Simplification of the transfer matrix model for acoustic screens

Modern sound packages often feature coatings which are, in most cases, made of porous media. Their potentially strong impact on the acoustic performance underscores the need to include them in simulations although their small thickness is an obstacle to precise characterisation. The usual physical models for poro-elastic and porous media are either too crude to correctly account for the film effects (equivalent fluid, limp, etc.) or may seem over-refined for the task (Biot theory). In this paper, a simplified approach based on a transfer matrix representation and the Biot theory is presented and tested. It includes assumptions on the evolution of fields in the films and lead to a sparser transfer matrix than the usual Biot model. The proposed expression is shown to be accurate for a wide range of films and even outperforms other simplified representations in some cases (for instance in a stochastic context).