Dispersion Analysis of Acoustic Circumferential Waves Using Time-Frequency Representations

Abstract

The dispersion estimation is an important objective in acoustic processing. This work presents a study of the group velocity dispersion of some circumferential waves propagating around an elastic tube. The dispersive character of the circumferential waves is theoretically known but the experimental measurement of the group velocity in a dispersive medium is still a complex operation. We have determined the characteristics of the circumferential waves dispersion for aluminium tube using a time-frequency representations. Among these time-frequency techniques the Wigner-Ville distribution, the spectrogram and the reassigned spectrogram are used here for its interesting properties in terms of acoustic applications. These techniques are applied on a measured acoustic signal scattered by an air-filled tube immersed in water. From these time-frequency images the symmetric (S0), antisymmetric (A1) and the symmetric (S1) circumferential waves are identified and the dispersion group velocities are also determined for these circumferential waves. The obtained image of the reassigned spectrogram technique allows a better visibility of the circumferential waves which are propagated around the tube through the good resolution of the time-frequency image. From the obtained image, one can go up easily with certain characteristics of the circumferential acoustic waves such as the group velocity and the cut-off frequencies of each circumferential waves. The results obtained from the time-frequency image of the reassigned spectrogram are in good agreement with those calculated values using the theoretical methods given in the scientific literature.