Backscattering near the coincidence frequency of a thin cylindrical shell: Surface wave properties from elasticity theory and an approximate ray synthesis

Abstract

A simple ray approximation is demonstrated for the backscattering of sound by a thin empty cylindrical shell in water at normal incidence. The approximation is applied to the region near the coincidence frequency and is used to interpret prominent features in that region associated with a subsonic guided wave. With increasing ka, the features exhibit a transition from resonance behavior dominated by interference with the specular reflection. Another feature is the interference of resonance contributions of the leaky s0 Lamb wave which may produce maxima or minima in the amplitude depending on the ka region. The cylinder studied is 2.5% thick stainless steel for ease of comparison with a similar spherical shell [P. L. Marston and N. H. Sun, J. Acoust. Soc. Am. 92, 3315–3319 (1992)] and the guided wave properties were computed from elasticity theory rather than shell approximations. A novel geometric derivation is given for the relative phases of the coupling coefficients of subsonic waves on cylinders and spheres and some implications for scattering by slightly eccentric spheroids are noted.