Asymptotic behavior of the added damping effect of a fuzzy substructure and the importance of modal overlap

Abstract

The theory of fuzzy structures was introduced by Christian Soize in 1986 as a means of predicting the average vibroacoustic behavior of complex structures with imprecisely known internals. The damping and mass loading effects of a fuzzy internal substructure, modeled by random 1-dof oscillators, are analyzed through a boundary impedance. The Pierce-Sparrow-Russell and Strasberg-Feit models of fuzzy structures simplify the mathematics involved and concentrate on the physical concepts behind the added damping and mass loading effects of the internal substructure. Both models contain a problematic step in which a discontinuous impedance sum is replaced with a smooth integral. This paper explores the asymptotic behavior of the impedance sum in the limits of a large number N of attachments and small attachment damping ζ in order to determine the viability of this step. Modal overlap plays a crucial role, since half power points of individual attachment resonances overlap for small ζ when the density of attachments is high enough or for fewer attachments when the damping of individual attachments is high enough. It is found that the impedance sum sufficiently approaches the integral limit when Nζ ≧2. [Work originally sponsored by ONR.]