Low frequency acoustic stop bands in cubic arrays of thick spherical shells with holes

Dupont, Guillaume, Movchan, Alexander, Enoch, Stefan and Guenneau, Sebastien (2017) Low frequency acoustic stop bands in cubic arrays of thick spherical shells with holes. Frontiers in Materials, 6. 50-.

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Abstract

We analyse the propagation of pressure waves within a fluid filled with a three-dimensional array of rigid coated spheres (shells). We first draw band diagrams for corresponding Floquet-Bloch waves. We then dig a channel terminated by a cavity within each rigid shell and observe the appearance of a low frequency stop band. The underlying mechanism is that each holey shell now acts as a Helmholtz resonator supporting a low frequency localized mode: Upon resonance, pressure waves propagate with fast oscillations in the thin water channel drilled in each shell and are localized in each fluid filled inner cavity. The array of fluid filled shells is approximated by a simple mechanical model of springs and masses allowing for asymptotic estimates of the low frequency stop band. We finally propose a realistic design of periodic macrocell with a large defect surrounded by 26 resonators connected by thin straight rigid wires, which supports a localized mode in the low frequency stop band.

Item Type:	Article
Additional Information:	7 pages, 12 figures
Uncontrolled Keywords:	physics.class-ph, physics.class-ph
Depositing User:	Symplectic Admin
Date Deposited:	15 Aug 2018 09:58
Last Modified:	16 Mar 2024 21:07
DOI:	10.3389/fmats.2019.00050
Open Access URL:	https://doi.org/10.3389/fmats.2019.00050
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3025005