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Analytical approximations for low frequency band gaps in periodic arrays of elastic shells

Krynkin, Anton; Umnova, Olga; Taherzadeh, Shahram and Attenborough, Keith (2013). Analytical approximations for low frequency band gaps in periodic arrays of elastic shells. Journal of the Acoustical Society of America, 133(2) pp. 781–791.

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DOI (Digital Object Identifier) Link: https://doi.org/10.1121/1.4773257
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Abstract

This paper presents and compares three analytical methods for calculating low frequency band gap boundaries in doubly periodic arrays of resonating thin elastic shells. It is shown that both Foldy-type equations (derived with lattice sum expansions in the vicinity of its poles) and a self-consistent scheme could be used to predict boundaries of low-frequency (below the first Bragg band gap) band gaps due to axisymmetric (n = 0) and dipolar (n = 1) shell resonances. The accuracy of the former method is limited to low filling fraction arrays, however, as the filling fraction increases the application of the matched asymptotic expansions could significantly improve approximations of the upper boundary of band gap related to axisymmetric resonance. The self-consistent scheme is shown to be very robust and gives reliable results even for dense arrays with filling fractions around 70%. The estimates of band gap boundaries can be used in analyzing the performance of periodic arrays (in terms of the band gap width) without using full semi-analytical and numerical models. The results are used to predict the dependence of the position and width of the low frequency band gap on the properties of shells and their periodic arrays.

Item Type: Journal Item
Copyright Holders: 2013 Acoustical Society of America
ISSN: 0001-4966
Project Funding Details:
Funded Project NameProject IDFunding Body
Not SetNot SetEPSRC (Engineering and Physical Sciences Research Council)
Keywords: acoustic resonance; acoustic waves; elasticity; energy gap; shells (structures)
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Engineering and Innovation
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 36579
Depositing User: Keith Attenborough
Date Deposited: 11 Feb 2013 10:28
Last Modified: 12 Nov 2016 15:29
URI: http://oro.open.ac.uk/id/eprint/36579
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