Influence of rigid boundary on the propagation of torsional surface wave in an inhomogeneous layer (original) (raw)
Related papers
Torsional wave propagation in Earth’s crustal layer under the influence of imperfect interface
Journal of Vibration and Control, 2014
In this paper, we study the propagation of a torsional surface wave in a homogeneous crustal layer over an initially stressed mantle with linearly varying directional rigidities, density and initial stress under the effect of an imperfect interface. Twelve different types of imperfect interface have been considered using triangular, rectangular and parabolic shapes. A variable separable technique is adopted for the theoretical derivations and analytical solutions are obtained for the dispersion relation by means of Whittaker function and its derivative. Dispersion equations are in perfect agreement with the standard results when derived for a particular case. The graph is self-explanatory and reveals that the phase velocity of a torsional surface wave depends not only on the wave number, initial stress, inhomogeneity and depth of the irregularity but also on the layer structure.
Propagation of Torsional Surface Waves in a NonHomogeneous Crustal Layer over a Viscoelastic Mantle
2012
The present paper studies the possibility of propagation of torsional surface waves in a non-homogeneous isotropic crustal layer lying over a viscoelastic mantle. Both rigidity and density of the crustal layer are assumed to vary exponentially with depth. Separation of variable method has been used to get the analytical solutions for the dispersion equation for the torsional surface waves. Further, in the absence of non-homogeneity and internal friction, this equation is in complete agreement with the classical result of Love. Also, the effects of non-homogeneity, internal friction (viscoelastic parameter), rigidity, wave number and time period on the phase velocity of torsional surface waves have shown graphically.
Latin American Journal of Solids and Structures
The present paper studies the Propagation of SH waves in a double non-homogeneous crustal layers lying over an isotropic homogeneous half-space, where upper layer ((i.e. rigidity and density varying trigonometrically with depth) and intermediate layer (i.e. rigidity and density varying parabolically with depth). The wave velocity equation has been obtained. Closed form solutions have been derived separately for the displacements in two non-homogeneous crustal layers and lower half-space. The dispersion curves are depicted by means of graphs for different values of non-homogeneity parameters and thickness ratio for layers.
International Journal of Applied Mechanics and Engineering
The present paper deals with the mathematical modeling of the propagation of torsional surface waves in a non-homogeneous transverse isotropic elastic half-space under a rigid layer. Both rigidities and density of the half-space are assumed to vary inversely linearly with depth. Separation of variable method has been used to get the analytical solutions for the dispersion equation of the torsional surface waves. Also, the effects of nonhomogeneities on the phase velocity of torsional surface waves have been shown graphically. Also, dispersion equations have been derived for some particular cases, which are in complete agreement with some classical results.
Dispersion of torsional surface waves in anisotropic layer over porous half space under gravity
Journal of Applied Mathematics and Mechanics, 2013
In this paper an attempt has been made to derive the frequency equation of torsional surface waves in initially stressed fiber reinforced layer lying over fluid saturated anisotropic porous half space under gravity. The dispersion equation has been obtained in terms of Whittaker function and its derivatives, which further expanded asymptotically and retain the terms upto second degree. The analysis of frequency equation bear out the pronounced effect of initial stress, transverse and longitudinal rigidity of reinforced material, gravity and porosity of the porous half space on the propagation of torsional surface waves. Moreover, it can be noted that in the absence of initial stress, reinforcement parameters, gravity and porosity, the frequency equation of torsional surface waves reduces to dispersion equation of Love waves in isotropic layer. This ensures the classical result that torsional surface waves do not propagate through isotropic homogeneous medium.
On the frequency equation for love waves due to abrupt thickening of the crustal layer
Geofisica Pura e Applicata, 1962
The effect of thickening of the crustal layer in mountainous region Gn the dispersion curve of Love waves has been studied. Perturbation method has been applied to obtain the modified frequency equation for Love waves through the surface of separation between a semi-infinite material and a layer the thickness of which abruptly increases throughout a certain length of the path. The effect is to decrease the phase velocity of the waves particularly in the low period range. It has been pointed out that by proper study, the amount of thickening may be obtained.
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.
Procedia Engineering, 2017
The Present Paper devoted to investigate the effect of presence of rigid boundary on the propagation of torsional surface waves in a gravitating earth with a dry sandy medium under initial stress. The mathematical analysis of the problem has been dealt with the Whittaker function. Assuming the expansion of the Whittaker function up to linear term, it is concluded that the gravity field will always allow torsional waves to propagate in elastic and sandy medium under initial stress and rigid layer. Finally, it reveals that the sandy medium without support of a gravity field can not allow the propagation of torsional surface waves in presence of initial stress under rigid layer , where as the presence of a gravity field always supports the propagation of torsional surface waves regardless of whether the medium is elastic or dry sandy under rigid layer.
Crustal Reflection of Plane SH Waves
Journal of Geophysical Research, 1960
An equation has been derived for the amplitude of the free surface displacement due to plane SH waves incident at any angle at the base of a layered crust. Numerical computations have been carried through for the case of a single-layered model of the continental crust. At any given angle of incidence the surface amplitude goes through a series of minima and maxima at periods which, in the single layered case, are harmonically related. At nearly grazing angles of incidence the surface amplitude is relatively small except at periods in the neighborhood of the cutoff periods of the second-and higher-order Love-wave modes.
Effect of Gravity and Magnetism on Surface Wave Propagation in Heterogeneous Earth Crust
Procedia Engineering, 2016
This 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.