Rigidly-backed micro-perforated panels (MPPs) are Helmholtz-type absorbers whose performance is usually limited to narrow frequency ranges. Multi-layer or multi-array partitions enable to extend their absorption properties over a broader bandwidth. Optimal selection of their parameters often leads to a distribution of macro and micro-perforated panels constitutive of the overall partition. However, there is not yet a full consensus on a unified impedance model whose end-correction terms may contribute to the dissipation of both macro- and micro-perforated panels. In this study, an enhanced multi-modal approach is formulated that is able to describe the dissipative and reactive properties of multi-layer backed or unbacked macro-or micro-perforated partitions. It provides a unit cell transfer impedance that accounts for visco-thermal boundary layers (VTBLs) and high-order evanescent modes within the perforation and at the panel walls. It is validated against Finite Element Visco-Thermal Acoustics models, but at a much lower computational cost. It is shown that the presence of VTBLs over the solid surfaces cannot be neglected for perforates with a thickness-to-hole diameter ratio lower than 0.5 or for multi-layer acoustic fishnets with thin air gaps lower than six times the VTBLs thickness.
This study was funded in Spain by the Ministerio de Economía y Competitividad project TRA2017- 87978-R, AEI/FEDER, UE, and the mobility program ILINK+2018. It was supported in France by the ANR VIRTECH (ANR-17-CE10-0012-01).