Frequency-Dependent Attenuation and Phase Velocity Dispersion of an Acoustic Wave Propagating in the Media with Damages

In frame of the self-consistent mathematical model, which includes the dynamics of a material and the state of its defects, the particular qualities of acoustic wave propagation in the material with damage is considered. In this study a constitutive equation of the damaged medium is derived and the similarity between the models for damaged materials and the medium with memory is confirmed. The dispersion analysis of the model is carried out, and it is shown that the damage of the material gives rise to frequency-dependent attenuation and anomalous dispersion of phase velocity of acoustic wave propagating through that material. This makes it possible to estimate the damage of the material by means of a nondestructive acoustic method.