Determination of the cut-off frequency of the anti-symmetric circumferential waves using the time-varying autoregressive TVAR

In this paper, we introduce the time-frequency AR model as a time-varying autoregressive (TVAR) approach for modeling non-stationary signals, and frequency information is then extracted from the TVAR parameters. The impulse response backscattered by Aluminium cylindrical shell is analysed from the parametric time-frequency representation. This representation is called TVAR spectrum. The parameters of this model are determined by the adaptive algorithm. The adaptive methods may be sufficient for the TVAR parameter estimation, if the non-stationary part of a signal changes slowly. The time-varying spectrum "TVARS" (power spectral density) is applied to determine much more accurately the cut-off frequency of the anti-symmetric circumferential waves (Al and A2) propagating around the circumference of the tube of radii ratio equal to 0.95. From the TFAR representation obtained, we have estimated the cut off frequencies with a precision. These frequencies and the transverse velocity of aluminium are compared with those computed by the proper modes theory given in the scientific literature. A good agreement is obtained.