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

摘要

Spectral analysis of ultrasonic pulses in elastic solids has attracted wide attention in recent years as a tool of the quantitative nondestructive test method. So far, a complete analysis of the power spectra of the scattered pulses of any geometry is still lacking. This has hindered the general understanding and the application of ultrasonic spectroscopy to the detection of inclusions of flaws in solids. This report presents a theory of the spectral analysis of the scattering of elastic waves and illustrates it 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 spectral analysis to quantitative nondestructive testing of materials is discussed. (Author)