• Acta Physica Sinica
  • Vol. 68, Issue 8, 084302-1 (2019)
Xin Chen, Hong Yao, Jing-Bo Zhao*, Shuai Zhang..., Zi-Hou He and Juan-Na Jiang|Show fewer author(s)
DOI: 10.7498/aps.68.20182102 Cite this Article
Xin Chen, Hong Yao, Jing-Bo Zhao, Shuai Zhang, Zi-Hou He, Juan-Na Jiang. Band gap of structure coupling Helmholtz resonator with elastic oscillator[J]. Acta Physica Sinica, 2019, 68(8): 084302-1 Copy Citation Text show less
Cross section of Helmholtz resonator coupled with elastic oscillator structureHelmholtz腔与弹性振子耦合结构横截面
Fig. 1. Cross section of Helmholtz resonator coupled with elastic oscillator structureHelmholtz腔与弹性振子耦合结构横截面
(a) Band diagram of the Helmholtz resonator coupled with elastic oscillator structure; (b) band diagram of the Helmholtz resonator structure(a) Helmholtz腔与弹性振子耦合结构带隙图; (b) Helmholtz腔结构带隙图
Fig. 2. (a) Band diagram of the Helmholtz resonator coupled with elastic oscillator structure; (b) band diagram of the Helmholtz resonator structure(a) Helmholtz腔与弹性振子耦合结构带隙图; (b) Helmholtz腔结构带隙图
(a) Band diagram of the Helmholtz resonator coupled with elastic oscillator structure; (b) the transmission spectra of the Helmholtz resonator coupled with elastic oscillator structure(a) Helmholtz腔与弹性振子耦合结构带隙图; (b) Helmholtz腔与弹性振子耦合结构隔声曲线
Fig. 3. (a) Band diagram of the Helmholtz resonator coupled with elastic oscillator structure; (b) the transmission spectra of the Helmholtz resonator coupled with elastic oscillator structure(a) Helmholtz腔与弹性振子耦合结构带隙图; (b) Helmholtz腔与弹性振子耦合结构隔声曲线
Sound pressure distribution diagrams of point A (a), B (b), C (c), and D (d).(a) A点, (b) B点, (c) C点, (d) D点的声场压力图
Fig. 4. Sound pressure distribution diagrams of point A (a), B (b), C (c), and D (d). (a) A点, (b) B点, (c) C点, (d) D点的声场压力图
The vibration mode of the elastic oscillatorat the first straight belt (a) and at the second straight belt (b); the sound pressure distribution diagrams of the first straight belt (c), and the second straight belt (d)(a) 第一平直带弹性振子振型图; (b) 第二平直带弹性振子振型图; (c) 第一平直带声场压力图; (d) 第二平直带声场压力图
Fig. 5. The vibration mode of the elastic oscillatorat the first straight belt (a) and at the second straight belt (b); the sound pressure distribution diagrams of the first straight belt (c), and the second straight belt (d)(a) 第一平直带弹性振子振型图; (b) 第二平直带弹性振子振型图; (c) 第一平直带声场压力图; (d) 第二平直带声场压力图
(a) The equivalent model of modal B and D; (b) the equivalent model of modal A and C(a) 模态B, D的等效模型; (b) 模态A, C的等效模型
Fig. 6. (a) The equivalent model of modal B and D; (b) the equivalent model of modal A and C(a) 模态B, D的等效模型; (b) 模态A, C的等效模型
The impact of different parameters a on first and second low frequency bandgap: (a) The lattice constant a; (b) the length of the cavity opening l2; (d) the volume of the left cavity V2; (e) the volume of the right cavity V4; (c) the impact of the parameter hr on each low frequency bandgap晶格常数a (a), 开口长度l2 (b), 左腔体积V2 (d), 右腔体积V4 (e), 弹性振子密度(f)对第一、二低频带隙的影响; (c) 橡胶长度hr对各低频带隙的影响;
Fig. 7. The impact of different parameters a on first and second low frequency bandgap: (a) The lattice constant a; (b) the length of the cavity opening l2; (d) the volume of the left cavity V2; (e) the volume of the right cavity V4; (c) the impact of the parameter hr on each low frequency bandgap 晶格常数a (a), 开口长度l2 (b), 左腔体积V2 (d), 右腔体积V4 (e), 弹性振子密度 (f)对第一、二低频带隙的影响; (c) 橡胶长度hr对各低频带隙的影响;
名称a/mm l2/mm l3/mm br/mm hr/mm bs/mm 振子材料
Helmholtz腔与弹性振子耦合结构带隙下限最低参数61 [61, 65]50 [1, 1680]40 [1, 56]4 [1, 5]9 [1, 9]25 [1, 25]
传统Helmholtz腔结构带隙下限最低参数61 [61, 65]848 [1, 1680]
初始结构参数655028.5111
Table 1. Combination of various structural parameters
材料名称硅橡胶环氧树脂
密度/k·m–3130011801750273045407780
弹性模量/1010 Pa 1.175 × 10–50.43523.017.7611.7021.06
剪切模量/1010 Pa 4 × 10–60.1598.852.874.438.10
Table 2. Material parameters
Xin Chen, Hong Yao, Jing-Bo Zhao, Shuai Zhang, Zi-Hou He, Juan-Na Jiang. Band gap of structure coupling Helmholtz resonator with elastic oscillator[J]. Acta Physica Sinica, 2019, 68(8): 084302-1
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