Spectral parametrization of wave scattering from a rigid aperture coupled enclosure with interior loading

Abstract

Wave interaction with complex structural environments can be analyzed by regarding the overall response as the response from coupled subsystems. The decomposition into subsystems is wavenumber-scale dependent, and the “best” classification involves weak coupling between subsystems but strong coupling of wave types within a subsystem. How to effect the classification is illustrated here for a cylindrical thin smoothly convex rigid shell, which grants access to an enclosed cylindrical convex rigid interior load via a narrow-slit aperture. The geometry suggests a parametrization of exterior wave phenomena by geometrically reflected, slit diffracted, and surface guided creeping waves, and of interior wave phenomena by guided local modes in the nonuniform waveguide formed by the region between the shell and interior boundary. The slit produces coupling among the exterior wave types and among the interior wave types, as well as between the exterior and interior. These couplings cause spatial wavenumber conversions from trapped, to radiating, etc. A system of state vectors, propagation matrices, and coupling matrices renders the overall description self-consistent, and permits the development of reduced forms by loading a significant (for example, resonant) subsystem with nonresonant remainders. The dynamics of the parametrization is illustrated by considering the numerical example of plane wave scattering as a function of aspect and frequency when the interior and exterior boundaries are eccentric circular cylinders. [Work supported by ONR and David Taylor NRDC.]