Page 100 - 《应用声学》2021年第6期
P. 100
896 2021 年 11 月
参 考 文 献
[1] 王季卿. 声场扩散与厅堂音质 [J]. 声学学报, 2001, 26(5):
417–421.
Wang Jiqing. Sound diffusion and auditorium acous-
tics[J]. Acta Acustica, 2001, 26(5): 417–421.
[2] 乐意, 赵其昌, 沈勇, 等. 大型厅堂的建筑声学设计方法研
(a) ካΓ࠰᫇ቇᫎᇨਓڏ (b) ካΓ࠰᫇ቇᫎᎪಫѳѬᇨਓڏ 究 [J]. 南京大学学报 (自然科学版), 2011, 47(2): 208–217.
Le Yi, Zhao Qichang, Shen Yong, et al. Study on the
图 10 算例 2 封闭空间及其网格划分示意图
acoustic design of large auditoriums[J]. Journal of Nan-
Fig. 10 The schematic of room environment 2 and jing University Natural Science, 2011, 47(2): 208–217.
its mesh for FEM [3] Deraemaeker A, Babuška I, Bouillard P. Dispersion and
pollution of the FEM solution for the Helmholtz equation
140 దᬍЋข
వவข in one, two and three dimensions[J]. International Jour-
͜ፒᄱࣰї͵ข
ܦԍጟ/dB 100 [4] Vergote K, van Genechten B, Vandepitte D, et al. On the
nal for Numerical Methods in Engineering, 1999, 46(4):
120
471–499.
80 analysis of vibro-acoustic systems in the mid-frequency
range using a hybrid deterministic-statistical approach[J].
60
100 200 300 400 500 600 700 800 900 1000 Computers and Structures, 2011, 89(11): 868–877.
ᮠဋ/Hz
[5] Krokstad A, Strom S, Sørsdal S. Calculating the acousti-
图 11 测点处不同方法的频率响应对比 cal room response by the use of a ray tracing technique[J].
Journal of Sound and Vibration, 1968, 8(1): 118–125.
Fig. 11 Comparison of frequency responses of dif-
[6] Gensane M, Santon F. Prediction of sound fields in
ferent methods at the measuring point
rooms of arbitrary shape: validity of the image sources
图11所示的频响曲线对比表明，与算例1类似， method[J]. Journal of Sound and Vibration, 1979, 63(1):
本文方法在低频段相较于传统相干几何法具有更 97–108.
[7] Lemire G, Nicolas J. Aerial propagation of spherical sound
高的精度，虽然本文方法与有限元法对比存在细微
waves in bounded spaces[J]. The Journal of Acoustical So-
的频率偏移，但是在频率曲线的结构方面吻合度较
ciety of America, 1989, 86(5): 1845–1853.
高。在较高频段，本文方法以及传统相干几何趋向 [8] Holford R L. Scattering of sound waves at the ocean sur-
于与有限元法结果一致，误差均较低。此对比说明 face: a diffraction theory[J]. The Journal of Acoustical
当空间内存在较为复杂的周期类型结构时，本文方 Society of America, 1981, 70(4): 1103–1103.
法依然能够给出良好的仿真结果。 [9] Holford R L. Scattering of sound waves at a periodic,
pressure-release surface: an exact solution[J]. The Journal
of Acoustical Society of America, 1981, 70(4): 1116–1128.
3 结论
[10] Sakamoto S, Mukai H, Tachibana H. Numerical study
on sound absorption characteristics of resonance-type
针对周期结构存在条件下的室内宽频声场仿
brick/block walls[J]. Journal of Acoustical Society of
真问题，本文发展了一种基于迭代散射模型的相干 Japan, 2001, 21(1): 9–15.
声线跟踪法。此方法在一定频段范围内将周期散射 [11] Embrechts J J, Geetere L D, Vermeir G, et al. Calcula-
结构视为平面，然后基于周期散射定理，依据周期结 tion of the random-incidence scattering coefficients of a
构的轮廓尺寸以及声波波长、入射角条件确定不同 sine-shaped surface[J]. Acta Acustica united with Acus-
tica, 2006, 92(4): 593–603.
的散射波，此时原始声线将会根据散射波情况迭代
[12] 王海涛, 曾向阳, 杜博凯, 等. 周期矩形轮廓声学散射体的散
分裂为多个子声线，此后继续按照经典相干法对子
射性质预测算法及其应用研究 [J]. 振动与冲击, 2017, 36(7):
声线展开跟踪，直到完成所有声线的跟踪。此迭代 80–85.
散射模型可准确模拟声波在周期结构界面上的散 Wang Haitao, Zeng Xiangyang, Du Bokai, et al. Predict-
射情况，相较于传统的相干几何法在低频段有了较 ing scattering properties of a periodic-type diffuser with
大的精度提高。此方法是对几何声学方法的有效补 a rectangular profile[J]. Journal of Vibration and Shock,
2017, 36(7): 80–85.
充，可为周期散射结构存在条件下的室内声场仿真
[13] Kuttruff H. Room acoustics[M]. 5th Edition. London:
提供简便且准确的新方法。 Spon, 2009.
