﻿ 复合材料吸声系数的理论计算及性能分析
 舰船科学技术  2017, Vol. 39 Issue (2): 65-69 PDF

1. 中国舰船研究设计中心, 湖北 武汉 430064;
2. 船舶振动噪声重点实验室, 湖北 武汉 430060

Theoretical calculation and performance analysis of the absorption coefficient of composite materials
FENG Ai-jing1, WEI Qiang1,2, ZHANG Da-hai1,2
1. China Ship Development and Design Center, Wuhan 430064, China;
2. National Key Laboratory on Ship Vibration and Noise, Wuhan 430064, China
Abstract: The noise-reduction needs in different noise environment are different. In order to design composite sound absorption material reasonably according to the noise spectrum, based on the sound absorption principle of perforated plate and porous sound absorption material, the improved acoustic-electro analogy method was derived. Using this method,the absorption coefficient of the compound sound absorption structure was calculated. Through numerical simulation the influence of perforation rate inner and outer layers, the porous material thickness, and cavity size on sound absorption properties has been analyzed profoundly. The analysis shows that the perforation rate of the first plate and the porous material thickness have obvious influence. And the results were verified by the acoustic experiment. The results showed that the improved acoustic-electro analogy method was feasible.
Key words: composite sound absorption structure     improved acoustic-electro analogy method     absorption coefficient     performance analysis
0 引 言

1 多孔吸声材料、穿孔板声阻抗

 图 1 复合吸声结构视图 Fig. 1 Composite sound absorption structure view
1.1 复合吸声材料中第n 层多孔材料声阻抗：

 ${\rho _n} = \frac{N}{\delta }{\rho _O} - i\frac{{{R_n}}}{\omega }\text{，}$ (1)
 ${\delta _n} = 1 - \frac{{{\rho _n}}}{{{\rho _{nm}}}}\text{，}$ (2)
 ${k_n} = \frac{{{K_{nT}}}}{{{\delta _n}}}\text{，}$ (3)
 ${K_{nT}} = \gamma {P_0}{\left[ {1 + \left( {\gamma - 1} \right)\frac{2}{{{k_n}\sqrt { - i} }}\frac{{{J_1}\left( {d\sqrt { - i} } \right)}}{{{J_0}\left( {d\sqrt { - i} } \right)}}} \right]^{ - 1}}\text{，}$ (4)
 ${J_0}\left( x \right) \approx 1 - \frac{{{x^2}}}{4} + \frac{{{x^4}}}{{192}}\text{，}$ (5)
 ${J_1}\left( x \right) \approx \frac{x}{2}\left( {1 - \frac{{{x^2}}}{2} + \frac{{{x^4}}}{{192}}} \right)\text{。}$ (6)

n 层多孔材料特性阻抗公式为：

 ${Z_{pcn}} = {\rho _n}{c_n}\text{，}$ (7)

n 层空腔声阻抗为[7]

 ${Z_{cn}} = {\rho _n}{c_n}\coth \left( {i{k_n}{l_n}} \right)\text{。}$ (8)

1.2 复合吸声材料中第n 层穿孔板声阻抗：

 ${Z_{pn}} = i\omega {\rho _0}t + \frac{2}{d} \cdot t\sqrt {2\omega \eta {\rho _0}} \left( {1 + i} \right)\text{。}$ (9)

 ${\beta _0} = \frac{8}{{3\pi}}\left( {1 - \frac{5}{4}\sqrt \sigma + \frac{{{\sigma ^2}}}{4}} \right)\text{。}$ (10)

 $\begin{array}{l} {Z_{pn}} = \displaystyle\frac{{i\omega }}{\sigma }[{\rho _0}t + \frac{d}{2}{\beta _0}\left( {{\rho _0} + {\rho _1}} \right)] + \frac{{\sqrt {2\omega \eta {\rho _0}} }}{\sigma } \times \\[8pt] \;\;\;\;\;\;\;\;\;\;\;\left[ {\displaystyle\frac{{2t}}{d} \cdot \left( {1 + i} \right) + \frac{1}{2}\left( {1 + \frac{{\sqrt {{\rho _1}} }}{{\sqrt {{\rho _0}} }}} \right)} \right]\text{。} \end{array}$ (11)

2 改进声电类比法及复合材料吸声系数 2.1 复合材料声阻抗计算

 图 2 声电类比原理示意图 Fig. 2 Acoustic- electro analogy method schematic diagram

 $Z = {Z_{p1}} + \frac{{\left( {{Z_{p2}} + {Z_{c2}} + {Z_{pc1}}} \right) \times {Z_{c1}}}}{{\left( {{Z_{p2}} + {Z_{c2}} + {Z_{pc1}}} \right) + {Z_{c1}}}}\text{，}$ (12)

 ${Z_s} = r + jx = \frac{z}{{{\rho _0}{c_0}}}\text{，}$ (13)

 $\alpha = \frac{{4r}}{{{{\left( {1 + r} \right)}^2} + {x^2}}}\text{。}$ (14)
3 复合吸声结构性能分析

3.1 第 1 层穿孔板开孔率的影响研究

 图 3 改进声电类比法 Fig. 3 Improved acoustic- electro analogy method
3.2 第 2 层穿孔板开孔率的影响研究

 图 4 改进声电类比法 Fig. 4 Improved acoustic- electro analogy method

 图 5 传统声电类比法 Fig. 5 Acoustic- electro analogy method

3.3 多孔材料及空腔厚度的影响研究

 图 6 空腔厚度影响图 Fig. 6 Effect of cavity thickness

 图 7 多孔材料厚度影响 Fig. 7 Effect of thickness of porous material

4 理论计算与实验

 图 8 试件与实验环境 Fig. 8 Specimen and experimental environment view

 图 9 多孔材料厚 30 mm 时理论与实验结果对比 Fig. 9 Comparison of theoretical and experimental results of porous materials with 30 mm thickness

 图 10 多孔材料厚 50 mm 时理论与实验结果对比 Fig. 10 Comparison of theoretical and experimental results of porous materials with 50 mm

5 结 语

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