Nonlinear Tunability of Elastic Waves in One-Dimensional Mass-Spring Lattices Attached with Local Resonators
Vibration propagates in the form of elastic waves. The tuning of elastic waves is of great significance for vibration and noise reduction. The elastic metamaterials (EMs), which can effectively prohibit elastic wave propagation in the band gap frequency range, have been widely studied. However, once...
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| Format: | Article |
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MDPI AG
2022-12-01
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| Series: | Aerospace |
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| Online Access: | https://www.mdpi.com/2226-4310/9/12/818 |
| _version_ | 1797461995211980800 |
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| author | Nansun Shen Jinhui Jiang Fang Zhang Ming Ding |
| author_facet | Nansun Shen Jinhui Jiang Fang Zhang Ming Ding |
| author_sort | Nansun Shen |
| collection | DOAJ |
| description | Vibration propagates in the form of elastic waves. The tuning of elastic waves is of great significance for vibration and noise reduction. The elastic metamaterials (EMs), which can effectively prohibit elastic wave propagation in the band gap frequency range, have been widely studied. However, once the structures of the EMs are determined, the band gap is also determined. In this paper, a discrete nonlinear elastic metamaterial is proposed. The harmonic balance method is used to derive the nonlinear dispersion relation combined with Bloch’s theorem. The low frequency band gap near the linear natural frequency of local resonators is obtained. The theoretical results show that the nonlinearity will change the starting and ending frequencies of the band gap. In addition, amplitude can also influence the band gap. This means that the amplitude can be changed to achieve the tunability of elastic waves in nonlinear elastic metamaterials. Finally, the theoretical results are verified by numerical simulation, and the results are in good agreement with each other. |
| first_indexed | 2024-03-09T17:27:17Z |
| format | Article |
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| institution | Directory Open Access Journal |
| issn | 2226-4310 |
| language | English |
| last_indexed | 2024-03-09T17:27:17Z |
| publishDate | 2022-12-01 |
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| record_format | Article |
| series | Aerospace |
| spelling | doaj.art-bd6b37e0752c4b43b9c72f9b59f41f3e2023-11-24T12:38:31ZengMDPI AGAerospace2226-43102022-12-0191281810.3390/aerospace9120818Nonlinear Tunability of Elastic Waves in One-Dimensional Mass-Spring Lattices Attached with Local ResonatorsNansun Shen0Jinhui Jiang1Fang Zhang2Ming Ding3State Key Laboratory of Mechanical Structure, Mechanics and Control, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, ChinaState Key Laboratory of Mechanical Structure, Mechanics and Control, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, ChinaState Key Laboratory of Mechanical Structure, Mechanics and Control, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, ChinaState Key Laboratory of Mechanical Structure, Mechanics and Control, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, ChinaVibration propagates in the form of elastic waves. The tuning of elastic waves is of great significance for vibration and noise reduction. The elastic metamaterials (EMs), which can effectively prohibit elastic wave propagation in the band gap frequency range, have been widely studied. However, once the structures of the EMs are determined, the band gap is also determined. In this paper, a discrete nonlinear elastic metamaterial is proposed. The harmonic balance method is used to derive the nonlinear dispersion relation combined with Bloch’s theorem. The low frequency band gap near the linear natural frequency of local resonators is obtained. The theoretical results show that the nonlinearity will change the starting and ending frequencies of the band gap. In addition, amplitude can also influence the band gap. This means that the amplitude can be changed to achieve the tunability of elastic waves in nonlinear elastic metamaterials. Finally, the theoretical results are verified by numerical simulation, and the results are in good agreement with each other.https://www.mdpi.com/2226-4310/9/12/818elastic wavesnonlinearityelastic metamaterialband gapharmonic balance methodBloch’s theorem |
| spellingShingle | Nansun Shen Jinhui Jiang Fang Zhang Ming Ding Nonlinear Tunability of Elastic Waves in One-Dimensional Mass-Spring Lattices Attached with Local Resonators Aerospace elastic waves nonlinearity elastic metamaterial band gap harmonic balance method Bloch’s theorem |
| title | Nonlinear Tunability of Elastic Waves in One-Dimensional Mass-Spring Lattices Attached with Local Resonators |
| title_full | Nonlinear Tunability of Elastic Waves in One-Dimensional Mass-Spring Lattices Attached with Local Resonators |
| title_fullStr | Nonlinear Tunability of Elastic Waves in One-Dimensional Mass-Spring Lattices Attached with Local Resonators |
| title_full_unstemmed | Nonlinear Tunability of Elastic Waves in One-Dimensional Mass-Spring Lattices Attached with Local Resonators |
| title_short | Nonlinear Tunability of Elastic Waves in One-Dimensional Mass-Spring Lattices Attached with Local Resonators |
| title_sort | nonlinear tunability of elastic waves in one dimensional mass spring lattices attached with local resonators |
| topic | elastic waves nonlinearity elastic metamaterial band gap harmonic balance method Bloch’s theorem |
| url | https://www.mdpi.com/2226-4310/9/12/818 |
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