Transient Green’s Function Behavior for a Prestressed Highly Elastic Half-Space

2000 ◽  
Vol 68 (2) ◽  
pp. 162-168 ◽  
Author(s):  
L. M. Brock
Keyword(s):  
Half Space ◽  
Rayleigh Waves ◽  
Arbitrary Constant ◽  
Elastic Half Space ◽  
Normal Surface ◽  
Poisson Effect ◽  
Wave Speeds ◽  
Wave Patterns ◽  
Infinitesimal Deformations ◽  
Surface Loads

A plane-strain study of a prestressed isotropic compressible neo-Hookean half-space subjected to shear and normal surface loads is performed. The loads are either stationary and applied for an instant, or travel at an arbitrary constant speed. The transient process is viewed as the superposition of infinitesimal deformations upon large, and exact expressions for the displacements, within and upon, the half-space are obtained. These, and the associated wave patterns, demonstrate the anisotropy induced by prestress. The wave speeds themselves are sensitive to prestress; in particular, Rayleigh waves disappear beyond a critical compressive prestress. A critical tensile prestress also exists, beyond which a negative Poisson effect occurs.

Stresses in an Elastic Half Space Due to Surface Loads Progressing at the Speed of Rayleigh Waves

1972 ◽  
Vol 39 (2) ◽  
pp. 372-377
Author(s):  
I. S. Sandler ◽  
H. H. Bleich
Keyword(s):  
Elastic Medium ◽  
Half Space ◽  
Rayleigh Waves ◽  
Elastic Half Space ◽  
Basic Form ◽  
Surface Loads

The nature of the singularity in the stresses produced near the front of a progressing step load of pressure on the surface of an elastic half space is investigated for the case when the velocity of the front coincides with that of Rayleigh waves in the elastic medium. The technique is based on the assumption of the basic form of the solution and the demonstration that this assumption is correct. It is found that for the particular velocity of the front considered here, unusually large stresses are produced in the medium.

scholarly journals Exponentially Decaying Pressure Pulse Moving With Constant Velocity on the Surface of a Layered Elastic Material (Superseismic Layer, Subseismic Half Space)

1970 ◽  
Vol 37 (1) ◽  
pp. 141-152 ◽  
Author(s):  
J. P. Wright ◽  
M. L. Baron
Keyword(s):  
Half Space ◽  
Constant Velocity ◽  
Moving Load ◽  
Elastic Half Space ◽  
Normal Surface ◽  
Entire Plane ◽  
Normal Loading ◽  
Wave Speeds ◽  
S Waves ◽  
Typical Configuration

The response of a layered elastic half space to a progressing exponentially decaying normal surface pressure is evaluated for a case in which the constant velocity V of the moving pressure is greater than that of the P and S waves, respectively, in the upper layer (superseismic) and smaller than these wave speeds in the underlying half space (subseismic). It is assumed that a steady state exists with respect to coordinate axis attached to the moving load. The superseismic-subseismic geometry results in a stress field that extends over the entire plane, with sharp shocks possible only in that portion of the layer that lies behind the front of the progressing normal loading. A computer program for evaluating stresses and velocities at points in the medium was developed and results are presented for a typical configuration of interest.

scholarly journals Surface waves in multilayered elastic media I. Rayleigh and Love waves from buried sources in a multilayered elastic half-space

1964 ◽  
Vol 54 (2) ◽  
pp. 627-679
Author(s):  
David G. Harkrider
Keyword(s):  
Surface Waves ◽  
Frequency Domain ◽  
Half Space ◽  
Rayleigh Waves ◽  
Elastic Half Space ◽  
Love Waves ◽  
Displacement Fields ◽  
Matrix Formulation ◽  
Total Displacement ◽  
Rayleigh And Love Waves

ABSTRACT A matrix formulation is used to derive integral expressions for the time transformed displacement fields produced by simple sources at any depth in a multilayered elastic isotropic solid half-space. The integrals are evaluated for their residue contribution to obtain surface wave displacements in the frequency domain. The solutions are then generalized to include the effect of a surface liquid layer. The theory includes the effect of layering and source depth for the following: (1) Rayleigh waves from an explosive source, (2) Rayleigh waves from a vertical point force, (3) Rayleigh and Love waves from a vertical strike slip fault model. The latter source also includes the effect of fault dimensions and rupture velocity. From these results we are able to show certain reciprocity relations for surface waves which had been previously proved for the total displacement field. The theory presented here lays the ground work for later papers in which theoretical seismograms are compared with observations in both the time and frequency domain.

Dynamic response of an elastic half-space to time-dependent surface tractions over an embedded spherical cavity. III (With comments on a paper by R. D. Gregory)

1969 ◽  
Vol 309 (1498) ◽  
pp. 313-329 ◽  
Keyword(s):  
Dynamic Response ◽  
Half Space ◽  
Rayleigh Waves ◽  
Spherical Cavity ◽  
Elastic Half Space ◽  
Time Dependent ◽  
Plane Boundary ◽  
Surface Motion ◽  
Harmonic Solution ◽  
Time Harmonic

Discussion of the problem of an elastic half-space with spherical cavity is continued in respect of Rayleigh waves on the plane boundary. Displacements in the initial and first group of higher order Rayleigh waves are derived by using the time-harmonic solution developed in part I of this series with attention confined to the case of time-harmonic normal stress at the cavity. These are employed to find also the response to an exponential shock at the cavity and graphs are presented showing the surface motion due to the initial Rayleigh waves. Finally, in an appendix to the paper, some comments are given on a recent paper by R. D. Gregory on the problem of the half-space with cavity.

Sign in / Sign up

Export Citation Format

Share Document