Torsional Wave Frequency in Corrugated Poroelastic Layer Bonded Between Anisotropic Media

An analytical solution is obtained for torsional surface wave propagating in pre-stressed poroelastic layer sandwiched between transversely isotropic and pre-stressed viscoelastic half-spaces with non-planer boundaries. Frequency equation has been established in closed form. Separation of variables method is adopted to obtain the dispersion relation. Substantial influence of corrugated boundary, initial stresses, porosity and inhomogeneity on the phase velocity of considered surface wave has been presented through graphs. Proposed study finds its possible applications in the fields of geophysics and seismology. Results may be extended to interpret the seismic activities near the crust-mantle boundary

Effect of Gravity and Magnetism on Surface Wave Propagation in Heterogeneous Earth Crust

AbstractThis paper aims to study the propagation of surface wave in two initially stressed heterogeneous magnetoelastic transversely isotropic media lying over a transversely isotropic half-space under the action of gravity. Heterogeneities of both the layers are caused due to exponential variation in elastic parameters. Dispersion relation is obtained in closed form by using Whittaker's asymptotic expansion. Magnetoelastic coupling parameters, heterogeneity, horizontal compressive initial stress and gravity parameters have remarkable effect on the phase velocity of surface wave. The obtained dispersion relation is found to be in well agreement with the classical Love-wave equation. Comparative study and graphical illustration has been made to exhibit the outcomes

Influence of rotation and initial stress on Propagation of Rayleigh waves in fiber-reinforced solidanisotropic magneto-thermo-viscoelastic media.

This paper is concerned with giving a mathematical model on the propagation of Rayleigh waves in a homogeneous magneto-thermo-viscoelastic,pre-stressed elastic half – space subjected to theinitial stress and rotation. The dispersion equation has been derived for a half-space, when both media are considered as pre-stressed and the effect of rotation and initial stressshown in earlier investigators.Numerical results have been obtained  in the physical domain. Numerical simulated results are depicted graphically to show the effect of rotation and magnetic field and initial stressonRayleigh wave velocity. Comparison was made with the results obtained in the presence and absence of the rotation , initial stressand magnetic field. The study shows that there is a variational effect of magneto-elasticityand rotation, initial stress on the Rayleigh wave velocity

Analysis of G-type Seismic Waves in Dry Sandy Layer overlying an Inhomogeneous Half-space

The paper investigates the dispersion of G-type seismic waves along the interface of dry sandy and inhomogeneous isotropic elastic media. The maximum energy flow which projects the fact that a large amount of energy can flow along the interface for horizontally polarized shear wave with group velocity lesser than the shear wave velocity in the upper mantle has been shown in closed form by means of dispersion equation. Effect of sandiness parameter and inhomogeneities on phase velocity has been shown in graphs. A case study has also been made for isotropic homogeneous over an inhomogeneous half-space

Shear Wave Models in Linear and Nonlinear Elastic Materials

Nonlinear shear wave models are of significant importance in a large number of areas, including engineering and seismology. The study of such wave propagation models has helped in the prediction and exploration of hidden resources in the Earth. Also, the frequent occurrences of earthquakes and the damage they cause to lives and properties are of more significant concern to the society. Augustus Edward Hough Love studied horizontally polarized shear waves (Love surface waves) in homogeneous elastic media. In the current thesis, after presenting some basic concepts of linear and nonlinear elasticity, we discuss linear Love waves in both isotropic and anisotropic elastic media, and consider extended linear and nonlinear wave propagation models in elastic media, including models of nonlinear Love-type surface waves. A new general partial differential equation model describing the propagation of one- and two-dimensional Love-type shear waves in incompressible hyperelastic materials is derived, holding for an arbitrary form of the stored energy function. The results can be further generalized to include an arbitrary viscoelastic contribution. We also discuss aspects of Hamiltonian mechanics in finite- and infinite-dimensional systems and present Hamiltonian formulations of some nonlinear wave models discussed in this thesis

Seismic Waves

The importance of seismic wave research lies not only in our ability to understand and predict earthquakes and tsunamis, it also reveals information on the Earth's composition and features in much the same way as it led to the discovery of Mohorovicic's discontinuity. As our theoretical understanding of the physics behind seismic waves has grown, physical and numerical modeling have greatly advanced and now augment applied seismology for better prediction and engineering practices. This has led to some novel applications such as using artificially-induced shocks for exploration of the Earth's subsurface and seismic stimulation for increasing the productivity of oil wells. This book demonstrates the latest techniques and advances in seismic wave analysis from theoretical approach, data acquisition and interpretation, to analyses and numerical simulations, as well as research applications. A review process was conducted in cooperation with sincere support by Drs. Hiroshi Takenaka, Yoshio Murai, Jun Matsushima, and Genti Toyokuni

Incorporation of macroscopic heterogeneity within a porous layer to enhance its acoustic absorptance

We seek the response, in particular the spectral absorptance, of a rigidly-backed periodically-(in one horizontal~~ direction) ~inhomogeneous ~layer ~composed ~of ~alternating rigid and macroscopically-homogeneous porous portions, submitted to an airborne acoustic plane body wave. The rigorous theory of this problem is given and the means by which the latter can be numerically solved are outlined. At low frequencies, a suitable approximation derives from one linear equation in one unknown. This approximate solution is shown to be equivalent to that of the problem of the same wave incident on a homogeneous, isotropic layer. The thickness $h$ of this layer is identical to that of the inhomogeneous layer, the effective complex body wave velocity therein is identical to that of the porous portion of the inhomogeneous layer, but the complex effective mass density, whose expression is given in explicit algebraic form, is that of the reference homogeneous macroscopically-porous layer divided by the filling factor (fraction of porous material to the total material in one grating period). This difference of density is the reason why it is possible for the lowest-frequency absorptance peak to be higher than that of a reference layer. Also, it is shown how to augment the height of this peak so that it attains unity (i.e., total absorption) and how to shift it to lower frequencies, as is required in certain applications