Acta Physica Sinica, Volume. 68, Issue 21, 214208-1(2019)
Figures & Tables(11)
Fig. 1. Cross section of Helmholtz resonator structure with a membrane wall.带薄膜壁的Helmholtz结构横截面
Fig. 2. Band diagram (a) and transmission spectrum (b) of the Helmholtz resonator structure with a membrane wall.带薄膜壁的Helmholtz结构 (a) 带隙图; (b) 隔声曲线
Fig. 3. Band diagram (a) and transmission spectrum (b) of the ordinary Helmholtz resonator structure.普通Helmholtz结构的(a)带隙图和(b)隔声曲线
Fig. 4. Vibration mode of the membrane and sound pressure distribution diagrams of point A (88.40 Hz) (a), B (119.06 Hz) (b), C (302.09 Hz) (c), D (533.03 Hz) (d), E (772.31 Hz) (e), and F (891.44 Hz) (f).(a) 模态A (88.40 Hz)、(b) 模态B (119.06 Hz)、(c) 模态C (302.09 Hz)、(d) 模态D (533.03 Hz)、(e) 模态E (772.31 Hz)、(f) 模态F (891.44 Hz) 的薄膜振型和声场压力图
Fig. 5. (a) System corresponding to starting frequency of band gaps; (b) system corresponding to cut-off frequency of band gaps.(a) 带隙下限系统示意图; (b) 带隙上限系统示意图
Fig. 6. Sound pressure distribution diagrams at starting frequency (a) and cutoff frequency (b) of the 3th band gap when
Table 1. Effect of the parameter ls on low-frequency band gaps.
View tableView in ArticleTable 1. Effect of the parameter ls on low-frequency band gaps.
ls/10–3 m 第一带隙下限 第一带隙上限 第二带隙下限 第二带隙上限 第三带隙下限 第三带隙上限 FEM TMM 误差/% FEM TMM 误差/% FEM TMM 误差/% FEM TMM 误差/% FEM TMM 误差/% FEM TMM 误差/% 4 89.2 3.7 121.4 4.4 314.2 2.8 557.7 0.6 790.7 2.2 900.3 1.6 92.5 126.7 323.0 561.2 808.3 914.7 6 88.9 3.6 120.1 4.2 297.7 1.8 526.8 –0.8 789.1 0.4 905.2 0.8 92.2 125.1 303.1 522.8 792.4 912.2 8 88.7 3.5 118.9 3.9 285.1 0.9 508.3 –2.1 795.6 –1.1 916.1 –0.5 91.9 123.5 287.6 497.5 786.8 912.0 10 88.6 3.4 117.9 3.5 275.6 –0.1 497.9 –3.5 815.9 –3.7 932.5 –2.3 91.6 122.0 275.4 480.5 786.0 910.8 12 88.5 3.1 117.2 3.0 268.4 –1.0 492.6 –4.8 843.8 –6.9 953.9 –5.2 91.3 120.7 265.6 469.1 785.3 904.4 14 88.5 2.8 116.7 2.3 262.9 –2.0 490.5 –5.9 878.5 –11 966.3 –8.2 91.0 119.4 257.6 461.5 779.9 887.3
Table 2. Effect of the parameter ls on natural frequency of membrane.
View tableView in ArticleTable 2. Effect of the parameter ls on natural frequency of membrane.
ls/10–3 m 4 6 8 10 12 14 1阶固有频率 252.4 237.9 226.8 218.2 211.6 206.6 2阶固有频率 751.3 782.8 794.0 814.8 843.4 879.1
Table 3. Effect of the parameter T on low-frequency band gaps.
View tableView in ArticleTable 3. Effect of the parameter T on low-frequency band gaps.
T/106N·m–1 第一带隙下限 第一带隙上限 第二带隙下限 第二带隙上限 第三带隙下限 第三带隙上限 FEM TMM 误差/% FEM TMM 误差/% FEM TMM 误差/% FEM TMM 误差/% FEM TMM 误差/% FEM TMM 误差/% 0.5 74.3 3.4 89.3 2.8 259.2 0.7 440.3 –1.2 574.1 0.1 770.1 0.5 76.8 91.8 261.0 434.9 574.4 774.3 1.5 96.3 3.4 143.1 4.6 345.5 3.2 589.6 0.2 952.1 2.2 1035.1 1.7 99.6 149.7 356.7 591.0 973.0 1053.1 2.5 103.3 2.9 174.6 4.6 415.0 4.2 648.0 0.7 1217.4 2.8 1274.1 2.3 106.4 182.7 432.6 652.4 1251.0 1303.2 3.5 106.8 2.7 196.4 4.4 474.9 4.8 691.4 1.1 1434.1 3.0 1478.6 2.5 109.6 205.0 497.6 698.8 1477.6 1516.1 4.5 108.8 2.5 212.5 4.1 528.2 5.1 729.6 1.4 1621.6 3.2 1642.5 3.3 111.5 221.3 555.2 740.1 1673.4 1696.5 10 113.0 2.1 257.8 3.0 757.3 5.9 907.9 2.7 1645.9 5.8 1741.8 3.1 115.3 265.6 801.7 932.8 1740.6 1796.2 100 116.2 1.8 311.0 1.2 1654.1 5.2 1737.3 3.1 2270.8 9.0 2375.3 6.1 118.3 314.9 1740.4 1791.6 2475.7 2520.3
Table 4. Effect of the parameter l1 on low-frequency band gaps.
View tableView in ArticleTable 4. Effect of the parameter l1 on low-frequency band gaps.
l1/mm 第一带隙下限 第一带隙上限 第二带隙下限 第二带隙上限 第三带隙下限 第三带隙上限 FEM TMM 误差/% FEM TMM 误差/% FEM TMM 误差/% FEM TMM 误差/% FEM TMM 误差/% FEM TMM 误差/% 99 88.4 4.4 119.1 5.7 302.1 3.4 533.0 1.3 772.3 3.4 891.4 2.4 92.3 125.9 312.5 540.0 798.6 912.9 148 74.5 3.4 101.5 5.1 301.2 3.5 513.3 1.1 772.6 3.4 873.7 2.4 77.1 106.7 311.7 519.1 798.9 894.4 197 66.0 2.9 89.9 4.7 301.9 3.5 500.0 1.1 772.4 3.3 836.0 1.9 67.9 94.1 312.5 505.3 798.2 851.8 246 60.1 2.6 81.4 4.5 303.2 3.5 488.5 1.0 697.6 1.2 734.1 0.9 61.7 85.1 313.7 493.3 705.9 740.6 295 55.8 2.5 75.0 4.3 304.7 3.4 475.7 0.9 587.8 0.7 637.5 0.7 57.2 78.2 315.2 479.9 591.9 642.3 344 52.5 2.4 69.8 4.2 306.3 3.4 458.4 0.7 507.5 0.6 558.9 3.1 53.7 72.7 316.6 461.5 510.8 576.4
Table 5. Effect of the parameter V2 on low-frequency band gaps.
View tableView in ArticleTable 5. Effect of the parameter V2 on low-frequency band gaps.
V2/10–4 m3 第一带隙下限 第一带隙上限 第二带隙下限 第二带隙上限 第三带隙下限 第三带隙上限 FEM TMM 误差/% FEM TMM 误差/% FEM TMM 误差/% FEM TMM 误差/% FEM TMM 误差/% FEM TMM 误差/% 7.07 108.5 6.3 120.5 5.8 406.9 1.0 566.2 1.0 809.9 1.9 953.1 1.2 115.3 127.6 411.0 571.8 825.3 964.2 10.57 103.3 4.8 121.1 4.8 361.4 1.6 558.3 –0.1 796.5 1.9 925.4 1.4 108.3 126.8 367.2 557.8 811.4 938.7 14.07 98.0 4.2 121.0 4.4 335.0 1.9 550.0 –0.1 790.9 1.8 913.1 1.4 102.2 126.4 341.3 549.4 804.9 925.8 17.57 93.3 3.9 120.9 4.3 317.7 2.1 544.4 –0.1 788.3 1.6 906.5 1.3 96.9 126.1 324.4 543.9 801.1 918.1 19.32 91.1 3.8 120.8 4.3 311.1 2.2 542.3 –0.1 787.4 1.6 904.1 1.2 94.5 126.0 317.9 541.8 799.7 915.3
Tools
Get Citation
Copy Citation Text
Xin Chen, Hong Yao, Jing-Bo Zhao, Shuai Zhang, Zi-Hou He, Juan-Na Jiang.
Paper Information
Received: May. 5, 2019
Accepted: --
Published Online: Sep. 17, 2020
The Author Email:
© Copyright 2018-2021 | Chinese Laser Press.
All Rights Reserved 沪ICP备15018463号-20