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Bandgap formation and chaos in periodic lattices with graded bistable resonators

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Abstract

The interest for the study of metamaterials and metastructures has been rapidly increasing in the scientific community. A number of different approaches for the configuration of such systems have already shown to produce unique and potentially useful dynamic behavior, such as broadband vibration attenuation and negative mechanical properties. Locally resonant metamaterials are of special interest in this domain because of its versatility in creating wide bandgaps for wave propagation while being relatively simple in terms of analysis and experimental reproduction. Two specific subcategories of this type of systems have shown to enable specially promising bandgap formation behavior: nonlinear resonators and functionally graded, or rainbow, metamaterials. This work presents the yet unexplored combination of these two characteristics, showing that graded bistable nonlinear resonators can further widen the broadband vibration attenuation for a simple 1-D periodic lattice system due to chaotic response. This work also presents an contribution on the phenomenology of the vibration attenuation mechanisms with chaotic behavior.

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Acknowledgements

The authors are grateful to the Brazilian National Council of Research (CNPq - Brazil), processes number 310850/2019-3, 433730/2018-8 and 314168/2020-6, the Federal District Foundation for Research Support (FAPDF -Brazil), project number 00193-00000766/2021-71, 00193-00001139/2021-57 and 00193-00001804/2022-93 for the support and the São Paulo Research Foundation (FAPESP - Brazil), project number 2018/15894-0.

Funding

The authors received funding from the Brazilian National Council of Research (CNPq - Brazil), processes number 310850/2019-3, 433730/2018-8 and 314168/2020-6, the Federal District Foundation for Research Support (FAPDF -Brazil), project number 00193-00000766/2021-71 and 00193-00001804/2022-93 and the São Paulo Research Foundation (FAPESP - Brazil), project number 2018/15894-0.

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Authors and Affiliations

  1. Mechanical Engineering Department, Universidade de Brasília, Universidade de Brasília - UnB, Brasília, 70910-900, DF, Brazil

    André Brandão, Aline Souza de Paula & Adriano Fabro

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  1. André Brandão
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  2. Aline Souza de Paula
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  3. Adriano Fabro
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Correspondence to André Brandão.

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Technical Editor: Marcelo Areias Trindade.

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Brandão, A., de Paula, A.S. & Fabro, A. Bandgap formation and chaos in periodic lattices with graded bistable resonators. J Braz. Soc. Mech. Sci. Eng. 46, 104 (2024). https://doi.org/10.1007/s40430-023-04675-z

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