Leaky helical flexural wave scattering contributions from tilted cylindrical shells: ray theory and wave-vector anisotropy.

Abstract

At sufficiently high frequencies, cylindrical shells support a wave whose properties are analogous to those of the lowest antisymmetric Lamb wave on plates. When the shell is in water and the frequency exceeds the coincidence frequency, the flexural wave is a leaky wave that can be a major contributor to the scattering by tilted shells [G. Kaduchak, C. M. Wassmuth, and C. M. Loeffler, J. Acoust. Soc. Am. 100, 64-71 (1996)]. While the meridional ray-scattering contributions for such leaky flexural waves were previously modeled, the helical contribution can also be significant. A ray theory for those contributions is compared with the exact partial wave series (PWS) solution for infinitely long empty shells. The agreement between the ray theory and the PWS is only possible when a weak anisotropy of the flexural wave parameters is included in the evaluation of the ray theory. The anisotropy is determined numerically from the roots of a denominator in the PWS because approximations for the anisotropy from thin-shell mechanics are not applicable significantly above the coincidence frequency.