Separation of interfering acoustic scattered signals using the invariants of the time-reversal operator. Application to Lamb waves characterization

The D.O.R.T. method (in French, Décomposition de l’Opérateur de Retournement Temporel) is a scattering analysis technique using arrays of transducers. The method was shown to be effective in detecting and focusing on pointlike scatterers in Prada et al. [J. Acoust Soc. Am. 99, 2067–2076 (1996)]. Here the D.O.R.T. method is extended to other geometries, applying it to an air-filled cylindrical shell embedded in water. It is shown that the diagonalization of the time-reversal operator permits the various elastic components of the scattered field to be extracted. For the considered cylinder, these components are mainly three circumferential waves (A0, A1, and S0 Lamb modes). Each Lamb mode is shown to correspond to an invariant of the time-reversal operator. The dispersion curves of these waves are calculated from the invariants. In particular, the cutoff frequency of the A1 mode is found and provides the thickness of the shell. Finally, resonance frequencies of the shell are deduced from the frequency dependence of the eigenvalues of the time-reversal operator.