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

Krynkin, A, Umnova, O, Taherzadeh, S and Attenborough, K 2013, 'Analytical approximations for low frequency band gaps in periodic arrays of elastic shells' , The Journal of the Acoustical Society of America (JASA), 133 (2) .

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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 ¼ 0) and dipolar (n ¼ 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: Article
Schools: Schools > School of Computing, Science and Engineering > Salford Innovation Research Centre (SIRC)
Journal or Publication Title: The Journal of the Acoustical Society of America (JASA)
Publisher: Acoustical Society of America
Refereed: Yes
ISSN: 0001-4966
Related URLs:
Funders: Engineering and Physical Sciences Research Council (EPSRC)
Depositing User: O Umnova
Date Deposited: 21 May 2015 12:59
Last Modified: 29 Oct 2015 00:23

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