Abstract
Wave propagation in nonlinear acoustic metamaterials (NAMs) has attracted broad attention. While showing the possibility of achieving low-frequency and broadband vibration suppression, most existing work focuses on harmonic waves. In this paper, we study the impact wave propagation and its mitigation in a nonlinear metamaterial beam. Thorough numerical analyses show that strongly nonlinear acoustic metamaterials can entail effective attenuation of impact waves in an infinite structure and the impact vibration in a finite structure with a much higher efficiency than what can be achieved in their linear counterparts. The attenuation properties, underlying mechanisms and the influence of key system parameters are clarified. Results show that the observed attenuation is dominated by the nonlinearity-induced self-broadening of the bandgaps whose bandwidths adaptively expand with the propagation distance/time, as a result of the amplitude-dependent nature of the band gaps in a NAM. In a finite NAM structure, significant attenuation of the impact vibration can be achieved, outperforming the corresponding linear cases. These findings shed lights on new physics relating to NAMs and might inspire their further study and application.
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Acknowledgements
This work is funded by the National Natural Science Foundation of China (Projects No. 52241103, No. 11991032), and the Science and Technology Innovation Program of Hunan Province (Projects No. 2020RC4022). Prof. Li Cheng thanks the Research Grant Council of the Hong Kong SAR for providing support through GRF project.
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Appendices
Appendix A: Flexural wave dispersion
The longitudinal vibration of the bare beam under the same longitudinal impact excitation amplitude is analyzed and compared with the flexural vibration under transverse impact excitation to obtain Fig. 19, and the time domain vibration responses at the 1th, 20th, 50th and 100th cells are selected to obtain Fig. 20. The vibration responses of the beam at different points almost remain intact when the longitudinal impact excitation is applied, which is almost the same as the applied pulse excitation waveform, indicating that there is no dispersion phenomenon in the longitudinal propagation process. However, the peak vibration level decreases before disappearing for larger propagation distance when the transverse impact excitation is applied, which is caused by the dispersion of the flexural waves in the beam.
Appendix B: Dispersion curves of 100 cells
See Fig. 21
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Hu, B., Fang, X., Cheng, L. et al. Attenuation of impact waves in a nonlinear acoustic metamaterial beam. Nonlinear Dyn 111, 15801–15816 (2023). https://doi.org/10.1007/s11071-023-08689-z
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DOI: https://doi.org/10.1007/s11071-023-08689-z