Increasingly intricate folded cavity absorbers are being proposed to minimize the thickness of metamaterials. Nevertheless, there has been scant research on determining the effective length of complex folded cavities. In this work, a new method for calculating the effective length of a complex folded cavity is established based on nonlinear regression analysis, and the effect of folding on the effective length of the cavity is evaluated. It is found that any complex folded cavity can typically be divided into multiple separate 90-degree and 180-degree folded cavities. The overall effect of folding on the entire absorber can be determined by calculating the individual fold’s actual change in effective length and then combining these changes. In addition, the actual effective length of the folded cavity is determined by using the resonant frequency obtained from the numerical simulation. The total cavity length, cross-sectional dimensions, and folding ratio of the cavity (the ratio of length before and after the folding location) are selected as variables for numerical simulation to create the data set to derive the nonlinear regression equations of the effective length of 90-degree and 180-degree folded cavities, respectively. The accuracy of the derived mathematical expressions is demonstrated through simulation verification and experimental validations.
AgarwallaDKMohantyAR (2024) Low-frequency wideband sound absorption properties of composite layer micro-perforated panel absorber. Journal of Vibration Engineering & Technologies12: 6251–6271.
2.
AlmeidaGDVergaraEFBarbosaLR, et al. (2021) A low-frequency sound absorber based on micro-slit and coiled cavity. Journal of the Brazilian Society of Mechanical Sciences and Engineering43(3): 124.
3.
FuCXZhangXNYangM, et al. (2017) Hybrid membrane resonators for multiple frequency asymmetric absorption and reflection in large waveguide. Applied Physics Letters110(2): 021901.
4.
GhaffarivardavaghRNikolajczykJHoltRG, et al. (2018) Horn-like space-coiling metamaterials toward simultaneous phase and amplitude modulation. Nature Materials9(1): 1349.
5.
GuanDWuJHWuJL, et al. (2015) Acoustic performance of aluminum foams with semiopen cells. Applied Acoustics87: 103–108.
6.
JaouenLChevillotteF (2018) Length correction of 2D discontinuities or perforations at large wavelengths and for linear acoustics. Acta Acustica United with Acustica104: 243–250.
7.
JungJWKimJELeeJW (2018) Acoustic metamaterial panel for both fluid passage and broadband soundproofing in the audible frequency range. Applied Physics Letters112(4): 041903.
8.
KrushynskaAOBosiaFMiniaciM, et al. (2017) Spider web-structured labyrinthine Acoustic metamaterials for low-frequency sound control. New Journal of Physics19(10): 105001.
9.
LeblancaALavieA (2017) Three-dimensional-printed membrane-type acoustic metamaterial for low frequency sound attenuation. Journal of the Acoustical Society of America141(6): 538–542.
10.
LiYAssouarBM (2016) Acoustic metasurface-based perfect absorber with deep subwavelength thickness. Applied Physics Letters108(6): 063502.
11.
LiYLiangBZouXY, et al. (2013) Extraordinary acoustic transmission through ultrathin acoustic metamaterials by coiling up space. Applied Physics Letters103(6): 063509.
12.
LiangZXLiJS (2012) Extreme acoustic metamaterial by coiling up space. Physical Review Letters108(11): 114301.
13.
LiangQXLvPYHeJ, et al. (2021) A controllable low-frequency broadband sound absorbing metasurface. Journal of Physics D: Applied Physics54(35): 355109.
14.
LongHYShaoCLiuC, et al. (2019) Broadband near-perfect absorption of low-frequency sound by subwavelength metasurface. Applied Physics Letters115(10): 103503.
15.
MaGCYangMXiaoSW, et al. (2014) Acoustic metasurface with hybrid resonances. Nature Materials13(9): 873–878.
16.
MaaDY (1998) Potential of microperforated panel absorber. Journal of the Acoustical Society of America104(5): 2861–2866. https://hal.science/hal-04161348v1
17.
MeiJMaGCYangM, et al. (2012) Dark acoustic metamaterials as super absorbers for low-frequency sound. Nature communications3(1): 756.
18.
RenFLiuH (2022) Strain induced low frequency broad bandgap tuning of the multiple re-entrant star-shaped honeycomb with negative poisson’s ratio. Journal of Vibration Engineering & Technologies10: 3157–3168.
19.
RyooHJeonW (2018) Perfect sound absorption of ultra-thin metasurface based on hybrid resonance and space-coiling. Applied Physics Letters113(12): 121903.
20.
StinsonMR (1991) The propagation of plane sound waves in narrow and wide circular tubes and generalization to uniform tubes of arbitrary cross‐sectional shape. Journal of the Acoustical Society of America89(2): 550–558.
21.
SuJChenHYangD (2024) Low-frequency still-air acoustic inertia of inclined circular aperture in an infinite flat plate of finite thickness. Journal of Sound and Vibration570: 118119. https://doi.org/10.1016/j.jsv.2023.118119
22.
WangYZhaoHGYangHB, et al. (2017) A space-coiled acoustic metamaterial with tunable low-frequency sound absorption. EPL (Europhysics Letters)120(5): 54001.
23.
WangYZhaoHGYangHB, et al. (2018) A tunable sound-absorbing metamaterial based on coiled-up space. Journal of Applied Physics123(18): 185109.
24.
WangXYuCXinF (2024) Tunable acoustic metamaterial for broadband low-frequency sound absorption by continuous acoustic impedance manipulation. Journal of Vibration and Control31(5-6): 940–952.
25.
WuFXiaoYYuDL, et al. (2019) Low-frequency sound absorption of hybrid absorber based on micro-perforated panel and coiled-up channels. Applied Physics Letters114(15): 151901.
26.
YanSLWuJWChenJ, et al. (2022) Optimization design and analysis of honeycomb micro-perforated plate broadband sound absorber. Applied Acoustics186: 108487.
27.
YangMMengCFuCX, et al. (2015) Subwavelength total acoustic absorption with degenerate resonators. Applied Physics Letters107(10): 104104.
28.
YangMChenSYFuabCX, et al. (2017) Optimal sound-absorbing structures. Proceedings of Meetings on Acoustics4(4): 673–680.
29.
ZhangZDe BieFDenayerH, et al. (2021) Optimized metamaterial using quarter-wavelength resonators for broadband acoustic absorption. Proceedings of DAGA 2021 in Wien. Deutsche Gesellschaft für Akustik (DEGA), 101–104. Available at: https://lirias.kuleuven.be/3541823&lang=en.
30.
ZhangTWuFBaiC, et al. (2023) Acoustic metamaterial composed of zigzag channel and micro-perforated plate for enhanced low-frequency sound absorption. Journal of Vibration and Control30(13-14): 2894–2903.
31.
ZhaoHGWangYWenJH, et al. (2018) A slim subwavelength absorber based on coupled microslits. Applied Acoustics142: 11–17.
32.
ZielińskiTGChevillotteFDeckersE (2019) Sound absorption of plates with micro-slits backed with air cavities: analytical estimations, numerical calculations and experimental validations. Applied Acoustics146: 261–279.
