Comparisons of backscattering from cylindrical shells described by shell and elasticity theories

Abstract

For kah < 1, where k is the fluid wave number, a is the radius of the cylinder, and h is the wall thickness, scattering from infinite cylindrical shells at normal incidence can be described by a combination of specular reflection and the zeroth‐order symmetric Lamb wave (S0). Thin‐shell theory is found to closely describe the resonance behavior from this two‐wave interaction. At higher values of kah, additional scattering from the antisymmetric Lamb modes above the plate coincidence frequency of the shell material is predicted by elasticity theory. For materials with longitudinal wave speeds greater than the fluid, and shear wave speeds less than for the fluid, no coincidence frequency is predicted by plate nor shell theory. Accordingly, backscattering from this class of materials described by shell theories, which include bending, show no evidence of the antisymmetric Lamb wave. For materials where both the compressional and shear wave speed are greater than the sound speed in fluid, the adequacy of the shell theory to describe the antisymmetric Lamb wave response is determined by comparison with full elasticity theory and with the results of Veksler and Korsunskii [J. Acoust. Soc. Am. 87, 943–962 (1990)].