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-offreedom 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 ( λ /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.

Modeling, design, and optimization of a dielectric elastomer acoustic liner

“…Due to this constrained frequency range and others for this problem, other optimized membrane liners do provide broad absorption, albeit at higher frequencies. As presented in related papers (Kohlenberg et al, 11 Svetgoff et al, 12 and Dodge et al, 15 ) the membrane may be more beneficial at targeting low frequency tones but over a narrow range, rather than the broad frequency range of 400-1600 Hz that was specified. However, this topic warrants further investigation.…”

“…Researchers have also split the cavity depth or replaced side walls with compliant membranes and plates [10][11][12][13] that resulted in low frequency attenuation, albeit without actuation. A compliant active material that has been incorporated into liners is a dielectric elastomer (DE), 14,15 a smart material capable of changing shape and stiffness when subjected to an electric field.…”

Experimental and Numerical Investigation of Novel Acoustic Liners and Their Design for Aero-Engine Applications

“…The results of the parameter studies of the Helmholtz resonator system with flexible walls are summarized in Figure 6. The analytical modeling of the FHR concept is based on the works of Kohlenberg et al [9], where the modeling was introduced and verified using experimental data. It combines one dimensional waveguide theory with lumped elements.…”

“…While these concepts offer a more broadband damping, they cannot lower the system's first resonance frequency. In contrast, different concepts, such as folded cavities [1][2][3][4], active elements [5][6][7][8] or attached mass elements [6,9], offer the possibility for low frequency damping, with certain drawbacks and limitations connected to each of these concepts.…”