Interaction of elastic waves with a curvilinear crack in a half-plane

1991 ◽  
Vol 57 (1) ◽  
pp. 2887-2891 ◽  
Author(s):  
A. M. Nazarenko ◽  
L. A. Fil'shtinskii
Keyword(s):  
Half Plane ◽  
Elastic Waves ◽  
Curvilinear Crack

Diffraction of elastic waves by the core of the Earth

1961 ◽  
Vol 51 (1) ◽  
pp. 35-49
Author(s):  
Leon Knopoff ◽  
Freeman Gilbert
Keyword(s):  
Half Plane ◽  
Elastic Waves ◽  
Amplitude Distribution ◽  
Laboratory Model ◽  
Shadow Zone ◽  
Adequate Explanation ◽  
Model Experiments ◽  
The Core ◽  
The Earth ◽  
Diffraction Of Elastic Waves

Abstract The problem of the diffraction of a seismic pulse by the core of the Earth is investigated theoretically. The result is compared to that of diffraction by a half-plane. The differences are striking. Laboratory model experiments have been performed to verify the theoretical approximations in their regions of validity, and to complement the theory elsewhere. The curves, thus obtained, of the theoretical amplitude distribution in the shadow of the Earth's core agree very well with the observations of Gutenberg. It is therefore concluded that diffraction is a completely adequate explanation for the amplitude distribution in the shadow zone.

An edge curvilinear crack in an elastic half-plane

1985 ◽  
Vol 21 (1) ◽  
pp. 66-70 ◽  
Author(s):  
A. P. Datsyshin ◽  
G. P. Marchenko
Keyword(s):  
Half Plane ◽  
Curvilinear Crack

Remarks on nonlinear elastic waves with null conditions

2020 ◽  
Vol 26 ◽  
pp. 121
Author(s):  
Dongbing Zha ◽  
Weimin Peng
Keyword(s):  
Initial Data ◽  
Global Existence ◽  
Elastic Waves ◽  
Wave Equations ◽  
Alternative Proof ◽  
Classical Solutions ◽  
Small Initial Data ◽  
Hyperelastic Materials ◽  
Variational Structure ◽  
Nonlinear Elastic

For the Cauchy problem of nonlinear elastic wave equations for 3D isotropic, homogeneous and hyperelastic materials with null conditions, global existence of classical solutions with small initial data was proved in R. Agemi (Invent. Math. 142 (2000) 225–250) and T. C. Sideris (Ann. Math. 151 (2000) 849–874) independently. In this paper, we will give some remarks and an alternative proof for it. First, we give the explicit variational structure of nonlinear elastic waves. Thus we can identify whether materials satisfy the null condition by checking the stored energy function directly. Furthermore, by some careful analyses on the nonlinear structure, we show that the Helmholtz projection, which is usually considered to be ill-suited for nonlinear analysis, can be in fact used to show the global existence result. We also improve the amount of Sobolev regularity of initial data, which seems optimal in the framework of classical solutions.

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