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Physical Ultrasonics of Composites$
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Dale Chimenti, Stanislav Rokhlin, and Peter Nagy

Print publication date: 2011

Print ISBN-13: 9780195079609

Published to Oxford Scholarship Online: November 2020

DOI: 10.1093/oso/9780195079609.001.0001

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Measurement of Scattering Coefficients

Measurement of Scattering Coefficients

8 (p.294) Measurement of Scattering Coefficients
Physical Ultrasonics of Composites

Dale Chimenti

Stanislav Rokhlin

Peter Nagy

Oxford University Press

In the previous chapters, we saw how waves in composites behaved under various circumstances, depending on material anisotropy and wave propagation direction. The most important function that describes guided wave propagation, and the plate elastic behavior on which propagation depends, is the reflection coefficient (RC) or transmission coefficient (TC). More generally, we can call either one simply, the scattering coefficient (SC). It is clear that the elastic properties of the composite are closely tied to the SC, and in turn the scattering coefficient determines the dispersion spectrum of the composite plate. Measuring the SC provides a route to the inference of the elastic properties. To measure the SC, we need only observe the reflected or transmitted ultrasonic field of the incident acoustic energy. In doing so, however, the scattered ultrasonic field is influenced by several factors, both intrinsic and extrinsic. Clearly, the scattered ultrasonic field of an incident acoustic beam falling on the plate from a surrounding or contacting fluid will be strongly influenced by the RC or TC of the plate material. The scattering coefficients are in turn dependent on the plate elastic properties and structural composition: fiber and matrix properties, fiber volume fraction, layup geometry, and perhaps other factors. These elements are not, however, the only ones to determine the amplitude and spatial distribution of energy in the scattered ultrasonic field. Extrinsic factors such as the finite transmitting and receiving transducers, their focal lengths, and their placement with respect to the sample under study can make contributions to the signal as important as the SC itself. Therefore, a systematic study of the role of the transducer is essential for a complete understanding and correct interpretation of acoustic signals in the scattered field. The interpretation of these signals leads ultimately to the inference of composite elastic properties. As we pointed out in Chapter 5, the near coincidence under some conditions of guided plate wave modes with the zeroes of the reflection coefficient (or peaks in the transmission coefficient) has been exploited many times to reveal the plate’s guided wave mode spectrum.

Keywords:   Auld and Kino reciprocity formulas, Bessel functions, Complex source point, Dirac delta function, Green’s function, Helmholtz equation, Numerical distance, Rayleigh surface waves, Sheet beams

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