Enhanced modal matching method for macro- and micro-perforated plates

Theoretical, numerical and experimental results are presented on the reactive and dissipative properties of backed or unbacked multilayer partitions made up of macro- or micro-perforated rigid panels in linear regime. The objective is to provide an enhanced multi-modal (EMM) formulation that accounts for high-order modes within the panel holes as well as visco-thermal boundary layers (VTBLs) over the panel surfaces while being computationally more efficient than the finite element method (FEM). The proposed model accounts for oblique incidence and finite-sized panel vibrations. Validation cases show that the EMM well captures the visco-thermal dissipation modelled by FEM on rigidly-backed macro- and micro-perforates. It also well correlates with a number of effective impedance models provided suitable end-corrections are used. The measured acoustical properties of unbacked multi-layer partitions are accurately predicted by the EMM, well beyond the validity range of the effective models. The thickness-to-hole diameter aspect ratio is found to be a key parameter that determines the relative contribution of the in-hole radial modes and VTBLs to the partition dissipation properties. For aspect ratios greater than unity where micro-perforates normally are operated, the dissipation is dominated by the high-order in-hole modes. Otherwise, both the VTBLs and in-hole modes contribute to the transmission and dissipation. The VTBLs also dominate the reactive and dissipative properties of acoustic fishnets embedding small air gaps comparable to the VTBL thickness. Despite the constant hole pitch limitation, the EMM appears to be well-suited for the optimisation study of the dissipative and reactive properties of backed or unbacked multi-layer partitions.