Modelling of Acoustic Liners Consisting of Helmholtz Resonators Coupled with a Second Cavity by Flexible Walls

Abstract

Acoustic liners are an effective way to dampen aircraft noise. Conventional single-degree-of-freedom liners consist of a perforated facesheet backed with a honeycomb structure and a rigid end plate. Their damping excels near their resonance frequency which is anti-proportional to the cavity depth (lambda/4-resonator) or the cavity volume (Helmholtz resonator). However, this is a challenge for low-frequency noise with long wavelengths due to the limited installation space. We therefore propose a resonator in which the back cavity is divided into two cavities by a flexible plate. The aim is to combine the damping mechanisms of the Helmholtz resonator with the material damping of the flexible plate. With carefully chosen parameters, this flexible plate resonates well below the Helmholtz frequency. We derived an analytic model based on waveguide theory to predict the impedance of the resonator concept. The Helmholtz equation was solved to (numerically) determine the scattering coefficients of a channel section in which one wall is lined with the predicted resonator impedance. The predicted dissipation agreed well with experimental data from measurements at the aero-acoustic wind tunnel DUCT-R.