In the statistical energy analysis (SEA) of high frequency noise and vibration, a complex engineering structure is represented as an assembly of subsystems. The response of the system to external excitation is expressed in terms of the vibrational energy of each subsystem, and these energies are found by employing the principle of power balance. Strictly the computed energy is an average taken over an ensemble of random structures, and for many years there has been interest in extending the SEA prediction to the variance of the energy. A variance prediction method for a general built-up structure is presented here. Closed form expressions for the variance are obtained in terms of the standard SEA parameters and an additional set of parameters alpha(k) that describe the nature of the power input to each subsystem k, and alpha(ks) that describe the nature of the coupling between subsystems k and s. The theory is validated by comparison with Monte Carlo simulations of plate networks and structural-acoustic systems.

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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.

Imperfections during the manufacturing process can cause significant variations in the noise and vibration levels exhibited by nominally identical structures. Any response calculations employed during the design process should ideally take account of these uncertainties and predict the expected range in performance. Recently a hybrid method has been developed to predict the ensemble average response of a built-up system by combining a deterministic model of parts of the system with a statistical model of other components [Shorter, P. J., and Langley, R. S. (2005) J. Sound. Vib., 288, 669-700]. In this paper the method is extended to predict the ensemble variance of the response. Expressions are derived for the variance of the vibrational energies in the statistical components, and for the variance of the cross spectrum of the response of the deterministic components, which augment the mean values of these quantities predicted by the original theory. The method employs a nonparametric model of uncertainty, in the sense that the statistical components are taken to carry diffuse wave fields, and this obviates the requirement for a detailed description of the system uncertainties. The method is validated by application to a range of coupled plate structures, and good agreement with detailed Monte Carlo simulations is found.

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This paper is concerned with the ensemble statistics of the energy density of a random system subjected to a harmonic point load. Both the mean and variance of the reverberant energy density ͑i.e., the total response minus the direct field͒ are investigated. It is shown that the ensemble average of the reverberant energy density is not spatially homogeneous, but rather the value at the drive point is between two and three times the spatially averaged value, depending on the modal overlap factor. This result is closely analogous to established results regarding the case of transient excitation. Expressions are also derived for the relative variance of the reverberant energy density both remote from the drive point and at the drive point, and a number of anomalies are found in existing results. A comparison is made with simulation results for a randomized plate, and this comparison highlights the importance of the ensemble size considered in the simulations. The present analysis is based on a random point process model of the system natural frequencies, and both Gaussian orthogonal ensemble ͑GOE͒ statistics and Poisson statistics are considered.

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