傳統低頻吸音裝置經常存在著尺寸過大的問題，因此為了降低吸音器的整體結構厚度，並提高吸音器內部的空間使用率，本研究基於空間盤繞的想法，提出了一種內含拱型雙通道的聲學共振器，將兩個通道以摺疊的方式蜷曲在薄板中，使共振器厚度被壓縮於次波長尺度之下，且每個通道皆具有三個分支通道。
首先，透過阻抗理論計算模型的聲音吸收率，再利用有限元素模擬軟體COMSOL Multiphysics對模型進行分析，探討通道截面固定與變化對於吸收頻譜的影響，並延伸研究內含四通道的雙層模型設計。得知藉由同時縮短兩邊通道的第二分支通道寬度，吸收率曲線會往低頻端移動，在共振頻率之下，最佳化模型有超過 99 % 的吸音效果，且厚度與波長比為1/94，屬於次波長厚度結構；而透過分別改變兩邊的通道寬度，可以有效的拓展頻寬，雖然在共振頻率下的最大吸收率會略為下降至0.9，但相較於前述模型，頻寬增加了超過75 %；雙層模型則可以用來再更進一步拓展吸收率頻寬。最後，經由三維列印機製作模型樣品，在符合ISO 10534-2規範下以阻抗管量測系統進行聲音吸收率實驗，將理論、模擬的計算結果與實驗量測所得數據相互比對，獲得了良好的驗證。

In this thesis, an acoustic resonator with double arch-like channels (ALCs) is proposed, and each ALC has three-branched channels. The channels are coiled up in the thin panel, so the thickness of the resonator can be reduced to the subwavelength scale. The acoustic impedance theory and the finite element simulation software COMSOL Multiphysics are used to analyze the absorption spectrum of the models. It is evident that the absorption peaks shift to low-frequency band as decreasing the width of the second branched channel of the ALCs. The sound absorption coefficient of the optimized model is higher than 0.99 at the resonance frequency. The ratio of the thickness and wavelength is 1/94. Moreover, the absorption bandwidth can be increased by more than 75 percent with two branches of different configurations. Finally, experimental results, theoretical and simulated results have been compared.

[1] X. Cai, Q. Guo, G. Hu, and J. Yang, "Ultrathin low-frequency sound absorbing panels based on coplanar spiral tubes or coplanar Helmholtz resonators," Appl. Phys. Lett., vol. 105, no. 12, 121901, 2014.
[2] D. Y. Maa, "Theory and design of microperforated panel sound-absorbing constructions," Sci. Sin., vol. 18, no. 1, pp. 55-71, 1975.
[3] D. Y. Maa, "Potential of microperforated panel absorber," J. Acoust. Soc. Am., vol. 104, no. 5, pp. 2861-2866, 1998.
[4] H. Von Helmholtz and A. J. Ellis, On the sensations of tone as a physiological basis for the theory of music, Longmans and Co., London, 1875.
[5] P. Tang and W. Sirignano, "Theory of a generalized Helmholtz resonator," J. Sound Vib., vol. 26, no. 2, pp. 247-262, 1973.
[6] R. Chanaud, "Effects of geometry on the resonance frequency of Helmholtz resonators," J. sound Vib., vol. 178, no. 3, pp. 337-348, 1994.
[7] A. Selamet and I. Lee, "Helmholtz resonator with extended neck," J. Acoust. Soc. Am., vol. 113, no. 4, pp. 1975-1985, 2003.
[8] J. Allard and N. Atalla, Propagation of sound in porous media: modelling sound absorbing materials 2e, Wiley, New York, 2009.
[9] L. Rayleigh, "On the theory of resonance," Phil. Trans. Roy. Soc. London, vol. 161, pp. 77-118, 1871.
[10] W. S. Gan, New acoustics based on metamaterials, Springer Nature, Singapore, 2017.
[11] Q. Zheng, H. Zhao, Y. Wang, J. Cao, and J. Wen, "Improvement of sound absorption and insulation using a double-layer metamaterial," AIP Advances, vol. 10, no. 9, 095010, 2020.
[12] L. Han, H. Ji, and J. Qiu, "A broadband sound-absorbing panel based on the coiled coplanar absorber with multiple absorption peaks," Phys. Scr., vol. 96, 085008, 2021.
[13] G. Ma and P. Sheng, "Acoustic metamaterials from local resonances to broad horizons," Sci. Adv., vol. 2, no. 2, e1501595, 2016.
[14] J. Li, W. Wang, Y. Xie, B. I. Popa, and S. A. Cummer, "A sound absorbing metasurface with coupled resonators," Appl. Phys. Lett., vol. 109, no. 9, 091908, 2016.
[15] C. R. Liu, J. H. Wu, F. Ma, X. Chen, and Z. Yang, "A thin multi-order Helmholtz metamaterial with perfect broadband acoustic absorption," Appl. Phys. Express, vol. 12, no. 8, 084002, 2019.
[16] J. S. Chen, Y. B. Chen, Y. H. Cheng, and L. C. Chou, "A sound absorption panel containing coiled Helmholtz resonators," Phys. Lett. A, vol. 384, no. 35, 126887, 2020.
[17] M. Duan, C. Yu, Z. Xu, F. Xin, and T.J. Lu, "Acoustic impedance regulation of Helmholtz resonators for perfect sound absorption via roughened embedded necks," Appl. Phys. Lett., vol. 117, no. 15, 151904, 2020.
[18] S. Huang, Z. Zhou, D. Li, T. Liu, X. Wang, J. Zhu, and Y. Li, "Compact broadband acoustic sink with coherently coupled weak resonances," Sci. Bull., vol. 65, no. 5, pp. 373–379, 2020.
[19] S. Xie, D. Wang, Z. Feng, and S. Yang, "Sound absorption performance of microperforated honeycomb metasurface panels with a combination of multiple orifice diameters," Appl Acoust, vol. 158, no. 15, 107046, 2020.
[20] L. Han, H. Ji, and J. Qiu, "Influence of interference among parallel absorbers on acoustic characteristics of an absorbing panel," Rev. Sci. Instrum., vol. 92, no. 6, 064901, 2021.
[21] J. P. Groby, W. Huang, A. Lardeau, and Y. Aurégan, "The use of slow waves to design simple sound absorbing materials," J. Appl. Phys., vol. 117, no. 12, 124903, 2015.
[22] J. P. Groby, R. Pommier, and Y. Aurégan, "Use of slow sound to design perfect and broadband passive sound absorbing materials," J. Acoust. Soc. Am., vol. 139, no. 4, pp. 1660-1671, 2016.
[23] Z. Liang and J. Li, "Extreme acoustic metamaterial by coiling up space," Phys. Rev. Lett., vol. 108, no. 11, 114301, 2012.
[24] Y. Cheng, C. Zhou, B. G. Yuan, D. J. Wu, Q. Wei, and X. J. Liu, "Ultra-sparse metasurface for high reflection of low-frequency sound based on artificial Mie resonances," Nat. Mater., vol. 14, pp. 1013-1019, 2015.
[25] A. O. Krushynska, F. Bosia, M. Miniaci, and N. M. Pugno, "Spider web-structured labyrinthine acoustic metamaterials for low-frequency sound control," New J. Phys., vol. 19, no. 10, 105001, 2017.
[26] A. O. Krushynska, F. Bosi, and N. M. Pugno, "Labyrinthine acoustic metamaterials with space-coiling channels for low-frequency sound control," Acta. Acust. Acust., vol. 104, no. 2, pp. 200-210, 2018.
[27] C. Zhang and X. Hu, "Three-dimensional single-port labyrinthine acoustic metamaterial," Phys. Rev. Applied, vol. 6, no. 6, 064025, 2016.
[28] Y. Wang, H. Zhao, H. Yang, J. Zhong, and J. Wen, "A space-coiled acoustic metamaterial with tunable low-frequency sound absorption," EPL, vol. 120, no. 5, 54001, 2017.
[29] F. Wu, Y. Xiao, D. Yu, H. Zhao, Y. Wang, and J. Wen, "Low-frequency sound absorption of hybrid absorber based on micro-perforated panel and coiled-up channels," Appl. Phys. Lett., vol. 114, no.15, 151901, 2019.
[30] C. R. Liu, J. H. Wu, Z. Yang, and F. Ma, "Ultra-broadband acoustic absorption of a thin microperforated panel metamaterial with multi-order resonance," Compos. Struct., vol. 246, no.15, 112366, 2020.
[31] W. Chen, F. Wu, J. Wen, Z. Ju, L. Yao, H. Zhao, Y. Wang, and Y. Xiao, "Low-frequency sound absorber based on micro-slit entrance and space-coiling channels," Jpn. J. Appl. Phys., vol. 59, 045503, 2020.
[32] Q. Liang, P. Lv, J. He, Y. Wu, F. Ma, and T. Chen, "A controllable low-frequency broadband sound absorbing metasurface," J. Phys. D: Appl. Phys., vol. 54, no. 35, 355109, 2021.
[33] I. Prasetiyo, I. Sihar, and A. S. Sudarsono, "Realization of a thin and broadband microperforated panel (MPP) sound absorber," Appl Acoust, vol. 183, no. 1, 108295, 2021.
[34] J. Hu, J. Wang, Y. Xie, C. Shi, and Y. Chen, "Finite element analysis on acoustic and mechanical performance of flexible perforated honeycomb-corrugation hybrid sandwich panel," Shock. Vib., vol. 2021, 2021.
[35] Y. Wang, Y. Wang, J. Xu, H. Yu, C. Zhang, and L. Ren, "Broadband low-frequency sound absorption by coiled-up space embedded in a porous layer," Appl Acoust, vol. 182, 108226, 2021.
[36] Y. Han, X. Wang, G. Xie, X. Tang, and T. Chen, "Low-frequency sound-absorbing metasurface with a channel of nonuniform cross section," J. Appl. Phys., vol. 127, no. 6, 064902, 2020.
[37] G. N. Almeida, E. F. Vergara, L. R. Barbosa, and R. Brum, "Low-frequency sound absorption of a metamaterial with symmetrical-coiled-up spaces," Appl Acoust, vol. 172, no. 15, 107593, 2021.
[38] G. C. Cohen, Higher-order numerical methods for transient wave equations, Springer-Verlag, Berlin, 2002.
[39] M. R. Stinson, "The propagation of plane sound waves in narrow and wide circular tubes, and generalization to uniform tubes of arbitrary cross‐sectional shape," J. Acoust. Soc. Am., vol. 89, no. 2, pp. 550-558, 1991.
[40] L. E. Kinsler, A. R. Frey, H. Coppens, and J. V. Sanders, Fundamentals of acoustics, Wiley, New York, 1982.
[41] "COMSOL Multiphysics", Acoustic Module User’s Guide version 5.0, 2014.
[42] EN ISO 10534-2, "Determination of sound absorption coefficient and acoustic impedance with the interferometer, Part2: Transfer function method," British Standard Institution, London, 1998.