Characteristics and calculation method of sound radiation of cylindrical shell with porous sound-absorbing material under acoustic excitation
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摘要:
目的 旨在研究声激励下内壁上敷设有多孔纤维吸声材料的环肋单层圆柱壳振动声辐射特性和计算方法。 方法 在Johnson–Champoux–Allard (JCA)等效流体理论模型和多层介质传递矩阵的基础上，推导多层吸声结构吸声系数的理论公式，验证对比用于计算声激励下敷设多孔吸声材料的环肋单层圆柱壳振动声辐射的3种方法（即多孔介质声学实体建模、有限元模型结合理论公式和设置吸声系数阻抗边界）。最后，研究吸声材料厚度、空气背衬层、材料静态流阻和排布顺序对该单层圆柱壳结构吸声效果的影响。 结果 敷设多孔吸声材料可降低圆柱壳结构振动声辐射。基于敷设了多孔吸声材料圆柱壳的吸声系数曲线的分析结果，可以快速有效地预测圆柱壳振动声辐射结果趋势。 结论 通过合理设计吸声材料属性和排布顺序可以有效提高吸声结构吸声性能，从而达到减振降噪的目的。 Abstract:Objective This paper aims to study the characteristics and calculation method of the vibration and sound radiation of single ring-stiffened cylindrical shells with porous fiber composite materials installed in the inner wall under acoustic excitation. Method Based on the equivalent fluid theory model of Johnson–Champoux–Allard (JCA) and the transfer matrix of the multilayer medium, a theoretical formula of the sound absorption coefficient of multilayer sound absorption structures is derived. The three methods for calculating the vibration and sound radiation of a single ring-stiffened cylindrical shell with porous fiber materials under acoustic excitation, namely acoustic solid modeling of porous media, finite element model combined with theoretical formula and imposition of impedance boundary on sound absorption coefficient, are then verified and compared. Finally, the influences of sound-absorbing material's thickness, backed-air gap, static flow resistance, and material arrangement order on the acoustic absorption performance of the cylindrical shell are investigated. Results The results show that laying porous fiber composite materials on the cylindrical shell internally can reduce the vibration and acoustic radiation of cylindrical shell structure. The sound absorption coefficient curve can quickly and effectively predict the resulting trend of the vibration and sound radiation of the cylindrical shell. Conclusion The acoustic absorption performance of sound absorption structures can be effectively improved through the rational design of their properties and arrangement order of the sound-absorbing materials in order to achieve the purpose of vibration and noise reduction. -
图 2 圆柱壳几何模型（上）和有限元模型（下）
Figure 2. Geometric model (upper) and finite element model (lower) of cylindrical shell
图 5 有无敷设多孔吸声材料的圆柱壳有限元模型
Figure 5. Finite element model of cylindrical shell with and without porous sound-absorbing material
图 6 不同方法计算的声激励下含多孔吸声材料圆柱壳均方振速（上）和辐射声功率（下）（d=15 mm）
Figure 6. Mean quadratic vibration velocity (upper) and sound radiation power (lower) vs. frequency plots showing results of a cylindrical shell with porous sound-absorbing material under acoustic excitation obtained by different methods (d = 15 mm)
图 7 不同厚度多孔吸声材料的圆柱壳声激励下计算的吸声系数曲线
Figure 7. Sound absorption coefficient vs. frequency plots showing results of a cylindrical shell with porous sound-absorbing material of different thicknesses under acoustic excitation
图 8 多孔吸声材料、空气和水的波数图
Figure 8. Wave number vs. frequency plots for porous sound-absorbing material, air and water
图 9 不同厚度多孔吸声材料的圆柱壳声激励下计算的均方振速（上）和辐射声功率（下）
Figure 9. Mean quadratic vibration velocity (upper) and sound radiation power (lower) vs. frequency plots showing results of a cylindrical shell with porous sound-absorbing material of different thicknesses under acoustic excitation
图 10 三层吸声结构介质层示意图
Figure 10. Schematic diagram of dielectric layer for three-layer sound absorption structure
图 11 不同吸声结构（无吸声材料、单层和三层）声激励下计算的圆柱壳均方振速(上)和辐射声功率（下）
Figure 11. Mean quadratic vibration velocity (upper) and sound radiation power (lower) vs. frequency plots showing results of a cylindrical shell without or with a single-and three-layer sound-absorbing material under acoustic excitation
图 12 不同敷设方案声激励下计算的三层吸声结构圆柱壳吸声系数
Figure 12. Sound absorption coefficient vs. frequency plots showing results of a cylindrical shell with three-layer sound absorption structure of different schemes under acoustic excitation
图 13 不同敷设方案声激励下计算的三层吸声结构圆柱壳圴方振速（上）和辐射声功率（下）
Figure 13. Mean quadratic vibration velocity (upper) and sound radiation power (lower) vs. frequency plots showing results of a cylindrical shell with three-layer sound absorption structure of different schemes under acoustic excitation
表 1 敷设多孔吸声材料圆柱壳的振动声辐射性能计算方法
Table 1. Calculation methods for vibration and sound radiation of cylindrical shell with porous sound-absorbing material
方法 描述 方法1 有限元方法，通过COMSOL软件中的多孔介质声学模块，实体构建出多孔吸声材料层，设置计算模型的材料孔隙率、流阻率、粘滞特征长度、热特征长度和曲折因子等各项参数 方法2 在有限元模型的基础上加入1.1节所述等效流体理论的各项公式，通过公式变量的形式得到吸声材料层的动态密度和动态声速 方法3 结合1.2节所述多层介质传递矩阵和1.1节所述等效流体理论方法，得到吸声材料层的吸声系数曲线，在COMSOL软件中构建吸声系数函数，使其作为阻抗边界附加在圆柱壳内壁上 
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表 2 多孔吸声材料及内部流场参数
Table 2. Parameters for porous sound-absorbing material and internal flow field
参数 数值 空气密度${\rho_0}/({\text{kg} } \cdot { {\text{m} }^{ - 3}) }$ 1.21 空气声速${c_0}/({\text{m} } \cdot { {\text{s} }^{ - 1}) }$ 343 多孔吸声材料静态流阻${R_{\rm{f} } }/{(\rm{N} }\cdot{\text{s} } \cdot { {\text{m} }^{ - 4}) }$ 24 000 多孔吸声材料普朗特数${N_{{\rm{pr}}} }$ 0.702 多孔吸声材料孔隙率$\sigma $ 0.95 空气的比热容率${\gamma _{\rm{s}}}$ 1.4 大气压${P_0}/{{\rm{Pa}}}$ 101 320
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表 3 两种多孔吸声材料及内部流场参数
Table 3. Parameters for two kinds of porous sound-absorbing material and internal flow field
参数 多孔吸声材料1 多孔吸声材料2 多孔吸声材料静态流阻${R}_{ {\rm{f} } }/（{\rm{N} }\cdot\text{s}\cdot {\text{m} }^{-4}）$ 24 000 42 多孔吸声材料普朗特数${N_{{\rm{pr}}} }$ 0.702 0.702 多孔吸声材料孔隙率$\sigma $ 0.95 0.95 空气的比热容率${\gamma _{\rm{s}}}$ 1.4 1.4 大气压${P_0}/{\rm{P}}{ {\text{a} }_{_{^{^{} } } }}$ 101 320 101 320
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表 4 三层吸声结构的圆柱壳计算方案
Table 4. Calculation schemes for cylindrical shell with three-layer sound-absorbing material
方案 吸声结构敷设顺序（第3层+第2层+第1层） 方案1 10 mm空气背衬层+20 mm吸声材料2 方案2 10 mm空气背衬层+10 mm吸声材料1+10 mm吸声材料2 方案3 10 mm空气背衬层+10 mm吸声材料2+10 mm吸声材料1 方案4 10 mm空气背衬层+20 mm吸声材料1
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