Closure to “Discussion of ‘Application of Kirchhoff’s Integral Equation Formulation to an Elastic Wave Scattering Problem’” (1968, ASME J. Appl. Mech., 35, pp. 428–429)

1968 ◽  
Vol 35 (2) ◽  
pp. 429-430
Author(s):  
W. L. Ko ◽  
T. Karlsson
Keyword(s):  
Integral Equation ◽  
Elastic Wave ◽  
Wave Scattering ◽  
Scattering Problem ◽  
Equation Formulation ◽  
Elastic Wave Scattering ◽  
Integral Equation Formulation

Application of the Singularity Expansion Method to Elastic Wave Scattering

1990 ◽  
Vol 43 (10) ◽  
pp. 235-249 ◽  
Author(s):  
Herbert U¨berall ◽  
P. P. Delsanto ◽  
J. D. Alemar ◽  
E. Rosario ◽  
Anton Nagl
Keyword(s):  
Elastic Wave ◽  
Elastic Waves ◽  
Wave Scattering ◽  
Scattering Amplitude ◽  
Scattering Problem ◽  
Expansion Method ◽  
Complex Frequency ◽  
Elastic Wave Scattering ◽  
Physical Measurements ◽  
Scattering Of Elastic Waves

The singularity expansion method (SEM), established originally for electromagnetic-wave scattering by Carl Baum (Proc. IEEE 64, 1976, 1598), has later been applied also to acoustic scattering (H U¨berall, G C Gaunaurd, and J D Murphy, J Acoust Soc Am 72, 1982, 1014). In the present paper, we describe further applications of this method of analysis to the scattering of elastic waves from cavities or inclusions in solids. We first analyze the resonances that appear in the elastic-wave scattering amplitude, when plotted vs frequency, for evacuated or fluid-filled cylindrical and spherical cavities or for solid inclusions. These resonances are interpreted as being due to the phase matching, ie, the formation of standing waves, of surface waves that encircle the obstacle. The resonances are then traced to the existence of poles of the scattering amplitude in the fourth quadrant of the complex frequency plane, thus establishing the relation with the SEM. The usefulness of these concepts lies in their applicability for solving the inverse scattering problem, which is the central problem of NDE. Since for the case of inclusions, or of cavities with fluid fillers, the scattering of elastic waves gives rise to very prominent resonances in the scattering amplitude, it will be of advantage to analyze these with the help of the resonance scattering theory or RST (first formulated by L Flax, L R Dragonette, and H U¨berall, J Acoust Soc Am 63, 1978, 723). These resonances are caused by the proximity of the SEM poles to the real frequency axis, on which the frequencies of physical measurements are located. A brief history of the establishment of the RST is included here immediately following the Introduction.

scholarly journals Mathematical interpretation of seismic wave scattering and refraction on tunnel structures of circular cross-section

2020 ◽  
Vol 18 (3) ◽  
pp. 241-260
Author(s):  
Elefterija Zlatanovic ◽  
Vlatko Sesov ◽  
Dragan Lukic ◽  
Zoran Bonic
Keyword(s):  
Elastic Wave ◽  
Wave Scattering ◽  
Scattering Problem ◽  
Circular Cross Section ◽  
Circular Cylinders ◽  
Elastic Wave Scattering ◽  
Incident Plane ◽  
Seismic Wave Scattering ◽  
Basic Equations ◽  
Mathematical Interpretation

Mathematical interpretation of the elastic wave diffraction in circular cylinder coordinates is in the focus of this paper. Firstly, some of the most important properties of Bessel functions, pertinent to the elastic wave scattering problem, have been introduced. Afterwards, basic equations, upon which the method of wave function expansions is established, are given for cylindrical coordinates and for plane-wave representation. In addition, steady-state solutions for the cases of a single cavity and a single tunnel are presented, with respect to the wave scattering and refraction phenomena, considering both incident plane harmonic compressional and shear waves. The last part of the work is dealing with the translational addition theorems having an important role in the problems of diffraction of waves on a pair of circular cylinders.

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