Addressing complexity in structural acoustics—Fuzzy structure and effective impedance theories

Abstract

The theory of fuzzy structures (TFS) and effective impedance theories (EIT) are presented as two frameworks for accommodating structural acoustic complexity, occasioned by incompletely described, small sized structural elements appended to a large sized main structure. The presentation identifies the TFS as part of an extensive literature spanning applications of statistical physics and composite materials. EIT are presented as renormalizations of a TFS, for estimating precisely described “smoothed” measures of the main structure response. The smoothing applied refers to either a statistical smoothing or a spatial smoothing. A special class of small scale structural elements, designated as isolated and point connected, is considered in some detail. Thus, two specific types, classified as added mass and added stiffness fuzzy structures, are identified and shown to result in fundamentally different EIT. The issue of an enhanced dissipation of the vibrations of a large scale main structure by the attachment of small scale detail structures is investigated and related to previous studies. Several outstanding research issues are identified.