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Elastic wave propagation in nonlinear two-dimensional acoustic metamaterials

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Abstract

This study describes the wave propagation in a periodic lattice which is formed by a spring-mass two-dimensional structure with local Duffing nonlinear resonators. The wave propagation characteristics of the system are evaluated by using the perturbation method to determine the dispersion relationships and wave propagation characteristics in the nonlinear two-dimensional acoustic metamaterials. A quantitative study of wave amplitude is carried out to determine the maximum allowable wave amplitude for the whole structures under the assumption of small parameters. In particular, the harmonic balance method is introduced to investigate the frequency response and effective mass of the nonlinear systems. We find that the dispersion relations and group velocity of unit cell are related to wave amplitude. Furthermore, the dual-wave vector is observed in the nonlinear systems. Numerical simulations validate the dispersion analytical results. The results can be used to tune wave propagation in the nonlinear acoustic metamaterials and provide some ideas for the study of nonlinear metamaterials.

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Data Availability

The datasets generated during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

The authors would also like to appreciate Associate Professor Xin Fang, National University of Defense Technology, for innumerable helpful discussions.

Funding

Funding for this work has been provided by the National Natural Science Foundation of China (Nos. 11872313 and12172297) and Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University (Grant Number: CX2021071).

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Authors and Affiliations

  1. School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi’an, 710072, People’s Republic of China

    Cheng Zhao, Kai Zhang, Pengcheng Zhao & Zichen Deng

  2. MIIT Key Laboratory of Dynamics and Control of Complex Systems, Northwestern Polytechnical University, Xi’an, 710072, People’s Republic of China

    Cheng Zhao, Kai Zhang, Pengcheng Zhao & Zichen Deng

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  1. Cheng Zhao
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Correspondence to Kai Zhang.

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Zhao, C., Zhang, K., Zhao, P. et al. Elastic wave propagation in nonlinear two-dimensional acoustic metamaterials. Nonlinear Dyn 108, 743–763 (2022). https://doi.org/10.1007/s11071-022-07259-z

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