Acoustic scattering from immersed composite cylindrical shells: Existence of zero group velocity circumferential waves

摘要

Some Lamb waves in a plate and some circumferential waves in a one-layer cylinder are characterized by the resonance frequencies where the group velocity is vanishing while the phase velocity remains finite. This paper investigates on the existence of these special waves which call zero group velocity waves (ZGV waves) in the case of the copper/polymer composite cylindrical shell immersed in water and filled with air. The acoustic scattering of a plane wave from this composite cylindrical shell is analyzed in the reduced frequency range (0: 1 < k(1)a(1) < 200; k(1) is the wave number and a(1) is the outer radius of the composite cylindrical shell). The study of the respective influence of the inner layer thickness (polymer) and the outer layer thickness (copper) shows that the existence of these waves is a function of these thicknesses. Moreover, this study depicts that the dispersion curves of the considered bilayer shell tend towards the dispersion curves of the one-layer cylindrical shell made from the material of the thicker layer of the bi-layer cylindrical shell (polymer or copper). The time-frequency representation of smoothed pseudo Wigner-Ville (SPWV) is used to extract some properties of the circumferential waves propagating in and around the bi-layer cylindrical shell. The obtained results by this representation are in good agreement with those obtained by the theoretical approach. (C) 2017 Elsevier Ltd. All rights reserved.