Abstract
This paper provides a detailed comparison of the two-scale homogenization method and of the Bloch-Floquet theory for the determination of band-gaps in locally resonant metamaterials. A medium composed by a stiff matrix with soft inclusions with 2D periodicity is considered and the equivalent mass density of the homogenized medium is explicitly obtained both for in-plane and out-of-plane wave propagation through two-scale asymptotic expansion. The intervals of frequency where the effective mass is negative identify the band-gaps of the material. The Bloch-Floquet problem is then considered and, through an asymptotic analysis, its is shown that it leads to the same prediction of the band-gaps. The results are confirmed by some examples and the limits of the asymptotic approach are explicitly given and numerically verified.
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The first Author wishes to thank the Colleagues of École polytechnique for kind hospitality and the Laboratoire de Mécanique des Solides, for financial support.
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Comi, C., Marigo, JJ. Homogenization Approach and Bloch-Floquet Theory for Band-Gap Prediction in 2D Locally Resonant Metamaterials. J Elast 139, 61–90 (2020). https://doi.org/10.1007/s10659-019-09743-x
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DOI: https://doi.org/10.1007/s10659-019-09743-x