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Low-frequency multi-mode vibration suppression of a metastructure beam with two-stage high-static-low-dynamic stiffness oscillators

  • Qichen Wu
  • Gangting Huang
  • Chong Liu
  • Shilin XieEmail author
  • Minglong Xu
Original Paper
  • 27 Downloads

Abstract

Metastructures with periodic local resonators are effective in attenuating waves in a special frequency range due to their band gap properties. A low-frequency multi-mode resonator based on a two-stage high-static-low-dynamic stiffness oscillator is proposed in this paper to create multiple low-frequency band gaps of flexural waves in a metastructure beam. The theoretical models of infinite and finite metastructure beams are established, respectively. The band structures obtained by the plane wave expansion method are thereafter verified by the mode superstition method. This demonstrates such metastructure features with multiple low-frequency band gaps. Multiple band gaps property is discussed, and a dynamic analysis of a simplified cell shows that locations of band gaps are determined by the natural frequencies of the resonator, which can be adjusted by configuring the physical parameters of the oscillators. The influence of mass ratio and damping on band gaps is numerically analysed, and the results show that mass ratio has an optimal value and damping can suppress the resonance effectively. Finally, a case study is performed, and the results show that the proposed metastructure has good performance in vibration suppression both around concerned multiple low-frequency modes and high-frequency range. The general design procedure of a metastructure beam is also summarized.

Notes

Acknowledgements

This work is supported by National Natural Science Foundation of China (Grant No. 11872290) and NSAF (Grant No. U1430129).

References

  1. 1.
    Sigalas, M.M., Economou, E.N.: Elastic and acoustic wave band structure. J. Sound Vibr. 158(2), 377–382 (1992)CrossRefGoogle Scholar
  2. 2.
    Kushwaha, M.S., Halevi, P., Dobrzynski, L., et al.: Acoustic band structure of periodic elastic composites. Phys. Rev. Lett. 71(13), 2022–2025 (1993)CrossRefGoogle Scholar
  3. 3.
    Mead, D.M.: Wave propagation in continuous periodic structures: research contributions from Southampton, 1964–1995. J. Sound Vibr. 190(3), 495–524 (1996)CrossRefGoogle Scholar
  4. 4.
    Liu, Z., Zhang, X., Mao, Y., et al.: Locally resonant sonic materials. Science 289(5485), 1734 (2000)CrossRefGoogle Scholar
  5. 5.
    Hussein, M.I., Leamy, M.J., Ruzzene, M.: Dynamics of phononic materials and structures: historical origins, recent progress, and future outlook. Appl. Mech. Rev. 66(4), 040802-040802-38 (2014)Google Scholar
  6. 6.
    Lan, M., Wei, P.: Band gap of piezoelectric/piezomagnetic phononic crystal with graded interlayer. Acta Mech. 225(6), 1779–1794 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Milton, G.W., Willis, J.R.: On modifications of Newton’s second law and linear continuum elastodynamics. Proc. R. Soc. A Math. Phys. Eng. Sci. 463(2079), 855 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Mei, J., Ma, G., Yang, M., et al.: Dark acoustic metamaterials as super absorbers for low-frequency sound. Nat. Commun. 3, 756 (2012)CrossRefGoogle Scholar
  9. 9.
    Fang, N., Xi, D., Xu, J., et al.: Ultrasonic metamaterials with negative modulus. Nat. Mater. 5, 452 (2006)CrossRefGoogle Scholar
  10. 10.
    Sam Hyeon, L., Choon Mahn, P., Yong Mun, S., et al.: Acoustic metamaterial with negative modulus. J. Phys. Condens. Matter 21(17), 175704 (2009)CrossRefGoogle Scholar
  11. 11.
    Brunet, T., Merlin, A., Mascaro, B., et al.: Soft 3D acoustic metamaterial with negative index. Nat. Mater. 14, 384 (2014)CrossRefGoogle Scholar
  12. 12.
    Wu, Y., Lai, Y., Zhang, Z.-Q.: Elastic metamaterials with simultaneously negative effective shear modulus and mass density. Phys. Rev. Lett. 107(10), 105506 (2011)CrossRefGoogle Scholar
  13. 13.
    Lee, S.H., Park, C.M., Seo, Y.M., et al.: Composite acoustic medium with simultaneously negative density and modulus. Phys. Rev. Lett. 104(5), 054301 (2010)CrossRefGoogle Scholar
  14. 14.
    Yu, D., Liu, Y., Zhao, H., et al.: Flexural vibration band gaps in Euler–Bernoulli beams with locally resonant structures with two degrees of freedom. Phys. Rev. B 73(6), 064301 (2006)CrossRefGoogle Scholar
  15. 15.
    Xiao, Y., Wen, J., Wang, G., et al.: Theoretical and experimental study of locally resonant and Bragg band gaps in flexural beams carrying periodic arrays of beam-like resonators. J. Vibr. Acoust. 135(4), 041006-041006-17 (2013)CrossRefGoogle Scholar
  16. 16.
    Sugino, C., Ruzzene, M., Erturk, A.: Design and analysis of piezoelectric metamaterial beams with synthetic impedance shunt circuits. IEEE/ASME Trans. on Mechatronics 23(5), 2144–2155 (2018)CrossRefGoogle Scholar
  17. 17.
    Pai, P.F., Peng, H., Jiang, S.: Acoustic metamaterial beams based on multi-frequency vibration absorbers. Int. J. Mech. Sci. 79, 195–205 (2014)CrossRefGoogle Scholar
  18. 18.
    Ma, J., Sheng, M., Guo, Z., et al.: Dynamic analysis of periodic vibration suppressors with multiple secondary oscillators. J. Sound Vibr. 424, 94–111 (2018)CrossRefGoogle Scholar
  19. 19.
    Fang, X., Wen, J., Yin, J., et al.: Broadband and tunable one-dimensional strongly nonlinear acoustic metamaterials: theoretical study. Phys. Rev. E 94, 1 (2016)Google Scholar
  20. 20.
    Chen, Y.Y., Huang, G.L.: Active elastic metamaterials for subwavelength wave propagation control. Acta Mech. Sinica 31(3), 349–363 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Cao, Q., Wiercigroch, M., Pavlovskaia, E.E., et al.: Archetypal oscillator for smooth and discontinuous dynamics. Phys. Rev. E 74(4), 046218 (2006)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Carrella, A., Brennan, M.J., Waters, T.P.: Static analysis of a passive vibration isolator with quasi-zero-stiffness characteristic. J. Sound Vibr. 301(3), 678–689 (2007)CrossRefGoogle Scholar
  23. 23.
    Zhou, J., Wang, K., Xu, D., et al.: Local resonator with high-static-low-dynamic stiffness for lowering band gaps of flexural wave in beams. J. Appl. Phys. 121(4), 044902 (2017)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  • Qichen Wu
    • 1
    • 2
  • Gangting Huang
    • 1
    • 2
  • Chong Liu
    • 1
    • 2
  • Shilin Xie
    • 1
    • 2
    Email author
  • Minglong Xu
    • 1
    • 2
  1. 1.State Key Laboratory for Strength and Vibration of Mechanical StructuresXi’an Jiaotong UniversityXi’anChina
  2. 2.School of Aerospace EngineeringXi’an Jiaotong UniversityXi’anChina

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