在人類文明科技進步的道路上，噪音汙染儼然為不可忽視的課題之一，如何抑制、隔離或是減少噪音，現今已成為工程師與科學家致力克服的一大目標。在近年來，超穎材料結構以及次波長厚度結構等新型設計，因其性質上特殊性，吸引許多研究關注，本研究設計出一款嵌入串聯型荷姆霍茲共振器，其屬於次波長厚度結構，可適用於受限制的空間，由聲波方程式配合阻抗理論匹配法，計算出共振器在各頻率下之吸音率曲線，並對其幾何進行最佳化設計。其減噪機制為共振腔在共振頻率下，由於空氣高速運動下黏滯及熱耗損聲能，而產生高吸收率。
接著延伸設計不同組合方式之模型，包括串聯型、並聯型以及串聯-並聯型，藉由不同組合方式，使其能拓寬吸收頻寬，並透過有限元素模擬軟體COMSOL Multiphysics探討共振器在各頻率之吸音率與速度、聲壓分布。將模擬結果與阻抗理論匹配法所獲得的吸收率做相互比對，整體比對結果誤差不大。
將設計模型透過三維列印機(Creality Ender3-V2)進行列印製作，接著將模型放置阻抗管(SW422)中，經雙麥克風法轉移函數法量測模型吸收率，在實驗上各模型都有最高達0.9以上之吸音率，雖然僅在特定頻段才有高吸收率，卻是許多吸音多孔性材料難以企及。實驗和有限元素模擬結果雖有三維列印造成粗糙度之差異，但透過將理論、模擬以及實驗結果進行疊圖比對，整體頻寬以及吸音率曲線相比誤差不大，證明能以阻抗匹配理論預測吸音薄板吸音率之曲線趨勢。總體來說，本文提出設計可有效使用吸音薄板空間，不僅能節省材料、降低設計成本，同時提高吸音效果。

Noise pollution has become a serious problem that cannot be ignored nowadays. How to effectively eliminate or reduce noise becomes a major research subject. In recent years, new designs such as metamaterial and sub-wavelength thickness structures have been widely used in many studies. In this study, a panel with Helmholtz resonators connected in series is proposed. The impedance method and finite element method are used to capture the sound absorption of the proposed structure. The noise reduction mechanism is attributed to the thermal and viscous loss of acoustic energy. For efficient use of the space, each resonator is comprised of an extended spiral neck and a semi-circular cavity. The resonator of different combinations not only can widen the absorption bandwidth but also can enhance the absorption performance. The 3D printing technique is utilized to fabricate the designed structure. The experimental results show that the sound absorption of the present panel is up to 0.9 or higher. Compared with the theoretical, simulated, and experimental results, the overall bandwidth and plot of sound absorption rate are close, which proves that the proposed method based on the impedance matching theory is valid.

[1]“Advantages and Challenges of Wind Energy.” [Online]. Available: https://www.energy.gov/eere/wind/advantages-and-challenges-wind-energy [Accessed: 03-Jun-2021]
[2]“Boeing AH-64 APACHE.” [Online]. Available: https://www.boeing.com/defense/ah-64-apache/ [Accessed: 06-May-2021]
[3]“NSSN Virginia-Class Attack Submarine.” [Online]. Available: https://www.naval-technology.com/projects/nssn/ [Accessed: 03-Jun-2021]
[4] 盧博堅 和 劉嘉俊, 噪音控制與防制. 滄海, 台中市 (2011)
[5]“Car Exhaust Basics, Working, Care, Upgrades and More.” [Online]. Available: https://motorbreaker.co.uk/news/car-exhaust-basics-working-care-upgrades [Accessed: 03-Jun-2021]
[6] 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)
[7] U. Ingard, “On the theory and design of acoustic resonators,” J. Acoust. Soc. Am., vol. 25, pp. 1037-1061, (1953)
[8] P. Tang and W. Sirignano, “Theory of a generalized Helmholtz resonator,” J. Sound Vib., vol. 26, pp. 247-262, (1973)
[9] R. Chanaud, “Effects of geometry on the resonance frequency of Helmholtz resonators,” J. Sound Vib., vol. 178, pp. 337-348 (1994)
[10] A. Selamet and I. Lee, “Helmholtz resonator with extended neck,” J. Acoust. Soc. Am., vol. 113, pp. 1975-1985 (2003)
[11] M. R. Stinson and E. A. G. Shaw, “Acoustic impedance of small, circular orifices in thin plates,” J. Acoust. Soc. Am., vol. 77, pp. 2039-2042 (1985)
[12] 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, pp. 550-558 (1991)
[13] S. Griffin, S. A. Lane and S. Huybrechts, “Coupled Helmholtz resonators for acoustic attenuation,” J. Vib. Acoust., vol. 123, pp. 11-17 (2001)
[14] C. H. Sohn and J. H. Park, “A comparative study on acoustic damping induced by half-wave, quarter-wave, and Helmholtz resonators,” Aerosp. Sci. Technol., vol. 15, pp. 606-614 (2011)
[15] S. H. Park, “Acoustic properties of micro-perforated panel absorbers backed by Helmholtz resonators for the improvement of low-frequency sound absorption,” J. Sound Vib., vol. 332, pp. 4895-4911 (2013)
[16] D. Yang, X.L. Wang and M. Zhu, “The impact of the neck material on the sound absorption performance of Helmholtz resonators,” J. Sound Vib., vol. 333, pp. 6843-6857 (2014)
[17] J. Carbajo, J. Ramis, L. Godinho, P. Amado-Mendes and J. Albac, “A finite element model of perforated panel absorbers including viscothermal effects,” Appl. Acoust., vol. 90, pp. 1-8 (2015)
[18] X.L. Gai, T. Xing, X.H. Li, B. Zhang and W.J. Wang, “Sound absorption of microperforated panel mounted with helmholtz resonators,” vol. 114, pp. 260-265 (2016)
[19] C. Cai, C.M. Mak and X. Shi, “An extended neck versus a spiral neck of the Helmholtz resonator,” Appl. Acoust., vol. 115, pp. 74-80 (2016)
[20] 林浩存及蔡定平,“超穎介面介紹與其應用,”物理雙月刊, 36卷,4期, 頁面
264-271 (2005)
[21] Y. Tang, S. Ren, H. Meng and F. Xin, “Hybrid acoustic metamaterial as super absorber for broadband low-frequency sound,” Sci. Rep., vol 7, 43340 (2017)
[22] S. Huang, X. Fang, X. Wang, B. Assouar, Q. Cheng and Y. Li, “Acoustic perfect absorbers via spiral metasurfaces with embedded apertures,” Appl. Phys. Lett., vol. 113, 233501 (2018)
[23] S. Huang, X. Fang, X. Wang, B. Assouar, Q. Cheng and Y. Li, “Acoustic perfect absorbers via Helmholtz resonators with embedded apertures,” J. Acoust. Soc. Am., vol. 145, pp. 254-262 (2019)
[24] K. Donda, Y. Zhu, S. W. Fan, L. Cao, Y. Li and B. Assouar, “Extreme low-frequency ultrathin acoustic absorbing metasurface,” Appl. Phys. Lett., vol. 115, 173506 (2019)
[25] L. E. Kinsler, A. R. Frey, H. Coppens and J. V. Sanders, Fundamentals of acoustics. Wiley, New York, (1982)
[26] 白明憲, 工程聲學, 全華圖書股份有限公司, 台北市 (2006)
[27] R. T. Randeberg, “Perforated panel absorbers with viscous energy dissipation enhanced by orifice design,” Doctoral Thesis, Norwegian University of Science and Technology, Trondheim (2000)
[28] J. F. Allard and N. Atalla, “On the theory of resonance,” Philos. Trans., vol. 161, pp. 77-118, (1871)
[29] W. Xu, D. Yu and J. Wen, “Simple meta-structure that can achieve the quasi-perfect absorption throughout a frequency range of 200-500 Hz at 350 °C,” Appl. Phys. Exp., vol. 13, 047001 (2020)
[30] J. Ji, D. Li, Y. Li and Y. Jing, “Low-frequency broadband acoustic metasurface absorbing panels,” Front. Mech. Eng., vol. 6, 586249 (2020)
[31] J. Guo, Y. Fang, Z. Jiang and X. Zhang, “Acoustic characterizations of Helmholtz resonators with extended necks and their checkerboard combination for sound absorption,” J. Phys. D: Appl. Phys., vol. 53, 505504 (2020)
[32] Y. J. Qian, J. Zhang, N. Sun, D. Y. Kong and X. X. Zhang, “Pilot study on wideband sound absorber obtained by adopting a serial-parallel coupling manner,” Appl. Acoust., vol. 124, pp. 48-51 (2017)
[33] “COMSOL Multiphysics”, Acoustic Module User’s Guide version 5.0, (2014)
[34] J. Cordioli, G. Martins, P. Mareze and R. Jordan, “A comparison of models for visco-thermal acoustic problems,” J. Acoust. Soc. Am., vol.127, pp. 6992-7001 (2010)
[35] A. I. Komkina, M. A. Mironovb and A. I. Bykova, “Sound absorption by a Helmholtz resonator,” Acoust. Phys., vol. 63, pp. 385-392 (2017)
[36] Y. Saadat, N. Fernandez, A. Samimi, M. R. Alam, M. Shakeri and R. Ghorbani, “Investigating of Helmholtz wave energy converter,” Ren. Ene., Vol. 87, pp. 67-76 (2016)
[37] 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, 151904 (2020)
[38] EN ISO 10534-2, Determination of sound absorption coefficient and acoustic impedance with the interferometer, Part2: Transfer function method. British Standard Institution, London, (1998)