Analysis of the acoustic signals backscattered by a tube using the time-frequency representations

Abstract

The normal excitation of a tube immersed in water by the acoustic plane wave, circumferential waves are generated inside the shell. These circumferential waves, standing form stationary waves on the circumference of the tube for some frequencies. These stationary waves, constituting resonances of the tube which are perfectly visible on the backscattered spectrum. Moreover, the studies carried out on the diffusion of a plane acoustic wave by target were based primarily on the use of the monodimensional methods (Temporal domain and/or frequencial domain). To exceed the disadvantages of these methods, in this work, we used the time-frequency representations such as the Short-Term Fourier Transform (STFT), Wigner-Ville Distribution (WVD) and Wavelet Transform method. These representations are applied to a theoretical signal backscattered by a tube of aluminium, copper and steel with radii ratio b/a = 0.95 (a is the external radius, and b the internal radius). From the time-frequency images obtained we have visualized the dispersion of circumferential waves (S0, A1, S1,œ) and identified these different waves. This analysis permits to compare between these time-frequency representations. And also we have compared between the cut-off frequencies of circumferential waves obtained from these representations and those computed by the proper modes theory of the vibration.