﻿ 基于复合阻尼的声学覆盖层吸声效率计算
 舰船科学技术  2022, Vol. 44 Issue (5): 32-36    DOI: 10.3404/j.issn.1672-7649.2022.05.007 PDF

Calculation of sound absorption efficiency based on compound damping
ZHANG Fan, CHE Chi-dong
School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University 200240, China
Abstract: In order to improve the simulation accuracy of the acoustic coating, the original calculation parameter model is improved. Based on the lumped parameter method and the transfer matrix method, a one-dimensional equivalent model of the acoustic coating is proposed. Combining the calculation of the acoustic coating with the finite element method, the calculation results show that damping has a significant effect on the sound absorption efficiency. Different types of damping have different effects on sound absorption. Structural damping mainly affects the low frequency range, and viscous damping mainly affects the high frequency range. According to the characteristics of rubber materials and the results of numerical calculations, a weighted composite damping model is proposed, and the effectiveness is verified by acoustic tube experiments. The simulation accuracy of the acoustic coating is improved, which is of great significance to the design of the acoustic coating.
Key words: acoustic coating     composite damping     sound absorption efficiency     sound tube experiment
0 引　言

1 理论分析

 图 1 声学覆盖层模型 Fig. 1 Model of acoustic overlay

 $\begin{split} \left( {\begin{array}{*{20}{c}} {{p_i}} \\ {{v_i}} \end{array}} \right) & = \left[ {\begin{array}{*{20}{c}} {\cos (k_{li}^el_i^e)}&{j\rho _i^ec_i^e\sin (k_{li}^el_i^e)} \\ {\dfrac{{j\sin (k_{li}^el_i^e)}}{{\rho _i^ec_i^e}}}&{\cos (k_{li}^el_i^e)} \end{array}} \right]\left( {\begin{array}{*{20}{c}} {{p_{i + 1}}} \\ {{v_{i + 1}}} \end{array}} \right) =\\ & \left[ {{T_i}} \right]\left( {\begin{array}{*{20}{c}} {{p_{i + 1}}} \\ {{v_{i + 1}}} \end{array}} \right)，\end{split}$ (1)

 $k_{li}^e = {k_{li}}\sqrt {\frac{1}{{1 + 3\delta _i^2}}\left(1 + \frac{\lambda }{\mu }\delta _i^2\right)} 。$ (2)

 图 2 集总参数的空腔模型等效 Fig. 2 Equivalent model of single cavity

 $\left[ T \right]{\text{ = }}\left[ {{T_1}} \right]\left[ {{T_2}} \right] \cdots \left[ {{T_n}} \right] ，$ (3)

 ${Z_r} = \frac{{{T_{11}}}}{{{T_{21}}}}{\text{ = }}\frac{{{p_1}}}{{{v_1}}} ，$ (4)
 $r = \frac{{{Z_r} - {\gamma _i}}}{{{Z_r} + {\gamma _i}}} = \frac{{{T_{11}} + \dfrac{1}{{{\gamma _i}}}{T_{12}} - {\gamma _i}{T_{21}}}}{{{T_{11}} + \dfrac{1}{{{\gamma _i}}}{T_{12}} + {\gamma _i}{T_{21}}}}。$ (5)

 $\alpha {\text{ = }}1 - {\left| r \right|^2}。$ (6)
2 数值仿真

 图 3 小孔隙率1 kHz速度响应 Fig. 3 Velocity response of small porosity 1 kHz

 图 4 小孔隙率2 kHz速度响应 Fig. 4 Velocity response of small porosity 2 kHz

 图 5 小孔隙率3 kHz速度响应 Fig. 5 Velocity response of small porosity 3 kHz

 图 6 大孔隙率2 kHz速度响应 Fig. 6 Velocity response of big porosity 2 kHz

 图 7 不同损失因子η下的吸声效率 Fig. 7 Absorption efficiency under different η

 图 8 不同阻尼比 $\zeta$ 下的吸声效率 Fig. 8 Absorption efficiency under different $\zeta$

 ${q_\eta }(\omega ) = \frac{1}{{\sqrt {1\;500} }}\sqrt {3\;000 - w} ，$ (7)
 ${q_\varsigma }(\omega ) = 1 - \frac{1}{{\sqrt {1\;500} }}\sqrt {3\;000 - w} 。$ (8)
3 实验验证

 图 9 实验设备装置框图 Fig. 9 Block diagram of experimental equipment

 图 10 声管测试原理图 Fig. 10 Sound tube test principle diagram
 ${P_1}(t) = {\text{(}}{\hat P_i}{e^{jk{d_1}}} + {\hat P_r}{e^{ - jk{d_1}}}){e^{j\omega t}} ，$ (9)
 ${P_2}(t) = {\text{(}}{\hat P_i}{e^{jk{d_2}}} + {\hat P_r}{e^{ - jk{d_2}}}){e^{j\omega }} 。$ (10)

 $r = \frac{{{{\hat P}_r}}}{{{{\hat P}_i}}}{\text{ = }}\frac{{{P_2}{e^{2jk{d_1}}} - {P_1}{e^{2jk{d_2}}}}}{{{P_1} - {P_2}}} ，$ (11)
 $\alpha {\text{ = 1 - }}{\left| {\frac{{{P_2}{e^{2jk{d_1}}} - {P_1}{e^{2jk{d_2}}}}}{{{P_1} - {P_2}}}} \right|^2} 。$ (12)

 图 11 样品1的吸声效率验证 Fig. 11 Absorption efficiency of sample 1

 图 12 样品2的吸声效率验证 Fig. 12 Absorption efficiency of sample 2
4 结　语

1）这种方法可以通过简便的计算得到较为精确的结果。

2）在低频段（1000～1500 Hz）结构阻尼起到主要作用，在高频段（3000～4000 Hz）粘性阻尼起主要作用。在过渡段（1500～3000 Hz），两者共同起作用，且随频率增加，结构阻尼起到的作用在消退，粘性阻尼的作用逐渐增强。

3）给出粘性阻尼、结构阻尼对吸声性能的影响规律，可以针对不同的需求，进行胶料的调整。在低频段调节材料的结构阻尼更有效，高频段调整材料的粘性阻尼更能起到作用。

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