Dispersion ofSH body waves in a continuously stratified elastic half space

1970 ◽  
Vol 82 (1) ◽  
pp. 46-54
Author(s):  
A. R. Banghar
Keyword(s):  
Half Space ◽  
Elastic Half Space ◽  
Body Waves

Body waves recorded inside an elastic half-space by an embedded, wideband velocity sensor

1998 ◽  
Vol 104 (3) ◽  
pp. 1404-1412 ◽  
Author(s):  
Steven D. Glaser ◽  
Gregory G. Weiss ◽  
Lane R. Johnson
Keyword(s):  
Half Space ◽  
Elastic Half Space ◽  
Body Waves ◽  
Velocity Sensor

Friction Reduction in the Sliding of an Elastic Half-Space Against a Rigid Surface Due to Incident Rectangular Dilatational Waves

1999 ◽  
Vol 122 (1) ◽  
pp. 10-15 ◽  
Author(s):  
George G. Adams
Keyword(s):  
Normal Stress ◽  
Half Space ◽  
Coefficient Of Friction ◽  
Tangential Velocity ◽  
Elastic Half Space ◽  
Body Waves ◽  
Friction Reduction ◽  
Rigid Surface ◽  
Rectangular Wave ◽  
The Coefficient Of Friction

The steady sliding of a flat homogeneous and isotropic elastic half-space against a flat rigid surface, under the influence of incident plane dilatational waves, is investigated. The interfacial coefficient of friction is constant with no distinction between static and kinetic friction. It is shown here that the reflection of a harmonic wave under steady sliding consists of a pair of body waves (a plane dilatational wave and a plane shear wave) radiated from the sliding interface. Each wave propagates at a different angle such that the trace velocities along the interface are equal and supersonic. The angles of wave propagation are determined by the angle of the incident wave, by the Poisson’s ratio, and by the coefficient of friction. The amplitude of the incident waves is subject only to the restriction that the perturbations in interface contact pressure and tangential velocity satisfy the inequality constraints for unilateral sliding contact. It is also found that an incident rectangular wave can allow for relative sliding motion of the two bodies with a ratio of remote shear to normal stress which is less than the coefficient of friction. Thus the apparent coefficient of friction is less than the interface coefficient of friction. This reduction in friction is due to periodic stick zones which propagate supersonically along the interface. The influences of the angle, amplitude, and shape of the incident rectangular wave, the interfacial friction coefficient, the sliding speed, and of the remotely applied normal stress, on friction reduction are determined. Under appropriate conditions, the bodies can move tangentially with respect to each other in the absence of an applied shear stress. [S0742-4787(00)00201-0]

The azimuthal and polar radiation patterns obtained from a horizontal stress applied at the surface of an elastic half space

1962 ◽  
Vol 52 (1) ◽  
pp. 27-36
Author(s):  
J. T. Cherry
Keyword(s):  
Surface Wave ◽  
Half Space ◽  
Rayleigh Waves ◽  
Poisson’S Ratio ◽  
Horizontal Stress ◽  
Elastic Half Space ◽  
The Body ◽  
Body Waves ◽  
Poisson's Ratio ◽  
A Value

Abstract The body waves and surface waves radiating from a horizontal stress applied at the free surface of an elastic half space are obtained. The SV wave suffers a phase shift of π at 45 degrees from the vertical. Also, a surface wave that is SH in character but travels with the Rayleigh velocity is shown to exist. This surface wave attenuates as r−3/2. For a value of Poisson's ratio of 0.25 or 0.33, the amplitude of the Rayleigh waves from a horizontal source should be smaller than the amplitude of the Rayleigh waves from a vertical source. The ratio of vertical to horizontal amplitude for the Rayleigh waves from the horizontal source is the same as the corresponding ratio for the vertical source for all values of Poisson's ratio.

The attenuation of a Rayleigh wave in a half-space by a surface impedance

1966 ◽  
Vol 62 (4) ◽  
pp. 811-827 ◽  
Author(s):  
R. D. Gregory
Keyword(s):  
Surface Wave ◽  
Rayleigh Wave ◽  
Half Space ◽  
Logarithmic Singularity ◽  
Elastic Half Space ◽  
Body Waves ◽  
Impedance Boundary Condition ◽  
Impedance Boundary ◽  
Elastic Potentials ◽  
Time Harmonic

AbstractA time harmonic Rayleigh wave, propagating in an elastic half-space y ≥ 0, is incident on a certain impedance boundary condition on y = 0, x > 0. The resulting field consists of a reflected surface wave, scattered body waves, and a transmitted surface wave appropriate to the new boundary conditions. The elastic potentials are found exactly by Fourier transform and the Wiener-Hopf technique in the case of a slightly dissipative medium. The ψ potential is found to have a logarithmic singularity at (0,0), but the φ potential though singular is bounded there. Analytic forms are given for the amplitudes of the reflected and transmitted surface waves, and for the scattered field. The reflexion coefficient is found to have a simple form for small impedances. A uniqueness theorem, based on energy considerations, is proved.

Dynamic response of an elastic half-space to time-dependent surface tractions over an embedded spherical cavity. II

1967 ◽  
Vol 300 (1461) ◽  
pp. 159-186
Keyword(s):  
Half Space ◽  
Spherical Cavity ◽  
Elastic Half Space ◽  
Body Waves ◽  
Time Dependent ◽  
Plane Boundary ◽  
Cavity Surface ◽  
Surface Displacements ◽  
Approximate Expressions ◽  
General Time

The general solution for the wave propagation in an elastic half-space containing a spherical cavity obtained in an earlier paper is worked out in detail in the case of a compressional force of excitation over the cavity surface. Explicit approximate expressions are derived for the displacements due to the direct and the reflected body waves as far as terms representing waves arising from not more than three reflexions. As an example of more general time-dependence, the case of an exponentially decaying shock exciting the cavity surface is discussed and the results are illustrated by graphs showing the variation of the surface displacements at three selected points of the plane boundary.

The Sliding of an Elastic Half-Space Against a Rigid Surface With Friction Reduction due to Incident Dilatational Waves

1999 ◽  
Author(s):  
George G. Adams
Keyword(s):  
Normal Stress ◽  
Half Space ◽  
Coefficient Of Friction ◽  
Tangential Velocity ◽  
Elastic Half Space ◽  
Body Waves ◽  
Friction Reduction ◽  
Rigid Surface ◽  
Rectangular Wave ◽  
The Coefficient Of Friction

Abstract The steady sliding of a flat homogeneous and isotropic elastic half-space against a flat rigid surface, under the influence of incident plane dilatational waves, is investigated. The interfacial coefficient of friction is constant with no distinction between static and kinetic friction. It is shown here that the reflection of a harmonic wave under steady sliding consists of a pair of body waves (a plane dilatational wave and a plane shear wave) radiated from the sliding interface. Each wave propagates at a different angle such that the trace velocities along the interface are equal and supersonic. The angles of wave propagation are determined by the angle of the incident wave, by the Poisson’s ratio, and by the coefficient of friction. The amplitude of the incident waves is subject only to the restriction that the perturbations in interface contact pressure and tangential velocity satisfy the inequality constraints for unilateral sliding contact. It is also found that an incident rectangular wave can allow for relative sliding motion of the two bodies with a ratio of remote shear to normal stress which is less than the coefficient of friction. Thus the apparent coefficient of friction is less than the interface coefficient of friction. This reduction in friction is due to periodic stick zones which propagate supersonically along the interface. Under appropriate conditions, the bodies can move tangentially with respect to each other in the absence of an applied shear stress. The influences of the angle, amplitude, and shape of the incident rectangular wave, the interfacial friction coefficient, the sliding speed, and of the remotely applied normal stress, on friction reduction are determined.

The non-existence of standing modes in certain problems of linear elasticity

1975 ◽  
Vol 77 (2) ◽  
pp. 385-404 ◽  
Author(s):  
R. D. Gregory
Keyword(s):  
Surface Wave ◽  
Half Space ◽  
Surface Defects ◽  
Elastic Half Space ◽  
Body Waves ◽  
Rayleigh Surface Wave ◽  
Contour Integrals ◽  
Elastic Potentials ◽  
Time Harmonic ◽  
Image Position

AbstractSuppose that an elastic half-space, which contains certain surface defects, inclusions and cavities, is in free, two-dimensional, time-harmonic vibration, with the wave field at infinity ‘outgoing’ in character. It is shown that the elastic potentials representing such a ‘standing mode’ can be expressed in the form of contour integrals, for instanceU(t) being an analytic function of t. By considering the far field of these potentials, it is shown that U(t) is zero on a certain arc in the t-plane and is therefore identically zero. It follows that ø(r) is zero everywhere and this proves the non-existence of such standing modes in these configurations.This uniqueness theorem justifies the solution given by the author (Gregory (2)) for the problem in which time harmonic stresses act on the walls of a cylindrical cavity lying beneath the surface of an elastic half-space. It is also shown that if a Rayleigh surface wave is incident on any system of surface defects, inclusions and cavities, then energy must be transferred from the surface wave to scattered outgoing body waves of both P and S types.

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