S-Transform–Based Time–Frequency Analysis of Backscattered Acoustic Signals

Acoustic scattering offers a reliable non-destructive route for investigating submerged monolayer cylindrical shells, enabling wall thickness, material properties, and degradation effects to be inferred without compromising structural integrity. Among the most informative descriptors, the reduced cut-off frequency of the antisymmetric circumferential guided mode A₁ is particularly attractive because it is highly sensitive to geometric variations and material contrast, providing a compact indicator for condition monitoring. Here, we employ a time–frequency analysis based on the S-transform to enhance modal energy localization in the backscattered response and to extract the A₁ reduced cut-off frequency under noisy conditions. The cut-off is identified by detecting the first statistically significant energy ridge after band selection and robust normalization. The extracted values show close agreement with resonance eigenmode theory over a broad range of configurations described by the radius ratio b/a, where a and b denote the outer and inner radii, respectively. Overall, these results demonstrate that S-transform-based cut-off tracking provides an efficient framework for reduced-frequency characterization of submerged cylindrical shells.