Local Kramers–Kronig Relations between the Attenuation Coefficient and Phase Velocity of Longitudinal Ultrasonic Waves in Polymer Composites

Abstract

The relationship between the experimentally obtained attenuation coefficient and dispersion of the phase velocity of longitudinal ultrasonic waves in polymer composite materials has been analyzed. The laser optoacoustic method has been used to measure the ultrasonic attenuation and velocity in a wide frequency range. Verification of the Kramers–Kronig relations for ultrasound-scattering and absorbing carbon fiber reinforced plastic (CFRP) composites has been performed using the analysis of the relationship between the frequency dependences of the attenuation coefficient and phase velocity of longitudinal acoustic waves in samples. We have shown that the Kramers–Kronig relations between the ultrasonic attenuation and phase velocity are valid within the 1–10 MHz frequency range without regard to a particular mechanism of the decay in the energy of an initial acoustic wave during its propagation in a composite.