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One-dimensional granular chains as transmitted force attenuators

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Abstract

We design a one-dimensional granular container in the form of a granular chain to reduce the force transmitted to a fixed barrier at its boundary. The granular chain considered is composed of ordered “heavy” and “light” beads (granules), and possesses strongly nonlinear acoustics due to Hertzian interactions, as well as zero tensile strength resulting in bead separations and subsequent collisions. We find the relationship between the transmitted force and the mass ratio of light beads to heavy beads and the relationship between the transmitted force and the number of beads in each subchain. We obtain an optimal design to minimize the transmitted force under the condition of a fixed total length of the chain. Computational predictions are validated by experiments, wherein we also estimate (i) the value of the damping between beads and (ii) the linear stiffness between the end bead and the barrier at the boundary of the granular chain. Transient, propagating localized oscillations are found in this system in both simulations and experiments, which result due to the strong nonlinearity of the granular chain. These results offer the possibility of systematically designing granular shock absorbers of enhanced performance compared to their linear counterparts.

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Data availability

The datasets generated during the performance of the work reported herein are not publicly available. Requests or questions regarding these data should be directed to the first author (Zhenjiang Zhou).

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Funding

This research was supported by the “One Belt One Road” program through Zhejiang Province and the Zhejiang University of Technology-Institute of Applied Physics, Russian Academy of Sciences Joint Research Laboratory of Innovative Technology of Acoustics and Vibration through Grant No. 2018C04018; the National Natural Science Foundation of China through Grants No. 51975525 and 52005443; the Natural Science Foundation of Zhejiang Province through Grant No. LQ21E050016; and the Ministry of Science and Technology of China through Grant No. 2017YFC0306202.

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Authors and Affiliations

  1. Sound and Vibration Laboratory, College of Mechanical Engineering, Zhejiang University of Technology, 18 Chaowang Road, Hangzhou, 310014, China

    Zhenjiang Zhou, D. Michael McFarland, Xiangle Cheng & Huancai Lu

  2. Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, 1208 West Green Street, Urbana, IL, 61801, USA

    Alexander F. Vakakis

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  1. Zhenjiang Zhou
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Contributions

All authors contributed to the planning, execution, and interpretation of the work reported. Zhenjiang Zhou carried out the simulations and experiments and wrote a first draft of the manuscript. Michael McFarland directed the research and wrote the final draft. Xiangle Cheng, Huancai Lu, and Alexander Vakakis assisted with technical and administrative problems. All authors read and approved the final manuscript.

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Correspondence to D. Michael McFarland.

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Zhou, Z., McFarland, D.M., Cheng, X. et al. One-dimensional granular chains as transmitted force attenuators. Nonlinear Dyn 111, 14713–14730 (2023). https://doi.org/10.1007/s11071-023-08658-6

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