| This thesis treats radiation and scattering of sound waves in the presence of fluid-loaded thin elastic cylindrical and spherical shells. The pressure fields in the fluid media are formulated in terms of Green's functions, which are attacked by a spectral analysis and synthesis procedure. This involves decomposition of the overall problem into one-dimensional constituents by the method of separation of variables, and reassembling of the one-dimensional solutions into the multi-dimensional Green's functions via a spectral integration over contours surrounding singularities of the one-dimensional Green's functions in the complex planes of (spatial) spectral parameters (separation parameters). Alternative representations that favor different parameter ranges are then derived directly from the general spectral integral forms, with emphasis placed on ray acoustic reductions that give rise to fundamental wave processes, such as incident and specularly reflected waves as well as shell-guided leaky, creeping, and trapped waves, on a physically observable base. In particular, a nonconventional extension is taken of the physical bounded angular domains descriptive of oscillatory waves into the nonphysical unbounded angular domains descriptive of traveling waves, with the relation between the two domains established via an infinite set of "image" sources placed in the infinite domain: it changes the discrete wavenumber spectra associated with conventional angular harmonics into spectral continua of traveling waves, thereby facilitating ray acoustic parametrizations without intervention of the conventional Sommerfeld-Watson transform. Furthermore, the exact spherical harmonic expansion and the rigorous ray-acoustic parametrization are implemented numerically for plane wave far field scattering (both monostatic and bistatic) from empty elastic thin spherical shells in water. Comparison with reference solutions based on full elastic equations establishes that the thin shell model is accurate at least for (shell thickness)-to-(radius) radios of 1% or so, and the ray acoustic algorithm is reliable over ranges 5 {dollar}<{dollar} ka {dollar}<{dollar} 50 (k is the wavenumber in the exterior fluid). The ray algorithm has also been extended phenomenologically to thick spherical shells of (h/a){dollar}sim{dollar} or {dollar}>{dollar}5%, with similar satisfactory results. Being physically based, the ray parametrizations can subsequently be adapted to accommodate deformations, truncations, and other perturbations of the cylindrical and spherical shell prototypes. |
