Plates with regular stiffening in acoustic media: Vibration and radiation

Abstract

Flat plates and cylindrical shells with regular and identical stiffening constitute spatially periodic structures. Specially convenient methods of vibration analysis are available for these, some of which are suitable for the inclusion of the effects of fluid loading from adjacent acoustic media. This paper outlines the nature of free wave motion in periodic structures stiffened either in one direction or in two orthogonal directions. The structural response to distributed harmonic pressure fields is analyzed by using displacement functions consisting of a series of space harmonics. The sound radiated or transmitted by the vibrating structure is also found. The method of space harmonics is next combined with the method of phased array receptance functions to yield equations for the propagation constants of fluid-loaded periodic plates, stiffened in just one direction. Some calculated propagation constants are presented. Recent developments in the application of the hierarchical finite-element method to periodic structures are described. Computed results are presented for the propagation constants of an orthogonally stiffened plate, without fluid loading. Consideration is given to those frequency ranges and wave motions that could radiate into an adjacent medium.