Wave and vibration analysis of elastic metamaterial and phononic crystal beams with slowly varying properties
Wave and vibration analysis of elastic metamaterial and phononic crystal beams with slowly varying properties
Periodic structures can be designed to exhibit elastic wave propagation band gap behaviour by varying material or geometrical properties, i.e. phononic crystals, or by periodically distributed resonators or boundary conditions, i.e. acoustic metamaterials, with various applications in passive noise and vibration control. However, variability in the manufacturing process causes material and geometry uncertainties that affect their band gap robustness and consequently their dynamic attenuation performance. In this work, the effects of slowly varying spatial properties on the vibration suppression performance of metamaterials and phononic crystals are investigated. The spectral element and the wave and finite element approaches are used for modelling the unit cells such that a wave-like interpretation can be derived for nearly-periodic structures. A beam with evenly spaced attached resonators and an undulating beam are analysed. In both cases, the band gap formation is investigated considering both non-uniform deterministic and spatially stochastic material and geometric variability. The proposed approach provides a framework to represent variability and randomness with spatial correlation of the periodic unit cell and then to assess their effects on the vibration suppression performance. It is shown that even a slowly varying spatial profile, or the correlation length in the case of random fields, plays a role on the band gap performance and that the presence of a critical section, i.e. a transition region between propagating and non-propagating waves, can significantly affect the band gap width and the amplitude of vibration attenuation. Moreover, it is shown the slowly varying approach is suitable to represent the ensemble statistics of band gaps, even considering the occurrence of such critical sections.
WKB approximation, band gap, near-periodic structures, random field,, slowly varying, uncertainty analysis
T. Fabro, Adriano
3d2a8581-2862-48f3-b7c2-3fe483f88adf
Beli, Danilo
74c52667-4633-4078-9e09-3d08c42cf97e
Ferguson, Neil
8cb67e30-48e2-491c-9390-d444fa786ac8
F. Arrudab, Jose Roberto
13684781-91ca-4e02-9dd8-092dc1699b88
Mace, Brian
cfb883c3-2211-4f3a-b7f3-d5beb9baaefe
June 2021
T. Fabro, Adriano
3d2a8581-2862-48f3-b7c2-3fe483f88adf
Beli, Danilo
74c52667-4633-4078-9e09-3d08c42cf97e
Ferguson, Neil
8cb67e30-48e2-491c-9390-d444fa786ac8
F. Arrudab, Jose Roberto
13684781-91ca-4e02-9dd8-092dc1699b88
Mace, Brian
cfb883c3-2211-4f3a-b7f3-d5beb9baaefe
T. Fabro, Adriano, Beli, Danilo, Ferguson, Neil, F. Arrudab, Jose Roberto and Mace, Brian
(2021)
Wave and vibration analysis of elastic metamaterial and phononic crystal beams with slowly varying properties.
Wave Motion, 103, [102728].
(doi:10.1016/j.wavemoti.2021.102728).
Abstract
Periodic structures can be designed to exhibit elastic wave propagation band gap behaviour by varying material or geometrical properties, i.e. phononic crystals, or by periodically distributed resonators or boundary conditions, i.e. acoustic metamaterials, with various applications in passive noise and vibration control. However, variability in the manufacturing process causes material and geometry uncertainties that affect their band gap robustness and consequently their dynamic attenuation performance. In this work, the effects of slowly varying spatial properties on the vibration suppression performance of metamaterials and phononic crystals are investigated. The spectral element and the wave and finite element approaches are used for modelling the unit cells such that a wave-like interpretation can be derived for nearly-periodic structures. A beam with evenly spaced attached resonators and an undulating beam are analysed. In both cases, the band gap formation is investigated considering both non-uniform deterministic and spatially stochastic material and geometric variability. The proposed approach provides a framework to represent variability and randomness with spatial correlation of the periodic unit cell and then to assess their effects on the vibration suppression performance. It is shown that even a slowly varying spatial profile, or the correlation length in the case of random fields, plays a role on the band gap performance and that the presence of a critical section, i.e. a transition region between propagating and non-propagating waves, can significantly affect the band gap width and the amplitude of vibration attenuation. Moreover, it is shown the slowly varying approach is suitable to represent the ensemble statistics of band gaps, even considering the occurrence of such critical sections.
Text
Fabro_WAVEMOT2020pure
- Accepted Manuscript
More information
Accepted/In Press date: 22 March 2021
e-pub ahead of print date: 24 March 2021
Published date: June 2021
Additional Information:
Funding Information:
The authors also grateful to the São Paulo Research Foundation (FAPESP - São Paulo, Brazil) , through project numbers 2014/19054-6 and 2018/15894-0 , Brazilian National Council of Research (CNPq - Brazil) , processes number 420304/2018-5 and 231744/2013-7 , the Federal District Research Foundation (FAPDF - Distrito Federal, Brazil) , process number 0193.001507/2017 and the Coordination for the Improvement of Higher Education Personnel (CAPES - Brazil) for the financial support.
Publisher Copyright:
© 2021 Elsevier B.V.
Keywords:
WKB approximation, band gap, near-periodic structures, random field,, slowly varying, uncertainty analysis
Identifiers
Local EPrints ID: 448043
URI: http://eprints.soton.ac.uk/id/eprint/448043
ISSN: 0165-2125
PURE UUID: 3beb146e-e975-4496-8228-7adf4d420adb
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Date deposited: 30 Mar 2021 16:38
Last modified: 16 Apr 2024 04:01
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Contributors
Author:
Adriano T. Fabro
Author:
Danilo Beli
Author:
Jose Roberto F. Arrudab
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