastic anisotropic and irregular layer. The irregular layer is taken as self-reinforced which is sandwiched between two isotropic elastic half-spaces. Irregularity in layer is considered at the lower interface. The perturbation method is used to find the dispersion equation. Effects of size of irregularity and different values of magnetoelastic coupling parameter on dispersion curves have been studied. Variation of phase velocity with wave number has been presented by graphs.
The object of the present paper is to investigate plane SH waves through a magneto-elastic crustal layer based over an elastic, solid semi space under the influence of surface stress on the free surface of the crustal layer and irregularity of the interface. Two types of irregularities of the interface namely, rectangular and parabolic have been considered. Modulations of wave velocity due to the presence of surface stress, irregularity and the magnetic field have been studied separately. Their combined effect has also been investigated. Graphs are drawn to highlight some important peculiarities. It is observed that surface stress, irregularity and magnetic field have their respective role to play in the propagation of SH waves in the crustal layer. Further modulation of wave velocity occurs due to their combined effect.
Viscoelastic Waves in Layered Media
The Journal of the Acoustical Society of America, 2009
This book is a rigorous, self-contained exposition of the mathematical theory for wave propagation in layered media with arbitrary amounts of intrinsic absorption. The theory, previously not published in a book, provides solutions for fundamental wave-propagation problems in the general context of any media with a linear response (elastic or anelastic). It reveals physical characteristics for two-and three-dimensional anelastic body and surface waves, not predicted by commonly used models based on elasticity or one-dimensional anelasticity. It explains observed wave characteristics not explained by previous theories. This book may be used as a textbook for graduate-level courses and as a research reference in a variety of fields such as solid mechanics, seismology, civil and mechanical engineering, exploration geophysics, and acoustics. The theory and numerical results allow the classic subject of fundamental elastic wave propagation to be taught in the broader context of waves in any media with a linear response, without undue complications in the mathematics. They provide the basis to improve a variety of anelastic wave-propagation models, including those for the Earth's interior, metal impurities, petroleum reserves, polymers, soils, and ocean acoustics. The numerical examples and problems facilitate understanding by emphasizing important aspects of the theory for each chapter.
Proceedings of The Indian Academy of Sciences-mathematical Sciences, 1995
In this paper the generation and propagation ofSH-type waves due to stress discontinuíty in a linear viscoelastic layered medium is studied. Using Fourier transforms and complex contour integration technique, the displacement is evaluated at the free surface in closed form for two special types of stress discontinuity created at the interface. The numerical result for displacement component is evaluated for different values of nondimensional station (distance) and is shown graphically. Graphs are compared with the corresponding graph of classical elastic case.
Journal of Mechanics of Materials and Structures, 2011
The dispersion relations of surface SH waves in an A/B/A heterostructure with magnetoelectroelastic properties and imperfect (electromagnetically permeable or absorbent, mechanically spring-type) bonding at the interfaces are obtained taking the geometric symmetry of the system into account. Consequently, the results for the symmetric and antisymmetric modes are presented. Different limit cases are considered. Numerical calculations for relevant realizations of the heterostructure are investigated for different values of the material parameter describing the assumed mechanically imperfect bonding. In all the studied cases, the propagation velocities of the SH waves increase for increasing values of this parameter and are limited by the velocities on the homogeneous phases A and B.