Prediction and uncertainty quantification of structure-borne sound radiation into a diffuse field

When predicting the radiation of structure-borne sound into a room, it is often assumed that the generated sound field is diffuse. A diffuse field is by definition a random field, composed of a large number of statistically independent plane waves, the spatial phase of which is uniformly distributed and independent from the amplitude. It may represent the sound field of a conceptual ensemble of rooms with the same modal density and total absorption, but otherwise any possible arrangement of boundaries and small objects that scatter incoming sound waves. Adopting a diffuse field model therefore inherently implies that uncertainty due to random wave scattering is present in the computed results. This uncertainty can be large, especially at low frequencies. In this work, practical formulas are derived for computing not only the mean, but also the variance of energetic level quantities, such as the band-integrated spatially averaged sound pressure level, in a diffuse sound field caused by a mechanically excited structure. The obtained expressions are first verified in a simulation study, and then experimentally validated for a point-loaded bare plate and a rib-stiffened plate. It is found that both the average sound pressure level and its standard deviation can be well predicted. Knowledge of this standard deviation then allows the analyst to estimate, for example, by how much the spatially averaged sound pressure level in one particular room can deviate from the ensemble averaged result, and this for any frequency band.