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

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

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

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

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

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

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 h_r 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h_r对各低频带隙的影响;

Table 1. Combination of various structural parameters

Table 2. Material parameters