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An analytical approach for calculating natural frequencies of finite one-dimensional acoustic metamaterials

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Abstract

In this paper, an analytical matrix method is presented to drive closed-form characteristic equations for natural frequencies of finite monoatomic and diatomic metamaterials with various boundary conditions. Here, we extend the matrix method introduced by Louck for monoatomic lattice chains. The proposed method is used to calculate the vibration frequencies of the monoatomic metamaterials with fixed–fixed, fixed-free and free-free boundary conditions. In addition, the natural frequencies of fixed–fixed diatomic metamaterials are calculated. The existence of band gaps in the frequencies of the metamaterials is numerically shown.

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Acknowledgements

This study is dedicated to Prof. Elias C. Aifantis on occasion of his 70th birthday.

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Authors and Affiliations

  1. School of Mechanical Engineering, Shiraz University, 71963-16548, Shiraz, Iran

    Esmaeal Ghavanloo & S. Ahmad Fazelzadeh

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  1. Esmaeal Ghavanloo
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  2. S. Ahmad Fazelzadeh
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Correspondence to Esmaeal Ghavanloo.

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Ghavanloo, E., Fazelzadeh, S.A. An analytical approach for calculating natural frequencies of finite one-dimensional acoustic metamaterials. Meccanica 56, 1819–1829 (2021). https://doi.org/10.1007/s11012-021-01332-4

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