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Auxetic vibration behaviours of periodic tetrahedral units with a shared edge

A very low-frequency mode supported within an auxetic structure is presented. We propose a constrained periodic framework with corner-to-corner and edge-to-edge sharing of tetrahedra and develop a kinematic model incorporating two types of linear springs to calculate the momentum term under infinite...

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Detalles Bibliográficos
Autores principales: Tanaka, H., Asao, S., Shibutani, Y.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: The Royal Society 2021
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8527201/
https://www.ncbi.nlm.nih.gov/pubmed/34703621
http://dx.doi.org/10.1098/rsos.210768
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author Tanaka, H.
Asao, S.
Shibutani, Y.
author_facet Tanaka, H.
Asao, S.
Shibutani, Y.
author_sort Tanaka, H.
collection PubMed
description A very low-frequency mode supported within an auxetic structure is presented. We propose a constrained periodic framework with corner-to-corner and edge-to-edge sharing of tetrahedra and develop a kinematic model incorporating two types of linear springs to calculate the momentum term under infinitesimal transformations. The modal analysis shows that the microstructure with its two degrees of freedom has both low- and high-frequency modes under auxetic transformations. The low-frequency mode approaches zero frequency when the corresponding spring constant tends to zero. With regard to coupled eigenmodes, the stress–strain relationship of the uniaxial forced vibration covers a wide range. When excited, a very slow motion is clearly observed along with a structural expansion for almost zero values of the linear elastic modulus.
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spelling pubmed-85272012021-10-25 Auxetic vibration behaviours of periodic tetrahedral units with a shared edge Tanaka, H. Asao, S. Shibutani, Y. R Soc Open Sci Engineering A very low-frequency mode supported within an auxetic structure is presented. We propose a constrained periodic framework with corner-to-corner and edge-to-edge sharing of tetrahedra and develop a kinematic model incorporating two types of linear springs to calculate the momentum term under infinitesimal transformations. The modal analysis shows that the microstructure with its two degrees of freedom has both low- and high-frequency modes under auxetic transformations. The low-frequency mode approaches zero frequency when the corresponding spring constant tends to zero. With regard to coupled eigenmodes, the stress–strain relationship of the uniaxial forced vibration covers a wide range. When excited, a very slow motion is clearly observed along with a structural expansion for almost zero values of the linear elastic modulus. The Royal Society 2021-10-20 /pmc/articles/PMC8527201/ /pubmed/34703621 http://dx.doi.org/10.1098/rsos.210768 Text en © 2021 The Authors. https://creativecommons.org/licenses/by/4.0/Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) , which permits unrestricted use, provided the original author and source are credited.
spellingShingle Engineering
Tanaka, H.
Asao, S.
Shibutani, Y.
Auxetic vibration behaviours of periodic tetrahedral units with a shared edge
title Auxetic vibration behaviours of periodic tetrahedral units with a shared edge
title_full Auxetic vibration behaviours of periodic tetrahedral units with a shared edge
title_fullStr Auxetic vibration behaviours of periodic tetrahedral units with a shared edge
title_full_unstemmed Auxetic vibration behaviours of periodic tetrahedral units with a shared edge
title_short Auxetic vibration behaviours of periodic tetrahedral units with a shared edge
title_sort auxetic vibration behaviours of periodic tetrahedral units with a shared edge
topic Engineering
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8527201/
https://www.ncbi.nlm.nih.gov/pubmed/34703621
http://dx.doi.org/10.1098/rsos.210768
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