Three-dimensional Green’s function for fluid-loaded thin elastic cylindrical shell: Alternative representations and ray acoustic forms

Abstract

In this paper, the general spectral integral form of the three-dimensional pressure Green’s function for a fluid-loaded thin elastic cylindrical shell [Felsen et al., J. Acoust. Soc. Am. 87, xxx–xxx (1990)] is reduced to furnish two alternative representations that emphasize propagation phenomena associated essentially with the radial–azimuthal (r,φ) and the radial–longitudinal (r,z) coordinates, respectively. For the former, a decomposition of the point source field into a continuum of linearly phased z-directed line sources defines the problem parametrization, whereas for the latter, the decomposition is into a discrete infinity of ring sources with azimuthally periodic (angular harmonic) linear phasing. The reduced forms obtained in this manner are then examined in appropriate parameter regimes. For external phenomena in the (r,φ)-favored formulation, asymptotics leads to ray acoustic interpretations for the total field in terms of the conventional incident and reflected waves, augmented by shell-guided creeping waves and leaky waves that are excited by phase matching on the shell surface, as well as trapped waves in the shell excited by evanescent tunneling from the source. The shell-guided ray fields, which represent quasicompressional, quasiflexural, and quasishear phenomena, exhibit anisotropic behavior. In parameter regimes that emphasize axial guiding along the shell and the interior fluid [favoring (r,z)], the trapped waves, which are less important for the external processes, become the dominant constituents.