四分之一波長共振腔之寬頻吸音薄板研究

Quarter-wavelength resonator-based thin panels for absorbing broadband audio waves

廖翊涵(Yi-Han Liao)

指導教授 ： 吳政忠

國立臺灣大學/工學院/應用力學研究所/碩士(2017年)

https://doi.org/10.6342/NTU201704363

摘要

聲波是經由固體振動對空氣擾動進而產生的，每個人對於聲音的感受不盡相同，不悅耳的聲音皆可稱為噪音。近年來噪音影響人們生活的新聞層出不窮，包括風力發電、機場捷運、高架鐵路等交通噪音，皆為急需克服的問題。
　　空氣於空腔型結構內共振時，邊界層的熱黏滯效應能有效地引起能量損失，可作為吸音板的用途。本文所採用的吸音結構為四分之一波長共振器，即第一共振頻率的波長為管長的四倍。首先，分別以聲阻抗的觀點與有限元素法的途徑分析四分之一波長共振器之幾何形狀與吸收頻率的對應關係，由於阻抗分析在熱黏滯效應上的簡化，兩者得到的結果有些微的差異，因此針對阻抗匹配法提出長度的修正公式。薄型化則是參考Cai提出的設計，將原本的直管盤繞而成螺旋狀共振腔，可大幅減低其厚度，接著以同樣的模擬方式確認四分之一波長共振腔與薄型吸音板的相關性後，並進一步提出雙螺旋共振腔的設計，使吸音頻寬大幅增加。
　　本研究經現場量測得知臺灣桃園國際機場聯外捷運系統於新北環河快速道路與疏洪東路一段轉彎處之噪音頻率為467 Hz，合適的共振腔長度為177 mm，開口率為0.017，以3D列印機印製此形狀的吸音薄板。實驗則根據美國材料試驗協會(ASTM)所提出的測試規範操作，以壓克力自行製作聲學阻抗管，搭配雙麥克風轉移函數法量測吸音薄板的吸音效率。實驗所得到的最大吸收係數為0.91，阻抗匹配法則為0.99，而實驗上擁有最大吸收率之頻率為473 Hz，阻抗匹配法則為468 Hz，主要吸收頻率的誤差為1.06 %，證實修正後的阻抗匹配法可以作為薄型吸音板的設計準則，免去有限元素法計算量過大的限制。而雙螺旋共振腔的設計也能大幅增加吸音頻寬，若兩共振腔的長度分別為170與181 mm，吸收係數達0.5以上的頻寬範圍由單共振腔的30 Hz增大至54 Hz。

關鍵字

四分之一波長共振器 ； 聲阻抗分析 ； 吸音係數 ； 寬頻吸音薄板

並列摘要

Sound is produced by a variety of pressure disturbance that can produces the sensation of hearing. The sensation of sound varies from person to person. Unpleasant sound can be judged as noise. In recent years, there have been a lot of news about noise reducing the quality of life, including wind turbine, airport MRT, and other traffic noise. All of them are urgent problems.
　　When air is resonant in the cavity structure, the thermal viscous effect of the boundary layer can effectively cause energy loss and cavity can be used as a sound absorbing plate. The quarter-wave resonator means wavelength of the first resonant frequency is four times of the length of the tube. First, impedance matching method and finite element method are employed to calculate the absorption coefficient of quarter-wave resonators. Since the impedance analysis is simplified on the thermal viscous effect, the length has to be modified.
　　By refering to the design proposed by Cai, the quarter-wave resonator is coiled up into coplanar spiral resonator, which can significantly reduce the thickness and its absorption coefficient is similar to quarter-wave resonator through the simulation method. To broaden the bandwidth of absorbing frequency, thin panel with two resonant cavities is proposed.
　　In this study, the noise frequency of Taiwan Taoyuan International Airport Access MRT System at the corner of New Taipei Huanhe Expressaway and Sec. 1, Shuhong E. Rd. is 467 Hz by measurement on site. The appropriate cavity length is 177 mm and porosity is 0.017. The sample with this geometry is fabricated by 3D printing. According to standard test method of ASTM, the absorption coefficient of thin panels had been measured with a tube and two microphones in experiment. The max absorption coefficient is 0.91 at 473 Hz in experiment, and the modified impedance matching method is 0.99 at 468 Hz. The error of main absorption frequency is 1.06 %. Modified impedance matching method can be a design rule for sound absorbing thin panels, to avoid the limitation of calculation in finite element method. The thin panel with dual resonant cavities can also broaden the absorption bandwidth. If the length of two resonators is 170 and 181 mm, the bandwidth of absorption coefficient more than 0.5 increases from 30 Hz in single resonator to 54 Hz.

並列關鍵字

Quarter-wave resonator ； Acoustic impedance analysis ； Absorption coefficient ； Broadband sound-absorbing panel

參考文獻

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