A Krynkin
Analytical approximations for low frequency band gaps
in periodic arrays of elastic shells
Krynkin, A; Umnova, O; Taherzadeh, S; Attenborough, K
Authors
O Umnova
S Taherzadeh
K Attenborough
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 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.
Citation
in periodic arrays of elastic shells. The Journal of the Acoustical Society of America (Online), 133(2), https://doi.org/10.1121/1.4773257
Journal Article Type | Article |
---|---|
Publication Date | Feb 1, 2013 |
Deposit Date | May 21, 2015 |
Publicly Available Date | Apr 5, 2016 |
Journal | The Journal of the Acoustical Society of America (JASA) |
Print ISSN | 0001-4966 |
Peer Reviewed | Peer Reviewed |
Volume | 133 |
Issue | 2 |
DOI | https://doi.org/10.1121/1.4773257 |
Publisher URL | http://dx.doi.org/10.1121/1.4773257 |
Related Public URLs | http://scitation.aip.org/content/asa/journal/jasa |
Additional Information | Access Information : Copyright (2015) Acoustical Society of America. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the Acoustical Society of America. Funders : Engineering and Physical Sciences Research Council (EPSRC) |
Files
JASA_13.pdf
(848 Kb)
PDF
You might also like
Nonlinear behaviour of lossy acoustic black holes
(2024)
Journal Article
FE Modelling Tibia Bone Vibration - The Influence of Shape, Twist, and Size
(2024)
Journal Article
Urban Hedges as Noise Barriers: Does Plant Species Choice Affect Insertion Loss?
(2024)
Journal Article
Multiple resonances in lossy acoustic black holes - theory and experiment
(2022)
Journal Article
Downloadable Citations
About USIR
Administrator e-mail: library-research@salford.ac.uk
This application uses the following open-source libraries:
SheetJS Community Edition
Apache License Version 2.0 (http://www.apache.org/licenses/)
PDF.js
Apache License Version 2.0 (http://www.apache.org/licenses/)
Font Awesome
SIL OFL 1.1 (http://scripts.sil.org/OFL)
MIT License (http://opensource.org/licenses/mit-license.html)
CC BY 3.0 ( http://creativecommons.org/licenses/by/3.0/)
Powered by Worktribe © 2024
Advanced Search