Enhanced modal matching formulation for a cost-efficient computation of the acoustical properties of multi-layer perforated and micro-perforated partitions

Abstract

As rigidly backed micro-perforated panels (MPPs) are Helmholtz-type absorbers, their performance is typically limited to narrow frequency bands. The use of multi-layer or multi-array partitions has been widely studied to extend their absorption over a broader range. Optimal selection often requires combination of macro and micro-perforated panels constitutive of the overall partition. However, it is difficult to find a unified impedance model that may account for the whole range of hole diameters variations encountered in an optimization process. In this study, an enhanced multi-modal (EMM) formulation is developed that overcomes limitations for the domain of validity of the MPP parameters. It provides a unit cell transfer impedance that accounts for visco-thermal dissipation and high-order evanescent modes both within the perforation and at the panel walls. It can be used as a Robin-type visco-thermal boundary condition in a pure Acoustic finite element model (FEM) of a complex micro-/macro-perforated structure. This approach leads to a mixed analytical-numerical approach with a much lower computational cost than a full visco-thermal Acoustic FEM model. The inclusion of hole or panel interaction effects is then achieved through the acoustic or structural FEM parts.