Skip to main content
Log in

Mass inertia moment-based design of band gap characteristics in zigzag beam-supported stepped phononic crystals

  • Published:
Applied Physics A Aims and scope Submit manuscript

Abstract

The material properties and geometrical features are key factors determining the structural performance of phononic crystals (PnCs). The systematic analysis revealed that the mass inertia moment is the basic physical nature in the zigzag beam-supported stepped PnCs connecting the structural performance with the material properties and geometrical features in design. The designed PnCs were fabricated by laser powder bed fusion additive manufacturing. The band gap width of the zigzag beam-supported stepped PnCs is higher than the straight one due to the change of the mass inertia moment. The zigzag beam in the PnCs based on analysis of the mass inertia moment revealed the increase of the first band gap by 17.25 kHz, which is 60% larger than the initial design.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

Data availability

The raw/processed data required to reproduce these findings cannot be shared at this time because of technical or time limitations.

References

  1. M.S. Kushwaha, P. Halevi, G. Martinez, Theory of acoustic band structure of periodic elastic composites. Phys. Rev. B 49, 2313–2322 (1994)

    Article  ADS  Google Scholar 

  2. M. Maldovan, Sound and heat revolutions in phononics. Nature 503, 209–217 (2013)

    Article  ADS  Google Scholar 

  3. K. Wang, J.X. Zhou, D.L. Xu et al., Tunable low-frequency torsional-wave band gaps in a meta-shaft. J. Phys. D Appl. Phys. 52, 055104 (2019)

    Article  ADS  Google Scholar 

  4. W. Zhao, Y.F. Xu, Y.T. Yang et al., Multiband acoustic waveguides constructed by two-dimensional phononic crystals. Appl. Phys. Expr. 13, 094001 (2020)

    Article  ADS  Google Scholar 

  5. P.F. Ji, W.L. Hu, J. Yang, Development of an acoustic filter for parametric loudspeaker using phononic crystals. Ultrasonics 67, 160–167 (2016)

    Article  Google Scholar 

  6. X. Xiao, Z.C. He, E. Li et al., Design multi-stopband laminate acoustic metamaterials for structural-acoustic coupled system. Mech. Syst. Signal Process. 115, 418–433 (2019)

    Article  ADS  Google Scholar 

  7. Z.Y. Liu, X.X. Zhang, Y.W. Mao et al., Local resonant sonic materials. Science 289, 1734–1736 (2000)

    Article  ADS  Google Scholar 

  8. R. Zhu, X.N. Liu, G.K. Hu et al., Negative refraction of elastic waves at the deep-subwavelength scale in a single-phase metamaterial. Nat. Commun. 5, 5510 (2014)

    Article  ADS  Google Scholar 

  9. Y.F. Wang, Y.Z. Wang, B. Wu et al., Tunable and active phononic crystals and metamaterials. Appl. Mech. Rev. 72, 040801 (2020)

    Article  ADS  Google Scholar 

  10. O. Oltulu, A.M. Mamedov, E. Ozbay, Wave propagation and acoustic band gaps of two-dimensional liquid crystal/solid phononic crystals. Appl. Phys. A-Mater. Sci. Process. 123, 23 (2017)

    Article  ADS  Google Scholar 

  11. C. Li, L.C. Miao, Q. You et al., Effects of material parameters on the band gaps of two-dimensional three-component phononic crystals. Appl. Phys. A-Mater. Sci. Process. 125, 170 (2019)

    Article  ADS  Google Scholar 

  12. M. Wormser, F. Warmuth, C. Koerner, Evolution of full phononic band gaps in periodic cellular structures. Appl. Phys. A-Mater. Sci. Process. 123, 661 (2017)

    Article  ADS  Google Scholar 

  13. Y.F. Wang, Y.S. Wang, C.Z. Zhang, Bandgaps and directional propagation of elastic waves in 2D square zigzag lattice structures. J. Phys. D Appl. Phys. 47, 485102 (2014)

    Article  ADS  Google Scholar 

  14. Q.J. Lim, P. Wang, S.J.A. Koh et al., Wave propagation in fractal-inspired self-similar beam lattices. Appl. Phys. Lett. 107, 221911 (2015)

    Article  ADS  Google Scholar 

  15. Muhammad, C.W. Lim, J.T.H. Li, et al., Lightweight architected lattice phononic crystals with broadband and multiband vibration mitigation characteristics. Extr. Mech. Lett. 41 (2020) 100994

  16. S. Choi, Y.Y. Kim, Higher-order beam bending theory for static, free vibration, and buckling analysis of thin-walled rectangular hollow section beams. Comput. Struct. 248, 106494 (2021)

    Article  Google Scholar 

  17. W.J. Zhou, W.Q. Chen, Muhammad, et al., Surface effect on the propagation of flexural waves in periodic nano-beam and the size-dependent topological properties. Compos. Struct. 216, 427–435 (2019)

    Article  Google Scholar 

  18. W.J. Zhou, Muhammad, W.Q. Chen, et al., Actively controllable flexural wave band gaps in beam-type acoustic metamaterials with shunted piezoelectric patches. Eur. J. Mech. A Solids. 77 (2019) 103807

  19. X.K. Han, Z. Zhang, Acoustic beam controlling in water by the design of phononic crystal. Extr. Mech. Lett. 34, 100602 (2020)

    Article  Google Scholar 

  20. B. Ahn, H. Lee, J.S. Lee et al., Topology optimization of metasurfaces for anomalous reflection of longitudinal elastic waves. Comput. Methods Appl. Mech. Eng. 357, 112582 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  21. L.Y. Yao, D.H. Zhang, K. Xu et al., Topological phononic crystal plates with locally resonant elastic wave systems. Appl. Acoust. 177, 107931 (2021)

    Article  Google Scholar 

  22. C.C. Luo, S.W. Ning, Z.L. Liu et al., Interactive inverse design of layered phononic crystals based on reinforcement learning. Extr. Mech. Lett. 36, 100651 (2020)

    Article  Google Scholar 

  23. Y.F. Chen, F. Meng, X.D. Huang, Creating acoustic topological insulators through topology optimization. Mech. Syst. Signal Process. 146, 107054 (2021)

    Article  Google Scholar 

  24. H.W. Dong, S.D. Zhao, P.J. Wei et al., Systematic design and realization of double-negative acoustic metamaterials by topology optimization. Acta Mater. 172, 102–120 (2019)

    Article  ADS  Google Scholar 

  25. X.K. Han, Z. Zhang, Topological optimization of phononic crystal thin plate by a genetic algorithm. Sci. Rep. 9, 8331 (2019)

    Article  ADS  Google Scholar 

  26. O.R. Bilal, M.I. Hussein, Ultrawide phononic band gap for combined in-plane and out-of-plane waves. Phys. Rev. E 84, 065701 (2011)

    Article  ADS  Google Scholar 

  27. Y.F. Li, X.D. Huang, F. Meng et al., Evolutionary topological design for phononic band gap crystals. Struct. Multidiscip. Optim. 54, 595–617 (2016)

    Article  MathSciNet  Google Scholar 

  28. Y. Lu, Y. Yang, J.K. Guest et al., 3-D phononic crystals with ultra-wide band gaps. Sci. Rep. 7, 43407 (2017)

    Article  ADS  Google Scholar 

  29. E. Li, Z.C. He, G. Wang et al., An efficient algorithm to analyze wave propagation in fluid/solid and solid/fluid phononic crystals. Comput. Methods Appl. Mech. Eng. 333, 421–442 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  30. J. Kennedy, R. Eberhart, Particle swarm optimization, IEEE international conference on neural networks proceeding. 1-6 (1995) 1942–1948

  31. W. Elmadih, D. Chronopoulos, W.P. Syam et al., Three-dimensional resonating metamaterials for low-frequency vibration attenuation. Sci. Rep. 9, 11503 (2019)

    Article  ADS  Google Scholar 

  32. M. Lei, W. Hong, Z.A. Zhao et al., 3D printing of auxetic metamaterials with digitally reprogrammable shape. ACS Appl. Mater. Interfaces. 11, 22768–22776 (2019)

    Article  Google Scholar 

  33. D. Beli, J.R.F. Arruda, M. Ruzzene, Wave propagation in elastic metamaterial beams and plates with interconnected resonators. Int. J. Solids Struct. 139, 105–120 (2018)

    Article  Google Scholar 

  34. A. Kruisova, M. Sevcik, H. Seiner et al., Ultrasonic bandgaps in 3D-printed periodic ceramic microlattices. Ultrasonics 82, 91–100 (2018)

    Article  Google Scholar 

  35. M.I. Hussein, M.J. Leamy, M. Ruzzene, Dynamics of phononic materials and structures: historical origins. Recent Prog. Future Outlook Appl. Mech. Rev. 66, 040802 (2014)

    Google Scholar 

  36. Muhammad, C.W. Lim, From photonic crystals to seismic metamaterials: a review via phononic crystals and acoustic metamaterials, Archiv. Comput. Methods Eng. https://doi.org/10.1007/s11831-021-09612-8

  37. J. Cao, M.A. Gharghouri, P. Nash, Finite-element analysis and experimental validation of thermal residual stress and distortion in electron beam additive manufactured Ti-6Al-4V build plates. J. Mater. Process. Technol. 237, 409–419 (2016)

    Article  Google Scholar 

  38. S.Y. Liu, Y.C. Shin, Additive manufacturing of Ti6Al4V alloy: a review. Mater. Des. 164, 107552 (2019)

    Article  Google Scholar 

  39. L.Y. Chen, J.Q. Xu, H. Choi et al., Processing and properties of magnesium containing a dense uniform dispersion of nanoparticles. Nature 528, 539–543 (2015)

    Article  ADS  Google Scholar 

  40. J.C. Guo, J.R. Li, Z. Zhang, Interface design of low-frequency band gap characteristics in stepped hybrid phononic crystals. Appl. Acoust. 182, 108209 (2021)

    Article  Google Scholar 

  41. Y.F. Wang, Y.S. Wang, Complete bandgap in three-dimensional holey phononic crystals with resonators. J. Vibr. Acoust. Trans. ASME 135, 041009 (2013)

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by Liaoning Provincial Natural Science Foundation (2019-KF-05-07).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Z. Zhang.

Ethics declarations

Conflict of interest

The authors declare that they have no conflicts of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Guo, J.C., Zhang, Z. Mass inertia moment-based design of band gap characteristics in zigzag beam-supported stepped phononic crystals. Appl. Phys. A 128, 126 (2022). https://doi.org/10.1007/s00339-022-05267-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00339-022-05267-9

Keywords

Navigation