On the reciprocity relationship between direct field radiation and diffuse reverberant loading

This analysis is concerned with the derivation of a "diffuse field" reciprocity relationship between the diffuse field excitation of a connection to a structural or acoustic subsystem and the radiation impedance of the connection. Such a relationship has been derived previously for connections described by a single degree of freedom. In the present work it is shown that the diffuse-field reciprocity relationship also arises when describing the ensemble average response of connections to structural or acoustic subsystems with uncertain boundaries. Furthermore, it is shown that the existing diffuse-field reciprocity relationship can be extended to encompass connections that possess an arbitrary number of degrees of freedom. The present work has application to (i) the calculation of the diffuse field response of structural-acoustic systems modeled by Finite Elements, Boundary Elements, and Infinite Elements; (ii) the general calculation of the Coupling Loss Factors employed in Statistical Energy Analysis (SEA); and (iii) the derivation of an alternative analysis method for describing the dynamic interactions of coupled subsystems with uncertain boundaries (a generalized "boundary" approach to SEA).