THE PRODUCTION OF ELASTIC WAVES BY EXPLOSION PRESSURES. I. THEORY AND EMPIRICAL FIELD OBSERVATIONS

Geophysics ◽  
1942 ◽  
Vol 7 (2) ◽  
pp. 144-154 ◽  
Author(s):  
Joseph A. Sharpe
Keyword(s):  
Elastic Medium ◽  
Elastic Waves ◽  
Qualitative Agreement ◽  
Spherical Cavity ◽  
Wave Motion ◽  
Arbitrary Form ◽  
Field Observations ◽  
Interior Surface ◽  
Shot Point ◽  
Empirical Field

A solution to the problem of the wave motion produced when a pressure of arbitrary form is applied to the interior surface of a spherical cavity in an ideally elastic medium is derived. This solution is shown to be in qualitative agreement with a number of field observations of the effect of shot‐point conditions on the characteristics of reflection seismograph recordings.

Discussions and Communications

Geophysics ◽  
1942 ◽  
Vol 7 (4) ◽  
pp. 419-419
Author(s):  
GEORGE R. LAMB
Keyword(s):  
Elastic Medium ◽  
Spherical Cavity ◽  
Wave Motion ◽  
Analytic Solution ◽  
Arbitrary Form ◽  
Interior Surface ◽  
Explosion Process ◽  
Wave Phenomena

To the Editor: In his paper in the April and July 1942 issues of GEOPHYSICS, Dr. Sharpe gives a very enlightening analytic solution to the problem of the wave motion generated in an elastic medium by application of a pressure of arbitrary form to the interior surface of a spherical cavity. It is very encouraging to find that deductions regarding the relation of the amplitude and frequency of the generated wave to the physicai characteristics of the medium agree so well with empirical operation. A thorough understanding of the explosion process and its accompanying wave phenomena is a prerequisite to the final refinement of the seismograph as a tool of Exploration Geophysics. It is to be hoped that Dr. Sharpe and his colleagues, as well as others, will continue the combined analytic and experimental attack.

Diffraction of impulsive elastic waves by a fluid cylinder

1974 ◽  
Vol 75 (3) ◽  
pp. 391-404 ◽  
Author(s):  
Ramanand Jha
Keyword(s):  
Exact Solution ◽  
Circular Cylinder ◽  
Elastic Medium ◽  
Elastic Waves ◽  
Line Source ◽  
Inviscid Fluid ◽  
Geometrical Theory ◽  
Shadow Zone ◽  
Integral Transformations ◽  
Geometrical Theory Of Diffraction

AbstractIn this paper, the problem of diffraction of an impulsive P wave by a fluid circular cylinder has been considered. The cylinder is embedded in an unbounded isotropic homogeneous elastic medium and it is filled with inviscid fluid material. The line source, giving rise to the incident front, is situated outside the cylinder parallel to its axis.The exact solution of the problem is obtained by using the method of dual integral transformations. The solution is evaluated approximately to obtain the motion on the wave front in the shadow zone of the elastic medium. Further, we interpret the approxi mate solutions in terms of Keller's geometrical theory of diffraction. Our result also gives a correction to an earlier investigation of the similar problem by Knopoff and Gilbert(s).

A Dispersive Homogenization Model Based on Lattice Approximation for the Prediction of Wave Motion in Laminates

2012 ◽  
Vol 79 (2) ◽  
Author(s):  
G. Carta ◽  
M. Brun
Keyword(s):  
Elastic Waves ◽  
Wave Motion ◽  
Impact Excitation ◽  
Stratified Medium ◽  
Model Approximation ◽  
Wide Range ◽  
Lattice Approximation ◽  
Homogenization Model ◽  
Elastic Impedance ◽  
Propagation Of Elastic Waves

The propagation of elastic waves in a periodic laminate is considered. The stratified medium is modeled as a homogenized material where the stress depends on the strain and additional higher order strain gradient terms. The homogenization scheme is based on a lattice model approximation tuned on the dispersive properties of the real laminate. The long-wave asymptotic approximation of the model shows that, despite the simplicity of the parameters identification, the proposed approach agrees well with the exact solution in a wide range of elastic impedance contrasts, also in comparison with different approximations. The effect of increasing order of approximation is also investigated. A final example of a finite structure under an impact excitation proves that the model behaves well when applied in the transient regime and that it can be considered a simple but consistent approach to build efficient algorithms for the numerical analysis of elastodynamics problems.

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