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A Bayesian approach for wavenumber identification of metamaterial beams possessing variability

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, wavenumber identification, uncertainty quantification, band gap, elastic metamaterial
0888-3270
1-15
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
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, 1-15, [106437]. (doi:10.1016/j.ymssp.2019.106437).

Record type: Article

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
Restricted to Repository staff only until 22 October 2020.
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More information

Accepted/In Press date: 10 October 2019
e-pub ahead of print date: 22 October 2019
Published date: 1 January 2020
Keywords: Bayesian estimation, wavenumber identification, uncertainty quantification, band gap, elastic metamaterial

Identifiers

Local EPrints ID: 435316
URI: http://eprints.soton.ac.uk/id/eprint/435316
ISSN: 0888-3270
PURE UUID: 1adcc8f6-e4ae-4f08-8dee-67a35de41290
ORCID for Neil Ferguson: ORCID iD orcid.org/0000-0001-5955-7477

Catalogue record

Date deposited: 30 Oct 2019 17:30
Last modified: 18 Feb 2020 01:24

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