Harnessing Geometric Frustration to Form Band Gaps in Acoustic Channel Lattices

Pai Wang (1) , Yue Zheng (2) , Matheus C Fernandes (1) , Yushen Sun (3) , Kai Xu (4) , Sijie Sun (1, 3) , Sung Hoon Kang (5) , Vincent Tournat (1, 6) , Katia Bertoldi (1, 7)

1 SEAS - Harvard John A. Paulson School of Engineering and Applied Sciences
2 UCSD Jacobs School of Engineering
3 THU - Tsinghua University [Beijing]
4 Peking University [Shenzhen]
5 Department of Mechanical Engineering [Johns Hopkins University]
6 LAUM - Laboratoire d'Acoustique de l'Université du Mans
7 KIBST - Kavli Institute for Bionano Science & Technology [Harvard University]

We demonstrate both numerically and experimentally that geometric frustration in two-dimensional periodic acoustic networks consisting of arrays of narrow air channels can be harnessed to form band gaps (ranges of frequency in which the waves cannot propagate in any direction through the system). While resonant standing wave modes and interferences are ubiquitous in all the analyzed network geometries, we show that they give rise to band gaps only in the geometrically frustrated ones (i.e., those comprising of triangles and pentagons). Our results not only reveal a new mechanism based on geometric frustration to suppress the propagation of pressure waves in specific frequency ranges but also open avenues for the design of a new generation of smart systems that control and manipulate sound and vibrations.

Domaines: Acoustique [physics.class-ph]

Pai Wang, Yue Zheng, Matheus C Fernandes, Yushen Sun, Kai Xu, et al.. Harnessing Geometric Frustration to Form Band Gaps in Acoustic Channel Lattices. Physical Review Letters, 2017, 118 (8), ⟨10.1103/PhysRevLett.118.084302⟩. ⟨hal-01703897⟩