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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).

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This analysis is concerned with wave propagation and damping in linear viscoelastic laminates. A spectral finite-element method is developed and used to calculate the dispersion properties of the first few wave types of a given laminate; the proposed approach provides a robust and numerically efficient alternative to the transfer matrix method in certain applications. The proposed approach is also well suited to the calculation of the wave types of sections whose material properties vary continuously throughout the thickness of the section. A one-dimensional finite-element mesh is used to describe the through-thickness deformation of the laminate, and the dispersion equation for plane-wave propagation is formulated as a linear algebraic eigenvalue problem in wave number at each frequency of interest. The resulting eigenvectors and eigenvalues can be computed using standard numerical routines and used to investigate the dispersion characteristics of the propagating wave types of the section. The damping loss factor of each wave type is estimated from the cross-sectional strain energy distribution of the laminate. The proposed approach is well suited to modeling the structural-acoustic response of sandwich panels, constrained layer damping treatments, and general viscoelastic laminate sections in statistical energy analysis (SEA) codes.

The finite element (FE) and statistical energy analysis (SEA) methods have, respectively, high and low frequency limitations and there is therefore a broad class of "mid-frequency" vibro-acoustic problems that are not suited to either FE or SEA. A hybrid method combining FE and SEA was recently presented for predicting the steady-state response of vibro-acoustic systems with uncertain properties. The subsystems with long wavelength behavior are modeled deterministically with FE, while the subsystems with short wavelength behavior are modeled statistically with SEA. The method yields the ensemble average response of the system where the uncertainty is confined in the SEA subsystems. This paper briefly summarizes the theory behind the method and presents a number of detailed numerical and experimental validation examples for structure-borne noise transmission.