Propagation of acoustic waves in a fluid-filled pipe with periodic elastic Helmholtz resonators<xref rid="cpb_27_6_064301_fn1" ref-type="fn">*</xref> <fn id="cpb_27_6_064301_fn1"> <label>*</label> <p>Project supported by the National Natural Science Foundation of China (Grant Nos. 11372346, 51405502, and 51705529).</p> </fn>

Propagation of acoustic waves in a fluid-filled pipe with periodic elastic Helmholtz resonators* *

Project supported by the National Natural Science Foundation of China (Grant Nos. 11372346, 51405502, and 51705529).

Yu Dian-Long^{1, †}, Shen Hui-Jie², Liu Jiang-Wei¹, Yin Jian-Fei, Zhang Zhen-Fang¹, Wen Ji-Hong¹

(color online) Mode shapes of the unit cell for various Bloch wave vectors, corresponding to points A, B, and C in Fig. 7.