Dm. Photiadis, ACOUSTICS OF A FLUID-LOADED PLATE WITH ATTACHED OSCILLATORS .1. FEYNMAN-RULES, The Journal of the Acoustical Society of America, 102(1), 1997, pp. 348-357
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.