Sound insulation prediction of complex building elements using a hybrid finite element - Statistical energy analysis approach

Predicting the airborne sound insulation of a complex building element generally requires a detailed model of that element, as simplified analytical models such as an equivalent orthotropic plate are only accurate for the first few natural frequencies. A commonly adopted strategy therefore consists of constructing a detailed finite element model and computing the expected value of the sound reduction index by numerically integrating the plane-wave transmission over all angles of incidence. This is not only computationally costly, but all information on the uncertainty of the predicted values due to the statistical nature of the diffuse field assumption for the rooms is also lost. In this work, an alternative method is therefore proposed, where a finite element model of a building element is coupled to statistical energy analysis models of the rooms. Both the mean and variance of the sound reduction index are computed, so that the uncertainty of the predicted values due to the generalized diffuse field assumption can be assessed. The method is then applied to the sound reduction index prediction of a rib-stiffened plate and a thicker masonry wall and validated against measured data. It is found that the proposed approach can capture both the complex dynamics of the walls and the uncertainty of the generalized diffuse field assumption of the rooms.