Derivation, verification and validation of a length correction factor for folded quarter-wavelength resonators

Acoustic metamaterials that consist of multiple λ/4-resonators in series or parallel can be tuned to realise high broadband absorption in a given frequency range. These resonators are often folded to obtain a structure with a (deep) sub-wavelength thickness, which allows an optimal use of the available space and enables low-frequency sound absorption in confined spaces. However, folding a resonator can lead to a significant change in resonance frequency, resulting in an off-design acoustic performance. Hence, in this paper, the effect of a single 90° fold on the resonance frequency of rectangle and slit-like λ/4-resonators is investigated numerically. Based on these numerical simulations, a length correction factor δ is derived to account for this effect in the analytical model. The use of the correction factor is verified for various single-fold resonator configurations and against existing length formulas. The length correction factor is then experimentally validated for rectangle resonators by means of impedance tube measurements on 3D printed samples. It is found that using the proposed length correction factor allows for an accurate prediction of the resonance frequency of the discussed resonator geometries.