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Attenuation of impact waves in a nonlinear acoustic metamaterial beam

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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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The majority data have been shown in this paper. All data in this study are available from the corresponding author on reasonable request.

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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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Authors and Affiliations

  1. Laboratory of Science and Technology on Integrated Logistics Support, College of Intelligent Science, National University of Defense Technology, Changsha, 410073, Hunan, China

    Bing Hu, Xin Fang, Jihong Wen & Dianlong Yu

  2. Department of Mechanical Engineering, Hong Kong Polytechnic University, Hung Hom, Kowloon, 999077, Hong Kong

    Li Cheng

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  1. Bing Hu
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  2. Xin Fang
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All authors contributed to the study. The first draft of the manuscript was written by BH and all authors commented on the manuscript. All authors read and approved the final manuscript.

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Correspondence to Xin Fang or Dianlong Yu.

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Appendices

Appendix A: Flexural wave dispersion

Fig. 19
figure 19

Vibration response curves of the bare beam with propagation distance and time. a Longitudinal impact excitation. b Transverse impact excitation

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Fig. 20
figure 20

Vibration time domain response curves of the bare beam at different points. a Longitudinal impact excitation. b Transverse impact excitation

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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

Fig. 21
figure 21

Dispersion curves of 100 cells with propagation distance at fr = 100 Hz. a LAM beam. b NAM beam

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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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