Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 505, Issue 2, Pages -Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2021.125503
Keywords
Fourier series expansion; Multiple resonators; Evanescent waves; Band gaps
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Funding
- Brazilian funding agency CAPES [001]
- Brazilian funding agency CNPq [313620/2018, 151311/2020-0]
- Brazilian funding agency FAPEMA [00857/19, 02730/19, 00824/20, 00133/21]
- Brazilian funding agency FAPESP [2018/15894-0]
- Natural Sciences and Engineering Research Council of Canada (NSERC)
- Canada Foundation for Innovation (CFI)
- New Brunswick Innovation Foundation (NBIF)
- Harrison McCain Foundation
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The study presents new formulations for analyzing the complex dispersion relation of flexural waves in a metamaterial Mindlin-Reissner thick plate with multiple periodic resonators, using the PWE and EPWE methods. These formulations provide more accurate results at higher frequencies compared to traditional thin plate theories. Multiple periodic resonators with multiple degrees of freedom attached to metamaterial plates broaden the applications for wave attenuation in high frequencies.
The plane wave expansion (PWE) and the extended plane wave expansion (EPWE) formulations are derived in order to obtain the complex dispersion relation of flexural waves in a metamaterial Mindlin-Reissner thick plate with multiple periodic resonators. These new formulations are useful to obtain more accurate results at higher frequencies than those based on Kirchhoff-Love thin plate theory. Multiple periodic resonators with multiple degrees of freedom (M-DOF) attached to metamaterial thick plates broaden the applications for wave attenuation in high frequencies. (C) 2021 Elsevier Inc. All rights reserved.
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