A Bayesian approach for wavenumber identification of metamaterial beams possessing variability
A Bayesian approach for wavenumber identification of metamaterial beams possessing variability
Recent developments in additive manufacturing have allowed for a number of innovative designs in elastic metamaterials and phononic crystals used in several applications, including vibration attenuation. Complex geometric patterns that were otherwise very expensive or unpractical to produce are currently feasible. However, the 3D printing also introduces variability, which can greatly affect the dynamic performance of the metastructure. This work investigates the effects of manufacturing variability on the wavenumber identification of beams with evenly attached resonators, produced from Selective Laser Sintering. A combination of a correlation-based technique and a Bayes framework is proposed to identify the effective wavenumber and the most probable values of some of the design parameters. Typically of interest, for vibration attenuation using metamaterials, are the mass ratio and the resonator natural frequency. For this purpose an analytical model is derived, assuming an infinite number of resonators tuned to the same frequency. These parameters can be highly affected by the manufacturing variability because they are dependent on complex geometrical features of the metastructure. It is shown that the proposed approach can estimate the most likely values of the parameters with less than 4% difference when compared to a benchmark approach; the latter is not only more complex and time demanding, but also based on indirect measurements. Understanding the effects of this variability on the wave propagation represents an important step towards proposing robust designs with respect to the attenuation performance.
Bayesian estimation, band gap, elastic metamaterial, uncertainty quantification, wavenumber identification
1-15
Souza, Marcos
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Beli, Danilo
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Ferguson, Neil
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Arruda, J.R.F.
bdc608d2-5107-4de9-9d86-162ed13a7357
Fabro, Adriano
ec8ae99f-417a-4e1e-a912-3c4cff5c11b7
1 January 2020
Souza, Marcos
c76b43db-74a1-43dc-ae25-79530d88d089
Beli, Danilo
c6d272af-8300-4eed-a9ad-502c2f00567d
Ferguson, Neil
8cb67e30-48e2-491c-9390-d444fa786ac8
Arruda, J.R.F.
bdc608d2-5107-4de9-9d86-162ed13a7357
Fabro, Adriano
ec8ae99f-417a-4e1e-a912-3c4cff5c11b7
Souza, Marcos, Beli, Danilo, Ferguson, Neil, Arruda, J.R.F. and Fabro, Adriano
(2020)
A Bayesian approach for wavenumber identification of metamaterial beams possessing variability.
Mechanical Systems and Signal Processing, 135, , [106437].
(doi:10.1016/j.ymssp.2019.106437).
Abstract
Recent developments in additive manufacturing have allowed for a number of innovative designs in elastic metamaterials and phononic crystals used in several applications, including vibration attenuation. Complex geometric patterns that were otherwise very expensive or unpractical to produce are currently feasible. However, the 3D printing also introduces variability, which can greatly affect the dynamic performance of the metastructure. This work investigates the effects of manufacturing variability on the wavenumber identification of beams with evenly attached resonators, produced from Selective Laser Sintering. A combination of a correlation-based technique and a Bayes framework is proposed to identify the effective wavenumber and the most probable values of some of the design parameters. Typically of interest, for vibration attenuation using metamaterials, are the mass ratio and the resonator natural frequency. For this purpose an analytical model is derived, assuming an infinite number of resonators tuned to the same frequency. These parameters can be highly affected by the manufacturing variability because they are dependent on complex geometrical features of the metastructure. It is shown that the proposed approach can estimate the most likely values of the parameters with less than 4% difference when compared to a benchmark approach; the latter is not only more complex and time demanding, but also based on indirect measurements. Understanding the effects of this variability on the wave propagation represents an important step towards proposing robust designs with respect to the attenuation performance.
Text
MSSP19-1027R1_NSF
- Accepted Manuscript
More information
Accepted/In Press date: 10 October 2019
e-pub ahead of print date: 22 October 2019
Published date: 1 January 2020
Additional Information:
Funding Information:
The authors would like to thank the NT3D group from CTI Renato Archer Brazilian Institute (Campinas-SP, Brazil) for manufacturing the metamaterial beam samples through the ProEXP program, and the Nondestructive Testing Laboratory (LabEND) from FEAGRI/UNICAMP for providing the ultrasound equipment used to measure the elastic properties of the cube specimens. The authors also grateful to the São Paulo Research Foundation (FAPESP – São Paulo, Brazil), through project numbers 2014/19054-6, 2018/18774-6 and 2018/15894-0, Brazilian National Council of Research CNPq (processes number 420304/2018-5 and 231744/2013-7) the Brazilian Federal District Research Foundation – FAPDF , process number 0193.001507/2017, and the Coordination for the Improvement of Higher Education Personnel ( CAPES – Brazil) for the financial support.
Publisher Copyright:
© 2019 Elsevier Ltd
Keywords:
Bayesian estimation, band gap, elastic metamaterial, uncertainty quantification, wavenumber identification
Identifiers
Local EPrints ID: 435316
URI: http://eprints.soton.ac.uk/id/eprint/435316
ISSN: 0888-3270
PURE UUID: 1adcc8f6-e4ae-4f08-8dee-67a35de41290
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Date deposited: 30 Oct 2019 17:30
Last modified: 17 Mar 2024 02:32
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Contributors
Author:
Marcos Souza
Author:
Danilo Beli
Author:
J.R.F. Arruda
Author:
Adriano Fabro
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