Application of the Singularity Expansion Method to Elastic Wave Scattering

[+] Author and Article Information
Herbert Überall

Department of Physics, Catholic University of America, Washington, DC 20064

P. P. Delsanto

Dipartamento di Fisica del Politecnico, I-10129 Torino, Italy

J. D. Alemar, E. Rosario

Department of Physics, University of Puerto Rico, Mayaguez, PR 00708

Anton Nagl

Palien-Johnson Associates, 8601 Westwood Center Drive, Vienna, VA 22182

Appl. Mech. Rev 43(10), 235-249 (Oct 01, 1990) (15 pages) doi:10.1115/1.3119152 History: Online April 30, 2009


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 Überall, 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 Überall, 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.

Copyright © 1990 by American Society of Mechanical Engineers
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