ACOUSTICS OF A FLUID-LOADED PLATE WITH ATTACHED OSCILLATORS .1. FEYNMAN-RULES

The ''fuzzy structure'' paradigm developed by Soize and others provide s a framework within which the acoustic properties of systems with com plex internal structure can be explored. In this two part paper, the a coustic properties of one of the simplest such systems, a fluid-loaded plate with attached internal oscillators, are explored. In Part I, th e theoretical tools needed in this investigation, the representation o f the Neumann series in terms of Feynman diagrams, is presented. In mo st ways, the formal aspects of this development are identical to simil ar results from other disciplines, but the presence of damping in the system, either internal or due to radiation into the fluid, requires o ne to make some modifications to existing theories. The rules for eval uating averaged quantities such as G...GG...G* involving higher-order products of the Green's function are given. These quantities are nece ssary to determine a number of relevant properties of the system inclu ding the scattering cross section and the size of typical fluctuations . The Feynman rules, detailed mathematical expressions which enable av eraged quantities to be evaluated for particular systems, are explicit ly given for the case in which the internals are simple oscillators di stributed uniformly and independently in both space and frequency. In Part II of this paper, the theoretical approach will be applied to pre dict a number of acoustic properties of the system.