On the use of the transfer matrix method to evaluate sound insulation in complex building partitions

The transfer matrix method (TMM) represents a powerful tool to investigate wave propagation through different media, which could be particularly suitable to compute sound transmission through building partitions. Even though layered structures can be easily modelled by using the TMM approach, it is not always easy to determine the elastic properties of each layer the partitions is made of. Traditional partitions, generally made in masonry with clay or concrete bricks coupled together with mortar joints, are inhomogeneous and anisotropic structures whose elastic properties are difficult to measure. Again, cross-laminated timber (CLT) panels, due to their peculiar substructure, might exhibit a highly orthotropic behaviour. A homogenisation approach, based on a minimization algorithm of the transmission loss (TL) of the bare structure, is proposed in this paper. It allows to consider inhomogeneous or anisotropic materials as an equivalent elastic solid described by effective frequency-depended elastic properties. The reliability of this approach is validated by comparing the TL of different building partitions computed using the TMM with the experimental sound insulation determined by means of laboratory measurements.