Plates with regular stiffening in acoustic media: Vibration and radiation

Abstract

Flat plates and cylindrical shells with identical stiffeners at regular intervals constitute spatially periodic structures, and specially convenient methods of analysis are available for the study of their vibrations. Some of the methods are suitable for the inclusion of the effects of fluid loading from adjacent acoustic media. This paper outlines the nature of the free wave motion that can occur in periodic structures that are stiffened either in one direction or in two orthogonal directions. It is shown how their responses to distributed sound fields can be determined by using displacement functions consisting of a series of space harmonics or of simple assumed polynomial modes. The sound that is reradiated or transmitted by the structure is also found. Methods that have been developed for analyzing the response and radiation due to line or point forces are reviewed. Recent developments in the analysis of periodically stiffened cylindrical shells are described. The hierarchical finite element method has been applied to determine flexural wave speeds in both flat reinforced plates and in reinforced cylinders. Symbolic computing has been used to set up the relevant stiffness and mass matrices. Some computed results are presented.