Reduction of fluid-loaded ribbed shells to equivalent uniform structures for mid- to high-frequency structural acoustic analysis

Abstract

The acoustic and vibratory behavior of fluid-loaded shells with ribs and other structural discontinuities is of great interest in naval applications. These structural discontinuities lead to complex phenomena, especially at mid- to high-frequencies where shell wavelengths are shorter than the discontinuity spacing. The methods of homogenization and local/global decomposition can be used to divide this problem into two parts. In the global problem, periodic discontinuities are replaced by an equivalent distributed suspension with slowly varying properties. This problem can be solved much more efficiently than the original problem since all rapidly varying scales have been removed. The local problem is solved separately and independently, except for amplitude information from the global problem. The local problem formulation provides transfer function information that defines the suspension in the global problem. Once the formulation has been developed for a specific structure, the global problem is solved first, and the local solution can be reconstructed afterward. The two constituent parts are then recombined to form a composite solution. As an illustration, this methodology is used to solve for Bloch waves on a structure with identical periodic discontinuities. The application of the theory to nonidentical discontinuities is also explained.