Acta Physica Sinica, Volume. 68, Issue 12, 128101-1(2019)
Fig. 1. Schematic of the poroelastic composite structure and its substructures: (a) The poroelastic composite structure; (b) the equivalent model; (c) the OU boundary connection; (d) the OB boundary connection; (e) the forces in OU boundary case; (f) the forces in OB boundary case; (g) the forces in a simple spring-mass resonator.含多孔介质复合结构及其子结构示意图 (a) 含多孔介质复合结构; (b) 等效模型; (c) OU边界; (d) OB边界; (e) 板受力情况(OU边界); (f) 板受力情况(OB边界); (g) 弹簧振子受力
Fig. 2. Schematic of the composite-resonator-structure: (a) Composite resonator type A, two resonators placed in serial connection; (b) composite resonator type B, two resonators placed in composite connection.组合振子系统示意图 (a) 串联弹簧振子系统A; (b) 复合弹簧振子系统B
Fig. 3. Schematic of the arrangement of periodic resonators: (a) An array of simple resonators, denoted as multiple resonators (N1SR, with constant
and
) or multiple kinds of resonators (NNSR, with different
and
); (b) an array of composite resonators, denoted as multiple resonators (N1CR, with constant
and
) or multiple kinds of resonators (NNCR, with different
or
). The area in the dash-line denotes the periodic lattice, in panel (b), the composite resonator can be type B in
Fig. 4. Validation of the results here with previous results: (a) The diffuse case in Ref. [35]; (b) the oblique incident cases in Ref. [35]; (c) the composite poroelastic structure without resonator in Ref. [3]. The lines are results obtained here, while the marks are the results in the references. 不同类型隔声结构验证算例 (a) 文献[35]随机入射情况; (b) 文献[35]斜入射情况; (c) 文献[3]含多孔介质复合结构; 其中, 各曲线为本文结果, 各标记为文献中结果
Fig. 5. Influence of porous material on the STL of the multiple-single-type-resonator composite structure with different characteristic frequencies: (a) OU case; (b) OB case. The solid lines correspond to cases with porous materials.有无多孔材料对含不同特征频率振子系统复合结构STL的影响 (a) OU边界情况; (b) OB边界情况; 有无多孔介质分别与相应实线和虚线对应
Fig. 6. The STL of multiple-single-type-resonator composite structure (
Fig. 7. Influences of resonators with different characteristic frequencies on the STL: (a) OU case; (b) OB case.采用不同特征频率简单振子系统对复合结构STL的影响 (a) OU边界; (b) OB边界
Fig. 8. (a) STL of OU and OB case in periodically-arranged single simple resonator case, and its displacement transmissibility
Fig. 9. Displacement transmissibility and dynamic mass of the mass components in the two composite resonators: (a1) Displacement transmissibility , of composite resonator type A; (a2) dynamic mass of composite resonator type A; (b1) displacement transmissibility , of composite resonator type B; (b2) dynamic mass of composite resonator type B. 两类组合振子系统中质量块的位移传递率 , 和动态质量 (a1) 组合振子系统A中各质量块的位移传递率 , ; (a2) 组合振子系统A的动态质量 ; (b1) 组合振子系统B中各质量块的位移传递率 , ; (b2) 组合振子系统B的动态质量
Fig. 10. STL of the proposed composite structure with 4 identical simple resonators (Single resonator), composite resonators of type A or B versus its STL without any resonators (Without resonator) in a periodic lattice: (a) OU boundary case; (b) OB boundary case.复合结构周期间隔内分布4个相同简单振子(Single resonator), 组合振子A或组合振子B时的STL和不含振子复合结构(Without resonator)的STL (a) OU边界情况; (b) OB边界情况
Fig. 11. STL of the composite structure with NNSR configuration under two boundary cases: (a1), (a2) Case A; (b1), (b2) case B, . Here (a1) and (b1) correspond to OU case, (a2) and (b2) correspond to OB case. NNSR分布时OU, OB边界情况下的STL (a1), (a2) 情况A; (b1), (b2) 情况B, ; 其中, (a1)和(b1)为OU边界情况, (a2)和(b2)为OB边界情况
Fig. 12. STL of the proposed composite structure under NNCR configuration: (a1), (a2) Composite resonator type A; (b1), (b2) composite resonator type B. Here (a1) and (b1) correspond to OU case, (a2) and (b2) correspond to OB case.采用组合振子复合结构的STL (a1), (a2) 采用组合振子A; (b1), (b2) 采用组合振子B; 其中, (a1)和(b1)对应于OU边界情况, (a2)和(b2)对应于OB边界情况
Fig. 13. STL of different resonator system configuration: (a), (a1) OU case; (b), (b1) OB case. and correspond to simple resonator case NNSR. Type A and Type B correspond to composite resonator case NNCR. 不同振子系统分布时STL对比 (a), (a1) OU边界情况; (b), (b1) OB边界情况; 和 对应简单振子情况NNSR; Type A和Type B对应组合振子情况NNCR
Table 1. Abbreviations of the distribution of resonator systems and their meanings.
View tableView in ArticleTable 1. Abbreviations of the distribution of resonator systems and their meanings.
振子系统分布 含义 N1SR 周期间隔内分布多个简单振子系统, 各振子系统 ${m_i}$ ${f_i}$ NNSR 周期间隔内分布多种简单振子系统, 各振子系统 ${m_i}$ ${f_i}$ N1CR 周期间隔内分布多个组合振子系统, 各振子系统 $m_n^i$ $f_n^i$ NNCR 周期间隔内分布多种组合振子系统, 各振子系统 $m_n^i$ $f_n^i$
Table 2. Parameters of plate and resonators.
View tableView in ArticleTable 2. Parameters of plate and resonators.
薄板 空气域(20 ℃, 1 atm) 简单振子 h /mmE /GPaν ${\rho _{\rm{p}}}$ ρ /kg·m–3c 0/m·s–1h a/mmf r/Hzγ 1 70 0.33 2700 1.204 343.21 2 300 0.2
Table 3. Parameters of the porous media used here
View tableView in ArticleTable 3. Parameters of the porous media used here
参数 值 参数 值 ${\rho _{\rm{s}}}$ 30 $\epsilon$ 0.9 ${\rho _{\rm{f}}}$ 1.204 ${\tau _\infty }$ 7.8 ${E_{\rm{s}}}$ 0.8(1+0.265 ${\rm{j}}$ ${\sigma _0}$ 25000 ${\nu _s}$ 0.4 h p/mm50
Table 4.
Parameters of the composite resonators.
振子系统参数
View tableView in ArticleTable 4.
Parameters of the composite resonators.
振子系统参数
参数 $\omega _1^i$ $\omega _2^i$ r s $\eta _1^i$ $\eta _2^i$ 值 600 ${\text{π}}$ 1088 0.075 0.0625 0.01 0.05
Table 5.
Parameters of the composite resonators.
组合振子系统参数
View tableView in ArticleTable 5.
Parameters of the composite resonators.
组合振子系统参数
参数 r s $\eta _1^i$ $\eta _2^i$ 值 0.045 0.040 0.01 0.05
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Hou Qiao, Zeng He, Heng-Kun Zhang, Wei-Cai Peng, Wen Jiang.
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Received: Jan. 28, 2019
Accepted: --
Published Online: Oct. 30, 2019
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