應用有限元素頻域聲學分析於施羅德擴散器的性能模擬

Performance Simulations of Schroeder Diffusers based on Finite Element Frequency Domain Acoustic Analysis

劉皓祥(Hao-Hsiung Liu)

指導教授 ： 蔡慧駿

淡江大學/工學院/機械與機電工程學系碩士班/碩士(2016年)

https://doi.org/10.6846/TKU.2016.01099

摘要

本研究應用多孔介質二維有限元素頻域分析計算聆聽室的頻率響應。分析驗證吸音泡棉的吸音係數與施羅德擴散器的極響應及擴散係數，並探討結合吸音泡棉與施羅德擴散器於聆聽室頻率響應的影響。
本研究首先應用有限元素頻域分析與雙麥克風法計算吸音泡棉的吸音係數，並與一維理論解進行比較，驗證於聆聽室附加吸音泡棉時亦可正確獲得吸音係數。接著應用有限元素頻域分析繪製500 Hz施羅德擴散器的極響應圖並驗證其擴散效果。從極響應圖中可觀察出七槽施羅德擴散器的擴散效果最佳，各個單槽均有顯著的集中反射現象，擴散效果差。最後本研究應用邊界條件與均佈脈衝聲壓模擬聆聽室的頻率響應，分析結合吸音泡棉與施羅德擴散器對聆聽室頻率響應的影響。結果顯示在聆聽室附加三個施羅德擴散器較附加一個施羅德擴散器的擴散效果為佳。結合吸音泡棉與施羅德擴散器後，聆聽點各三分之一倍頻帶的位移振幅皆顯著下降，顯見吸音泡棉的吸音效果。惟擴散器與吸音泡棉的結合使用，須考量適切的聆聽頻率響應需求予以適當的設計。

關鍵字

有限元素頻域分析 ； 吸音係數 ； 擴散係數 ； 吸音泡棉 ； 施羅德擴散器 ； 聆聽室

並列摘要

The two-dimensional finite element frequency domain analysis (FEFDA) of a porous medium is used to calculate the frequency responses of a listening room in this study. Sound absorption coefficient of acoustic foam and polar plots as well as diffusion coefficient of Schroeder diffuser are analyzed and validated. The effects of acoustic foams and Schroeder diffusers on the frequency responses of a listening room are studied.

FEFDA and two-microphone method are applied to calculate the sound absorption coefficient of acoustic foam and the results are further compared with the one-dimensional analytical result. It is found that the correct sound absorption coefficient can be obtained while the acoustic foam is applied to the listening room. Polar plots of 500 Hz Schroeder diffuser are prepared using the FEFDA and the related diffusion coefficients are verified. Results show that the 7-slot Schroeder diffuser has better diffusion effect and single-slot diffusers have worse diffusive performance due to the concentrated reflections. Finally, the impulsive pressure and suitable boundary conditions are applied to study the frequency responses of a listening room. The influences of the combination of the acoustic foams and Schroeder diffusers are explored. It is learned that a better diffusion performance is obtained when applying three Schroeder diffusers as compared with that has only one diffuser. The decreasing of the displacement amplitude at each one-third octave band shows that the acoustic foams have significant sound adsorbing effect. However, an appropriate frequency response should be taken into consideration while providing the treatments of acoustic foams and Schroeder diffusers to a listing room.

並列關鍵字

Finite Element Frequency Domain Analysis ； Sound Absorption Coefficient ； Diffusion Coefficient ； Acoustic Foam ； Schroeder Diffuser ； Listening Room

參考文獻

1. M. R. Schroeder, “Binaural Dissimilarity and Optimum Ceilings for Concert Halls: More Lateral Sound Diffusion”, The Journal of the Acoustical Society of America, Vol. 65, No. 4, pp. 958-963, 1979.

2. M. R. Schroeder, “Diffuse Sound Reflection by Maximum-Length Sequences”, The Journal of the Acoustical Society of America, Vol. 57 , No. 1, pp. 149-50, 1975.

4. M. A. Biot, “General Theory of Three-Dimensional Consolidation”, Journal of Applied Physics, Vol. 12, pp. 155-164, 1941.

5. M. A. Biot, “Theory of Elasticity and Consolidation for a Porous Anisotropic Solid”, Journal of Applied Physics, Vol. 26, pp. 182-185, 1955.

6. M. A. Biot, “Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid. I. Low-Frequency Range”, The Journal of the Acoustical Society of America, Vol. 28, No. 2, pp. 168-178, 1956.