Spectral Analysis of Elastic Waves Scattered by Objects with Smooth Surfaces

This is a summary of the research on NDE performed during the last two years by the authors and Professor W. Sachse and Messrs . S. Sancar and G. C. C. Ku of the Department of Theoretical and Applied Mechanics at Cornell University. The report is divided into t hree par ts: (1) Theoretical SpectraResults based on the method of wave function expansion and the method of transition n~trix (T-~trix) will be presented for the scattering by a circular cylindrica l , ellipt ic cyl indrical, spherical, and spheroidal (prolate or oblate) i nclusi ons in solids. Additional resul ts for the scattering by two circular cylindrical inclusions wi l l also be shown. (2) Interpretation of Spectra Spectra of a fluid inclusion may be interpreted on the basis of the theory of norma l modes, and those of a cavity from the principle of interference. Spectra for two cyl indrical cavities exhibit new features whi ch are related to the interferences of waves di ffracted by each cavity. (3) Comparison with Experiments Some of the theoretical spectra are compared with experimental results obtained by Professor W. Sachse and his associates. Introduction As discussed in Ref. 1, the spectrum of the pulses scattered by an obstacle in an elastic sol id equals the product of the spectrum of the incident pulse and the spectrum of responses of the obstacle when it is excited by monochro~tic waves. In an experiment, the spectrum of the incident pulse can be isolated from the total spectrum; hence,we consider only the spectrum generated by t he obstacle when radiated with monochromatic waves. Let , 1(x,w) exp(-iwt) be the displacement vector due to the incident harmonic waves of angular frequency w.. and ~(~,w) exp(-i, .. t) be the total wave field in the medium at the location x. The amplitude of the scattered waves can 5e expressed as