Dispersion in bilaminated cylindrical shells: Incidence angle and thickness impacts

Abstract

Under oblique incidence acoustic wave, we investigate theoretically and numerically the dispersion curves of bilaminated cylindrical shell which composed of copper and stainless steel, immersed in water and filled with air. The investigation delves into the influence of the incidence angle on the phase and group velocities of guided waves. As the incidence angle increases, circumferential and helical guided waves are initiated parallel to the axis of the cylindrical shell. This initiation transpires at an incident angle denoted as αl=sin−1(C1/Cl) (where C1 represents the wave velocity in water and Cl signifies the phase velocity of the lth guided wave). Beyond this angle, the respective guided wave undergoes a transition to a “cut off” state, adopting an evanescent character. This investigation also unveils that at a particular angle of incidence, resonance trajectories of certain guided waves manifest at cut-off frequencies, and these frequencies escalate with the angle of incidence. Concurrently, we examine how varying thicknesses impact the dispersion curves of waves in both the outer layer (copper) and inner layer (stainless steel) of the bilaminated shell. Notably, we observe a sensitivity in the phase and group velocities concerning changes in these thicknesses. Furthermore, the dispersion curves of the bilaminated cylindrical shell presents a tendency to shift towards low frequencies as either the outer or inner layer progressively thickens. This trend brings the dispersion curves closer to those of a single-layered cylindrical shell composed of the material with the greater thickness in the bilaminated shell. The obtained results demonstrate a commendable agreement with the existing experimental findings on copper and stainless steel single-layered cylindrical shells.