Theory of Normal Modes and Ultrasonic Spectral Analysis of the Scattering of Waves in Solids

by Y. H. Pao, C. C. Mow

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A theory of the spectral analysis of the scattering of elastic waves is presented and illustrated with numerical results for the scattering by a circular cylindrical fluid inclusion in a solid. When the spectral frequencies are nearly equal to the real parts of the principal frequencies of the fluid inclusion in free vibration, the power spectrum of the scattered pulses undergoes a rapid rise and fall in magnitude because of the selective transmission of an incident wave. The conspicuous peaks and valleys of the backward and forward scattering spectra can be identified with the overtone frequencies of the two lowest normal modes of the cylinder, from which the characteristics of the fluid inclusion, the ratio of the wave speed to radius, can be determined. An application of the spectral analysis to quantitative nondestructive testing of materials is also discussed.

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