Appendix 3: Translation of spherical waves

Keyword(s):  

1983 ◽  
Vol 16 (3) ◽  
pp. 163-168
Author(s):  
R. Seznec ◽  
M. Berengier ◽  
V. Legeay
Keyword(s):  


Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 220
Author(s):  
Alexey Samokhin

We studied, for the Kortweg–de Vries–Burgers equations on cylindrical and spherical waves, the development of a regular profile starting from an equilibrium under a periodic perturbation at the boundary. The regular profile at the vicinity of perturbation looks like a periodical chain of shock fronts with decreasing amplitudes. Further on, shock fronts become decaying smooth quasi-periodic oscillations. After the oscillations cease, the wave develops as a monotonic convex wave, terminated by a head shock of a constant height and equal velocity. This velocity depends on integral characteristics of a boundary condition and on spatial dimensions. In this paper the explicit asymptotic formulas for the monotonic part, the head shock and a median of the oscillating part are found.



1979 ◽  
Vol 16 (7) ◽  
pp. 1388-1401 ◽  
Author(s):  
Larry W. Marks ◽  
F. Hron

The classical problem of the incidence of spherical waves on a plane boundary has been reformulated from the computational point of view by providing a high frequency approximation to the exact solution applicable to any seismic body wave, regardless of the number of conversions or reflections from the bottoming interface. In our final expressions the ray amplitude of the interference reflected-head wave is cast in terms of a Weber function, the numerical values of which can be conveniently stored on a computer disk file and retrieved via direct access during an actual run. Our formulation also accounts for the increase of energy carried by multiple head waves arising during multiple reflections of the reflected wave from the bottoming interface. In this form our high frequency expression for the ray amplitude of the interference reflected-head wave can represent a complementary technique to asymptotic ray theory in the vicinity of critical regions where the latter cannot be used. Since numerical tests indicate that our method produces results very close to those obtained by the numerical integration of the exact solution, its combination with asymptotic ray theory yields a powerful technique for the speedy computation of synthetic seismograms for plane homogeneous layers.



2021 ◽  
pp. 104522
Author(s):  
Binpeng Yan ◽  
Shangxu Wang ◽  
Yongzhen Ji ◽  
Nuno Vieira da Silva ◽  
Xingguo Huang


1964 ◽  
Vol 54 (2) ◽  
pp. 737-754
Author(s):  
Sathyanarayana Hanagud

ABSTRACT The mechanical behavior of some types of soils can be idealized by that of a “Locking Solid.” This paper investigates the spherical shock wave and the stress distribution behind the wave in a simple locking solid due to a sudden explosion at the surface of a small spherical cavity. The cases of infinitesimal and finite deformations are considered. The effect of an elastic shear resistance and the consequent phenomenon of “unlocking” are also studied.



2007 ◽  
Vol 46 (32) ◽  
pp. 7862 ◽  
Author(s):  
Sunil Vyas ◽  
P. Senthilkumaran


2017 ◽  
Vol 19 (10) ◽  
pp. 105608 ◽  
Author(s):  
Yitzi M Calm ◽  
Juan M Merlo ◽  
Michael J Burns ◽  
Michael J Naughton
Keyword(s):  


Sign in / Sign up

Export Citation Format

Share Document