A hybrid deterministic-diffuse approach to the analysis of vibration transmission across finite junctions

The average vibro-acoustic performance of a junction between two-dimensional structural elements is often quantified by its diffuse vibration reduction index, especially for building structures. Existing prediction methods either assume an infinite junction length or consider non-diffuse transmission. In this work an approach for predicting the diffuse vibration reduction index of finite junctions of arbitrary complexity is developed. First, the mean and (co)variance of the diffuse coupling loss factor of a finite junction are obtained within the hybrid deterministic-statistical energy analysis framework. Dedicated basis functions are proposed to efficiently describe the interface displacements of the diffuse subsystems. Subsequently, the relation between the mean vibration reduction index and the coupling loss factor is established. It is demonstrated that this relation involves both the mean and the variance of the coupling loss factor. Additionally, the relation between the variance of the vibration reduction index and the (co)variances of the coupling loss factors is derived. Finally, the proposed approach is both numerically validated and compared to experimental results for several finite junctions between building elements, which are modelled as plates. For the numerical validation, the results obtained with the proposed approach are compared with those of an ensemble of junctions with the same bare structure but with point masses attached at random locations on the walls and floors. The validations demonstrate that an accurate prediction of the mean and variance of the diffuse vibration reduction index is possible when the uncertainty across the random ensemble is sufficiently large. The comparison to experimental results involves T and X junctions between directly coupled plates. At low and medium frequencies, the experimental data are well captured within the 95% confidence interval of the hybrid model results. At high frequencies, the uncertainty on the hybrid results is very small; such differences with the experimental data are caused by modelling errors.