Creeping wave description of surface wave modes on elastic cylindrical shells

Abstract

Dispersion and attenuation curves are given for identified surface modes in the scattered pressure from elastic cylindrical shells insonified by a normally incident plane wave. The results are derived using two different techniques for air‐filled aluminum shells of several different wall thicknesses, b/a (ratio of inner to outer radius). The first series of numerical results are calculated using the Sommerfeld‐Watson transformation and determining the roots of a 6 × 6 secular determinant. The second method is used to derive similar results by analysis of the partial wave responses. The second method results, for a thick shell, are favorably compared with previously obtained creeping wave results for a solid elastic cylinder. For low values of b/a, the Rayleigh and Stoneley waves on the shell are shown to approach limiting values for increasing ka which correspond to the Rayleigh and Stoneley wave speeds defined for the infinite half‐space, and the Franz and Whispering Gallery modes approach the bulk wave velocities for the external and shell materials respectively. For thin shells (b/a → 1), Whispering Gallery and Rayleigh modes have vanished and the symmetric and antisymmetric Lamb modes are prevalent over limited regions of ka. Calculations are carried out over the range 0.1 ⩽ ka ⩽ 200, the first method valid for higher ka, and the partial wave method valid at lower ranges of ka.