An efficient hybrid transfer matrix-statistical energy analysis approach for predicting the sound transmission through thick and layered walls

Layered wall and floor systems are very frequently applied in building construction in order to achieve a high thermal and/or sound insulation with a relatively low weight. Examples are double walls with decoupled wall leafs, roof panels, floors with floating screeds, double and triple glazing, etc.At high frequencies, the airborne or impact sound transmission through such layered systems can be efficiently computed with a transfer matrix approach. It is then assumed that the wall or floor is of infinite lateral extent. This enables modeling the sound transfer through each solid, fluid and/or poro-elastic layer analytically in the frequency-wavenumber domain.At lower frequencies however, neglecting the modal behavior of the wall can lead to large prediction errors, especially when very stiff solid layers or very thin air layers are present. For this reason, the transfer matrix approach is extended here in such a way that for rectangular walls and floors, the boundary conditions can be approximately accounted for. The fundamental idea is to limit the possible wavelengths in a given layer at a given frequency to those wavelengths that are compatible with the boundary conditions. The developments are validated against more expensive numerical prediction models and experimental data.