Predicting the sound insulation of finite double-leaf walls with a flexible frame

With double-leaf wall systems such as plasterboard walls, a high sound insulation can potentially be achieved with a relatively low weight. The accurate sound transmission analysis of this type of wall is challenging since the leafs are usually coupled to a common frame, and since the finite dimensions play a role at lower frequencies. Existing analytical models for sound insulation prediction account for the deformation of the wall in an approximate way, while detailed numerical models are computationally very demanding. In this work, a sound insulation prediction model that achieves a high prediction accuracy at a low computational cost is developed. The wall components that display low geometrical complexity, such as the wall leafs and the cavity, are modelled in an analytical way. Sound absorbents in the cavity are modelled as equivalent fluids. The metal studs, which have a highly deformable cross section, are modelled in full detail with finite elements. The sound fields in the sending and receiving rooms are modelled as diffuse; they are rigorously coupled to the deterministic wall model by employing a hybrid deterministic-statistical energy analysis framework. With the resulting room-wall-room model, the airborne sound insulation is predicted for a range of double-leaf plasterboard walls with single, double and triple plating and with different cavity depths. The obtained transmission losses are validated against the results of an extensive set of experimental tests. A very good agreement between predicted and measured transmission loss values is observed. The single number ratings for the airborne sound insulation for nearly all walls differ from the experimental values by 0–2 dB, which is close to the average experimental reproducibility. At the same time, the computational cost is more than three orders of magnitude lower than for recently proposed models of similar accuracy.