Raghib R., Naciri I., Khalfi H., Elmaimouni L., Yu J., Benami A., Bybi A. «A Semi-Analytical Approach for Analyzing Acoustic Wave Propagation in Three-Dimensional Hexagonal FGM pipes» Акустический журнал, 70, № 6, с. pp1-24 (2024)

This study presents a semi-analytical approach for analyzing acoustic wave propagation in three-dimensional hexagonal functionally graded (FGM) pipes composed of Aluminum (Al) and silicon nitride (SN), employing the Legendre polynomial method. Two different configurations of FGM pipes, namely (SN/Al/SN) and (Al/SN/Al), are investigated by solving the governing motion equations. The characteristics of phase velocity and normalized frequency dispersion curves for various modes and frequencies are analyzed, revealing the complex wave behavior arising from the hexagonal structure. The study examines the effects of material gradients, pipe geometry, and boundary conditions, highlighting the strong influence of normal stresses on boundary conditions. Additionally, the distribution of acoustic wave energy is found to be mainly confined to the interior of the cylinder. Our results demonstrate a high level of agreement with existing research, affirming the precision and reliability of our method. The Legendre polynomial method accurately captures wave propagation in functionally graded pipes, offering a versatile approach applicable to various structures. These findings provide valuable insights into acoustic wave behavior in functionally graded pipes, with potential applications in non-destructive testing, material characterization, and structural health monitoring.