Investigation into the bistatic evolution of the acoustic scattering from a cylindrical shell using time-frequency analysis

Abstract

The time and frequency analyses of the acoustic scattering by an elastic cylindrical shell in bistatic method show that the arrival times of the echoes and the resonance frequencies of the elastic waves propagating in and around the cylindrical shell are a function of the bistatic angle, β, between the emitter and receiver transducers. The aim of this work is to explain the observed results in time and frequency domains using time-frequency analysis and graphical interpretations. The performance of four widely used time-frequency representations, the Smoothed Pseudo Wigner-Ville (SPWV), the Spectrogram (SP), the reassignment SPWV, and the reassignment SP, are studied. The investigation into the evolution of the time-frequency plane as a function of the bistatic angle β shows that there are the waves propagating in counter-clockwise direction (labeled wave+) and the waves which propagate in clockwise direction (labeled waves−). In this paper the A, S0, and A1 circumferential waves are investigated. The graphical interpretations are used to explain the formation mechanism of these waves and the acoustic scattering in monostatic and bistatic configurations. The delay between the echoes of the waves+ and those of the waves− is expressed in the case of the circumnavigating wave (Scholte-Stoneley wave). This study shows that the observed waves at β=0° and β=180° are the result of the constructive interferences between the waves+ and the waves−. A comparative study of the physical properties (group velocity dispersion and cut-off frequency) of the waves+, the waves− and the waves observed in monostatic configuration is conducted. Furthermore, it is shown that the ability of the time-frequency representation to highlight the waves+ and the waves− is very useful, for example, for the detection and the localization of defaults, the classification purposes, etc.