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Numerical and experimental study on bandgap property of two-dimensional lattice with nested core

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Abstract

A new two-dimensional lattice structure was proposed by embedding a core to a square lattice. Wave propagation of the periodic structure was studied based on Bloch’s theorem and finite element method. The effects of similarity ratio (\(\eta\)) and the shape of nested core (square core, circular core and re-entrant core) on bandgap distribution were investigated. The anisotropy of wave propagation was studied by analyzing phase velocity and group velocity. Via frequency dispersion analysis, the mechanism of \(\eta\) tuning the bandgap distribution was demonstrated. With \(\eta\) increasing, the first bandgap of the square lattice with nested core widened and the total bandgap width increased. The square lattice with nested core of Lf = 50 mm at \(\eta\) = 0.95 had the lowest opening frequency (30.60 Hz) of the first bandgap whose width of the first bandgap was 366.26 Hz and also exhibited apparent anisotropy of wave propagation in the first and fourth mode. Concerning the practical application, a single-phase structure was proposed and studied. Thanks to additive manufacturing technology, the single-phase structure was prepared, and a low amplitude test was performed. The experimental result demonstrated the presence of an ultrawide vibration attenuation zone identical to the numerical results, which may pave the way for the practical application of the proposed lattice metamaterial.

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Acknowledgements

This work is supported by “National Key Research and Development Program of China (2018YFF0300502),” “Liaoning Province Key Research and Development Program (2020JH2/10300112)” and “The Fundamental Research Funds for the Central Universities (N2105022).”

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  1. School of Mechanical Engineering and Automation, Northeastern University, Shenyang, 110819, People’s Republic of China

    Jiahong Hou & Zhijun Zhang

  2. College of Sciences, Northeastern University, Shenyang, 110819, People’s Republic of China

    Dong Li

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  1. Jiahong Hou
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Hou, J., Zhang, Z. & Li, D. Numerical and experimental study on bandgap property of two-dimensional lattice with nested core. Appl. Phys. A 128, 164 (2022). https://doi.org/10.1007/s00339-022-05280-y

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