A novel approach for modeling of the ultrasonic signal backscattered in immersed multilayer structures at normal incidence: Time, Frequency, and Velocity dispersion representation

• Published in: Mechanical systems and signal processing 2023-09, Vol.198, p.110415, Article 110415
• Main Authors: Tafkirte, Mounir, Hamine, Adil, Mesbah, Hicham, Aboudaoud, Idris, Décultot, Dominique
• Format: Article
• Language: English
• Subjects: Dispersion curves; Frequency spectrum; Longitudinal modes; Multilayer structures; Time–frequency distribution; Transfer matrix method
• ISSN: 0888-3270; 1096-1216
• DOI: 10.1016/j.ymssp.2023.110415

This study proposes a theoretical procedure for modeling ultrasonic signal backscattered in normal incidence by a multilayer structure (MS) immersed in water. The propagation of a longitudinal ultrasonic wave in a MS is studied analytically by using the transfer matrix method (TMM), in which each layer is established as a quadrupole formalism combining the stresses and velocities. The transfer matrices allow us to determine the reflection coefficient of the multilayer structure. The MS solid/liquid/solid case is studied in both insonation configurations (direct and reverse). The modeled ultrasonic response is represented in both time and frequency domains and validated by comparison with experimental data published previously. The time–frequency methods such as spectrogram (SP) and the smoothed pseudo-Wigner–Ville (SPWV) are also used to investigate the character and the value of the non-dispersive of the longitudinal wave. Moreover, the TMM method is used under different conditions (different layer thicknesses, non-uniform distribution of layers, and any frequency range), which are among the causes of MS dispersion. TMM method is able to show this behavior and is exploited to produce (Distance versus Time) and (Distance versus Frequency) representations of wave propagation for each studied MS. The perfect agreement of the comparison of TMM dispersion results with the results is achieved by using time–frequency methods in the case of a 5 MHz central frequency. •The TMM models ultrasonic signal backscattering through multilayer structures in water and avoids numerical instability caused by Frequency × Thickness problem.•Ultrasonic signals modeled by TMM showed nondispersive character under normal incidence for certain frequencies via spectrogram.•Dispersive character of multilayer structures studied via TMM method in (X; t) and (X; f) planes.•The TMM method is exploited to generate dispersion curves of longitudinal modes for each of the studied multilayers.