Torsional‐Wave Propagation from a Rigid Sphere Semiembedded in an Elastic Half‐Space

1966 ◽  
Vol 40 (2) ◽  
pp. 376-379 ◽  
Author(s):  
James L. Hill
Keyword(s):  
Wave Propagation ◽  
Half Space ◽  
Elastic Half Space ◽  
Torsional Wave ◽  
Rigid Sphere

Torsional wave propagation in an inhomogeneous crustal layer over an inhomogeneous elastic half space

2015 ◽  
Vol 24 (1-2) ◽  
pp. 47-52
Author(s):  
Rajneesh Kakar ◽  
Kishan Chand Gupta
Keyword(s):  
Wave Propagation ◽  
Dispersion Relation ◽  
Half Space ◽  
General Equation ◽  
Elastic Half Space ◽  
Boundary Plane ◽  
Torsional Wave ◽  
Crustal Layer ◽  
Inhomogeneity Parameter ◽  
Upper Boundary

AbstractThe present study considers the propagation of torsional wave in an inhomogeneous crustal layer over an inhomogeneous half space when the upper boundary plane is assumed to be rigid. The inhomogeneity in density and rigidity in the crustal layer varies linearly with depth, whereas for the elastic half space, the inhomogeneity in density and rigidity is hyperbolic. The dispersion relation for propagation of such waves is derived by using Whittaker’s function. When the upper boundary plane is assumed to be free and in the absence of inhomogeneity of the crustal layer and lower half space, our derived equation is in agreement with the general equation for Love waves. Numerically, it is observed that the velocity of torsional wave changes remarkably with the presence of inhomogeneity parameter of the layer.

Guided Surface Waves on an Elastic Half Space

1971 ◽  
Vol 38 (4) ◽  
pp. 899-905 ◽  
Author(s):  
L. B. Freund
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Surface Waves ◽  
Half Space ◽  
Body Wave ◽  
Three Dimensional ◽  
Elastic Half Space ◽  
Normal Displacement ◽  
Rigid Barrier ◽  
Wave Disturbances

Three-dimensional wave propagation in an elastic half space is considered. The half space is traction free on half its boundary, while the remaining part of the boundary is free of shear traction and is constrained against normal displacement by a smooth, rigid barrier. A time-harmonic surface wave, traveling on the traction free part of the surface, is obliquely incident on the edge of the barrier. The amplitude and the phase of the resulting reflected surface wave are determined by means of Laplace transform methods and the Wiener-Hopf technique. Wave propagation in an elastic half space in contact with two rigid, smooth barriers is then considered. The barriers are arranged so that a strip on the surface of uniform width is traction free, which forms a wave guide for surface waves. Results of the surface wave reflection problem are then used to geometrically construct dispersion relations for the propagation of unattenuated guided surface waves in the guiding structure. The rate of decay of body wave disturbances, localized near the edges of the guide, is discussed.

Asymmetric Wave Propagation in an Elastic Half-Space by a Method of Potentials

1987 ◽  
Vol 54 (1) ◽  
pp. 121-126 ◽  
Author(s):  
R. Y. S. Pak
Keyword(s):  
Wave Propagation ◽  
Dynamic Response ◽  
Half Space ◽  
Elastic Half Space ◽  
Displacement Potential ◽  
Uniform Distributions ◽  
Time Harmonic ◽  
Method Of Potentials ◽  
Transformed Stress ◽  
Asymmetric Wave

A method of potentials is presented for the derivation of the dynamic response of an elastic half-space to an arbitrary, time-harmonic, finite, buried source. The development includes a set of transformed stress-potential and displacement-potential relations which are apt to be useful in a variety of wave propagation problems. Specific results for an embedded source of uniform distributions are also included.

Stress Wave Propagation in a Coated Elastic Half-Space due to Water Drop Impact

2000 ◽  
Vol 68 (2) ◽  
pp. 346-348 ◽  
Author(s):  
Hyun-Sil Kim ◽  
Jae-Seung Kim ◽  
Hyun-Ju Kang ◽  
Sang-Ryul Kim
Keyword(s):  
Wave Propagation ◽  
Half Space ◽  
Stress Wave ◽  
Coating Thickness ◽  
Water Drop ◽  
Elastic Half Space ◽  
Drop Impact ◽  
Stress Wave Propagation ◽  
Singular Behavior ◽  
Reflected Waves

Stress wave propagation in a coated elastic half-space due to water drop impact is studied by using the Cagniard-de Hoop method. The stresses have singularity at the Rayleigh wavefront whose location and singular behavior are determined from the pressure model and independent of the coating thickness, while reflected waves cause minor changes in amplitudes.

The Alekseev–Mikhailenko method applied to P–SV wave propagation in an elastic medium

1988 ◽  
Vol 25 (2) ◽  
pp. 226-234
Author(s):  
L. J. Pascoe ◽  
F. Hron ◽  
P. F. Daley
Keyword(s):  
Wave Propagation ◽  
Finite Difference ◽  
Half Space ◽  
Elastic Half Space ◽  
Low Velocity ◽  
Seismic Modelling ◽  
Wave Propagation Problem ◽  
Modelling Techniques ◽  
Explicit Finite Difference ◽  
The Stability

The Alekseev–Mikhailenko method (AMM) is the name given to a series of algorithms that use one or more finite spatial transforms to reduce the dimensionality of a wave-propagation problem to that of one space dimension and time. This reduced equation is then solved using finite-difference techniques, and the space–time solution is recovered by applying inverse finite spatial transform(s). In this paper the elastodynamic wave equation that governs the coupled P–Sv motion in an isotropic, vertically inhomogeneous elastic half space is investigated using the AMM. Two types of impulsive body forces that may be used to excite the medium are examined, as is the problem of obtaining accurate transformed finite-difference analogues at the free surface. The second of these is accomplished by introducing the boundary conditions that the shear and normal stress must vanish here and by incorporating their transforms into the transformed elastodynamic equations. The stability criterion for the explicit finite-difference method is given cursory treatment, as detailed discussion of this aspect may be found in many texts that deal with the subject of finite differences.A coal-seam model (two thin, low-velocity layers embedded in a half space) illustrates the method. Both horizontal and vertical seismic traces are computed for this model and the results examined in relation to other seismic-modelling techniques.

Axisymmetric contact with friction of a rigid sphere with an elastic half-space

2009 ◽  
Vol 465 (2108) ◽  
pp. 2565-2588 ◽  
Author(s):  
O. I. Zhupanska
Keyword(s):  
Contact Problem ◽  
Half Space ◽  
Integral Transform ◽  
Elastic Half Space ◽  
Rigid Sphere ◽  
Analytical Treatment ◽  
Normal Contact ◽  
Exact Analytical Solutions ◽  
Single Integral ◽  
Toroidal Coordinates

The problem of normal contact with friction of a rigid sphere with an elastic half-space is considered. An analytical treatment of the problem is presented, with the corresponding boundary-value problem formulated in the toroidal coordinates. A general solution in the form of Papkovich–Neuber functions and the Mehler–Fock integral transform is used to reduce the problem to a single integral equation with respect to the unknown contact pressure in the slip zone. An analysis of contact stresses is carried out, and exact analytical solutions are obtained in limiting cases, including a full stick contact problem and a contact problem for an incompressible half-space.

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