Analysis of Low Frequency Acoustic Stop Bands in Cubic Arrays of Thick Spherical Shells With Holes

Dupont, Guillaume, Movchan, Alexander, Enoch, Stefan and Guenneau, Sebastien (2019) Analysis of Low Frequency Acoustic Stop Bands in Cubic Arrays of Thick Spherical Shells With Holes. FRONTIERS IN MATERIALS, 6.

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Abstract

We analyse the propagation of airborne pressure waves through a three-dimensional array of rigid coated spheres (shells) in air. When we dig a channel terminated by an air cavity in each rigid shell we observe the appearance of a low frequency stop band. Each shell with a hole acts as a Helmholtz resonator supporting a low frequency localized mode. Isofrequency surfaces and contours reveal the strong anisotropy of the periodic structure at the edge of the stop band. A simple mechanical model of springs and masses allows for asymptotic estimates of the low frequency stop band for elongated channels. Increasing the radius of an air channel shifts up the position, and enlarges, the low frequency stop band. Adding holes in shells also shifts up the frequency of the stop band, and embedded shells lead to additional stop bands. Localization effect induced by a large defect in a periodic macrocell of Helmholtz resonators is finally investigated.

Item Type:	Article
Uncontrolled Keywords:	finite elements, bloch waves, acoustic metamaterials, Helmholtz resonators, multiscale asymptotic, stop band, localized mode
Depositing User:	Symplectic Admin
Date Deposited:	10 Sep 2019 15:05
Last Modified:	19 Jan 2023 00:27
DOI:	10.3389/fmats.2019.00050
Open Access URL:	https://doi.org/10.3389/fmats.2019.00050
Related URLs:	Author
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3054131