Theory of normal modes and ultrasonic spectral analysis of the scattering of waves in solids

Abstract

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. Subject Classification: [43]20.15, [43]20.30.

Elastic Waves in Solids

“…This was found first for a 1158/ Vol. 50, DECEMBER 1983 Transactions of the AS ME circular fluid cylinder in an elastic solid [106] and an elastic sphere in a fluid. A general theory of resonance scattering and numerous recent contributions were reviewed by Flax, Gaunaurd, and Uberall [1.07].…”

Study of beamforming techniques for ultrasound imaging in nondestructive testing

“…The method proved to give exact solutions for problems with simple obstructions such as a permyshaped crack [53], spherically-shaped inclusions [55,56], or cylindrical discontinuities [57,58]. Elastic wave propagation in isotropic [59,60] and transversely isotropic media was also predicted through the use of seminumerical techniques involving this method.…”

Finite element study of ultrasonic imaging

“…Separation of variables in certain coordinate systems gives a solution in the form of an eigenfunction (special function) expansion for problems with simple penny-shaped cracks [1], cylindrical [2,3] or spherical [4,5] inclusions in an infinite full or an infinite half space. Semi-numerical techniques also predict elastic wave propagation for isotropic [6,7] or transversely isotropic [8,9] materials.…”