Research PapersNo Access

Extremely low frequency band gaps of beam-like inertial amplification metamaterials

Mingming Hou

http://orcid.org/0000-0002-9358-2569

School of Mechanical Engineering, Xi’an Jiaotong University, 28 Xianning West Road, Xi’an, Shaanxi 710049, China

E-mail Address: houmingming1314@163.com

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Jiu Hui Wu

School of Mechanical Engineering, Xi’an Jiaotong University, 28 Xianning West Road, Xi’an, Shaanxi 710049, China

E-mail Address: ejhwu@mail.xjtu.edu.cn

Corresponding author.

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Songhua Cao

School of Mechanical Engineering, Xi’an Jiaotong University, 28 Xianning West Road, Xi’an, Shaanxi 710049, China

E-mail Address: 1260816467@qq.com

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Dong Guan

School of Mechanical Engineering, Xi’an Jiaotong University, 28 Xianning West Road, Xi’an, Shaanxi 710049, China

E-mail Address: 1104894931@qq.com

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, and

Yanwei Zhu

Department of Mathematics and Information Sciences, Tangshan Normal University, Tangshan, Hebei 063000, China

E-mail Address: zhuyw79@163.com

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https://doi.org/10.1142/S0217984917502517Cited by:9 (Source: Crossref)

Abstract

In this paper, extremely low frequency band gaps of beam-like inertial amplification metamaterials are investigated based on local resonance theory. Inertial amplification mechanism is proposed to obtain extremely low frequency band gaps by altering geometry parameters of the beam-like structures rather than modulating material properties, which allow first lower band gap (BG) to be attained easily compared to traditional local resonance structures. Band structures, frequency response functions (FRFs) plots and vibration modes of the beam-like structures are calculated and analyzed by employing finite element method. Numerical results show that first BG of the structure ranges from 23 Hz to 21 Hz. FRFs are in accordance with the dispersion relationship. It is found that interaction between inertial amplification and traveling wave modes in the proposed structure are responsible for formation of the first BG. This type of beam-like inertial amplification metamaterials has many potential applications in the field of low frequency vibration and noise reduction.

Keywords:

References

1. L. Brillouin, Wave Propagation in Periodic Structures (McGraw-Hill, New York, 1946). Google Scholar
2. M. Sigalas and E. N. Economou, Solid State Commun. 86 (1993) 141. Web of Science, ADS, Google Scholar
3. M. S. Kushwaha, P. Halevi, G. Martinez, L. Dobrzynski and B. Djafari-Rouhani, Phys. Rev. B 49 (1994) 2313. Web of Science, ADS, Google Scholar
4. M. Kafesaki, M. M. Sigalas and E. N. Economou, Solid State Commun. 96 (1995) 285. Web of Science, ADS, Google Scholar
5. M. S. Kushwaha, Int. J. Mod. Phys. B 10 (1996) 977. Link, Web of Science, ADS, Google Scholar
6. I. E. Psarobas, N. Stefanou and A. Modinos, Phys. Rev. B 62 (2000) 278. Web of Science, ADS, Google Scholar
7. M. S. Kushwaha, B. Djafari-Rouhani, L. Dobrzynski and J. O. Vasseur, Eur. Phys. J. B 3 (1998) 155. Web of Science, ADS, Google Scholar
8. Z. Liu, C. T. Chan and P. Sheng, Phys. Rev. B 65 (2002) 165116. Web of Science, ADS, Google Scholar
9. Z. Liu, X. Zhang, Y. Mao, Y. Y. Zhu, Z. Yang, C. T. Chan and P. Sheng, Science 289 (2000) 1734. Web of Science, ADS, Google Scholar
10. C. Goffaux and J. Sanchez-Dehesa, Phys. Rev. B 67 (2003) 144301. Web of Science, ADS, Google Scholar
11. M. Hirsekorn, P. P. Delsanto, N. K. Batra and P. Matic, Ultrasonics 42 (2004) 231. Web of Science, Google Scholar
12. Z. Xu, F. Wu and Z. Guo, Phys. Lett. A 376 (2012) 2256. Web of Science, ADS, Google Scholar
13. C. C. Claeys, K. Vergote, P. Sas and W. Desmet, J. Sound Vib. 332 (2013) 1418. Web of Science, ADS, Google Scholar
14. X. Zhou and C. Chen, Phys. B: Condens. Matter 431 (2013) 23. Web of Science, ADS, Google Scholar
15. M. S. Kushwaha, B. Djafari-Rouhani and L. Dobrzynski, Phys. Lett. A 248 (1998) 252. Web of Science, ADS, Google Scholar
16. C. Yilmaz, G. M. Hulbert and N. Kikuchi, Phys. Rev. B 76 (2007) 054309. Web of Science, ADS, Google Scholar
17. C. Yilmaz and G. M. Hulbert, Phys. Lett. A 374 (2010) 3576. Web of Science, ADS, Google Scholar
18. S. Taniker and C. Yilmaz, Phys. Lett. A 377 (2013) 1930. Web of Science, ADS, Google Scholar
19. S. Taniker and C. Yilmaz, Int. J. Solids Struct. 72 (2015) 88. Web of Science, Google Scholar
20. S. Taniker and C. Yilmaz, Proc. ASME 2013 Int. Mechanical Engineering Congress and Exposition (San Diego, USA) 15–21 November 2013. Google Scholar
21. G. Acar and C. Yilmaz, J. Sound Vib. 332 (2013) 6389. Web of Science, ADS, Google Scholar
22. O. Yuksel and C. Yilmaz, J. Sound Vib. 355 (2015) 232. Web of Science, ADS, Google Scholar
23. O. Sigmund and J. S. Jensen, Philos. Trans. R. Soc. Lond. A: Math. Phys. Eng. Sci. 361 (2003) 1001. Web of Science, ADS, Google Scholar
24. S. Halkjær, O. Sigmund and J. S. Jensen, Struct. Multidiscip. O. 32 (2006) 263. Web of Science, Google Scholar
25. J. S. Jensen and N. L. Pedersen, J. Sound Vib. 289 (2006) 967. Web of Science, ADS, Google Scholar
26. O. R. Bilal and M. I. Hussein, Phys. Rev. E 84 (2011) 065701. Web of Science, ADS, Google Scholar
27. N. Olhoff, B. Niu and G. Cheng, Int. J. Solids Struct. 49 (2012) 3158. Web of Science, Google Scholar
28. H. Hashimoto, M.-G. Kim, K. Abe and S. Cho, J. Sound Vib. 332 (2013) 5283. Web of Science, ADS, Google Scholar
29. J. C. Hsu, J. Phys. D: Appl. Phys. 44 (2011) 05540. Google Scholar
30. M. Oudich, Y. Li, B. M. Assouar and Z. L. Hou, New J. Phys. 12 (2010) 083049. Web of Science, Google Scholar
31. H. B. Zhang, J. J. Chen and X. Han, J. Appl. Phys. 112 (2012) 054503. Web of Science, ADS, Google Scholar
32. Y. Cheng, X. J. Liu and D. J. Wu, J. Appl. Phys. 109 (2011) 064904. Web of Science, Google Scholar