Hybrid ray-mode parametrization of acoustic scattering from submerged internally loaded thin cylindrical elastic shells: Direct construction from continuous wave spectra.

Abstract

In a companion paper [L. B. Felsen and Y. P. Guo, preceding paper], an observable-based hybrid ray-mode parametrization (OBP) for a broad class of axially-invariant two-dimensional acoustic plane wave scattering from submerged internally loaded thin cylindrical elastic shells has been developed by reformulation of solutions constructed in terms of angular harmonic resonant modes. Now, the solution is developed directly in terms of the continuous wave-number spectra that lead naturally to the hybrid ray-mode OBP, thereby incorporating the wave phenomenon from the beginning. The previous resonant-mode and present traveling-wave formulations are compared at various stages. These comparisons are aided by the Poisson sum formula which establishes the analytic connection between the resonant-mode series and the wave-number continuum, showing the exact equivalence of the two approaches. The paper concludes with observations concerning the numerical implementation of these alternative algorithms, especially in regard to characterizing the induced forces on the shell that account for the interior loads. [Work supported by ONR.]