Skip to main content

Advertisement

SpringerLink
Log in

A new circular-maze-shaped phononic crystal with multiband and broadband vibration filtration feature: design and experiment

  • Original Paper
  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

Here, the elastic wave dispersion characteristics of a new circular-maze-shaped (CMS) phononic crystal are numerically and experimentally investigated. A parametric study is performed on the critical parameters of the unit cell, and the geometry effects on bandgaps formation are discussed. Then, applying the genetic algorithm approach integrated with the FE method, the geometric parameters of the unit cell are fine-tuned and optimized based on three objective functions consisting of the lowest, widest, and maximum summation of bandgaps. It is found that this novel architected phononic crystal, with its unique CMS scheme, can provide multiple, broad, and mutable bandgaps in the frequency range of 0 to 10 kHz. Over the frequency range, about 8215 Hz bandgap summation and a low band frequency of 184 Hz with a 95% bandgap ratio are achieved for the optimized case studies. Subsequently, one of the optimized unit cells is employed to develop a two-dimensional meta-plate as a filter tool to attenuate the bending vibration transmission through the meta-plate. The dynamic frequency response functions of the meta-plate are numerically and experimentally investigated, and the results are correlated to the bandgap diagram attained from Bloch's theory. It is observed that the meta-plate structure is capable of confining the elastic waves inside the specified region and can remarkably attenuate the propagation of elastic waves.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

References

  1. Wang, Y.F., Wang, Y.Z., Wu, B., Chen, W., Wang, Y.S.: Tunable and active phononic crystals and metamaterials. Appl. Mech. Rev. (2020). https://doi.org/10.1115/1.4046222

    Article  Google Scholar 

  2. Vasileiadis, T., Varghese, J., Babacic, V., Gomis-Bresco, J., Navarro Urrios, D., Graczykowski, B.: Progress and perspectives on phononic crystals, (2021)

  3. Liu, J., Guo, H., Wang, T.: A review of acoustic metamaterials and phononic crystals, (2020)

  4. Patil, G.U., Matlack, K.H.: Review of exploiting nonlinearity in phononic materials to enable nonlinear wave responses, (2022)

  5. Ren, T., Liu, C., Li, F., Zhang, C.: Active tunability of band gaps for a novel elastic metamaterial plate. Acta Mech. (2020). https://doi.org/10.1007/s00707-020-02728-1

    Article  MathSciNet  MATH  Google Scholar 

  6. Gazonas, G.A., Weile, D.S., Wildman, R., Mohan, A.: Genetic algorithm optimization of phononic bandgap structures. Int. J. Solids Struct. (2006). https://doi.org/10.1016/j.ijsolstr.2005.12.002

    Article  MATH  Google Scholar 

  7. Muhammad, Lim, C.W.: Phononic metastructures with ultrawide low frequency three-dimensional bandgaps as broadband low frequency filter. Sci. Rep. (2021). https://doi.org/10.1038/s41598-021-86520-8

    Article  Google Scholar 

  8. D’Alessandro, L., Belloni, E., Ardito, R., Corigliano, A., Braghin, F.: Modeling and experimental verification of an ultra-wide bandgap in 3D phononic crystal. Appl. Phys. Lett. (2016). https://doi.org/10.1063/1.4971290

    Article  Google Scholar 

  9. Panahi, E., Hosseinkhani, A., Frangi, A., Younesian, D., Zega, V.: A novel low-frequency multi-bandgaps metaplate: Genetic algorithm based optimization and experimental validation. Mech. Syst. Signal Process. 181, 109495 (2022). https://doi.org/10.1016/J.YMSSP.2022.109495

    Article  Google Scholar 

  10. Zhang, G., Gao, Y.: Tunability of band gaps in two-dimensional phononic crystals with magnetorheological and electrorheological composites. Acta Mech. Solida Sin. (2021). https://doi.org/10.1007/s10338-020-00189-6

    Article  Google Scholar 

  11. Wu, Q., Huang, G., Liu, C., Xie, S., Xu, M.: Low-frequency multi-mode vibration suppression of a metastructure beam with two-stage high-static-low-dynamic stiffness oscillators. Acta Mech. (2019). https://doi.org/10.1007/s00707-019-02515-7

    Article  MathSciNet  MATH  Google Scholar 

  12. Wen, G., Ou, H., Liu, J.: Ultra-wide band gap in a two-dimensional phononic crystal with hexagonal lattices. Mater. Today Commun. (2020). https://doi.org/10.1016/j.mtcomm.2020.100977

    Article  Google Scholar 

  13. Zhang, G.Y., Shen, W., Gu, S.T., Gao, X.L., Xin, Z.Q.: Band gaps for elastic flexural wave propagation in periodic composite plate structures with star-shaped, transversely isotropic, magneto-electro-elastic inclusions. Acta Mech. (2021). https://doi.org/10.1007/s00707-021-03050-0

    Article  MathSciNet  MATH  Google Scholar 

  14. Vakilifard, M., Mahmoodi, M.J.: Effects of the nanofiller addition on the band gap and complex dispersion curve of phononic crystals. Acta Mech. (2021). https://doi.org/10.1007/s00707-021-02981-y

    Article  MATH  Google Scholar 

  15. Krushynska, A.O., Anerao, N., Badillo-Ávila, M.A., Stokroos, M., Acuautla, M.: Arbitrary-curved waveguiding and broadband attenuation in additively manufactured lattice phononic media. Mater. Des. (2021). https://doi.org/10.1016/j.matdes.2021.109714

    Article  Google Scholar 

  16. Wang, Y., Li, J., Fu, Y., Bao, R., Chen, W., Wang, Y.S.: Tunable guided waves in a soft phononic crystal with a line defect. APL Mater. (2021). https://doi.org/10.1063/5.0049574

    Article  Google Scholar 

  17. Du, Y., Wu, W., Chen, W., Lin, Y., Chi, Q.: Control the structure to optimize the performance of sound absorption of acoustic metamaterial: A review, (2021)

  18. Li, J., Yang, P., Ma, Q., Xia, M.: Complex band structure and attenuation performance of a viscoelastic phononic crystal with finite out-of-plane extension. Acta Mech. (2021). https://doi.org/10.1007/s00707-021-02969-8

    Article  MathSciNet  MATH  Google Scholar 

  19. Zaccherini, R., Colombi, A., Palermo, A., Dertimanis, V.K., Marzani, A., Thomsen, H.R., Stojadinovic, B., Chatzi, E.N.: Locally resonant metasurfaces for shear waves in granular media. Phys. Rev. Appl. (2020). https://doi.org/10.1103/PhysRevApplied.13.034055

    Article  Google Scholar 

  20. Liu, Z., Zhang, X., Mao, Y., Zhu, Y.Y., Yang, Z., Chan, C.T., Sheng, P.: Locally resonant sonic materials. Science (2000). https://doi.org/10.1126/science.289.5485.1734

    Article  Google Scholar 

  21. Sugino, C., Ruzzene, M., Erturk, A.: Merging mechanical and electromechanical bandgaps in locally resonant metamaterials and metastructures. J. Mech. Phys. Solids. (2018). https://doi.org/10.1016/j.jmps.2018.04.005

    Article  MathSciNet  Google Scholar 

  22. Krushynska, A.O., Kouznetsova, V.G., Geers, M.G.D.: Towards optimal design of locally resonant acoustic metamaterials. J. Mech. Phys. Solids. (2014). https://doi.org/10.1016/j.jmps.2014.07.004

    Article  Google Scholar 

  23. El-Borgi, S., Fernandes, R., Rajendran, P., Yazbeck, R., Boyd, J.G., Lagoudas, D.C.: Multiple bandgap formation in a locally resonant linear metamaterial beam: Theory and experiments. J. Sound Vib. (2020). https://doi.org/10.1016/j.jsv.2020.115647

    Article  Google Scholar 

  24. Hu, G., Austin, A.C.M., Sorokin, V., Tang, L.: Metamaterial beam with graded local resonators for broadband vibration suppression. Mech. Syst. Signal Process. (2021). https://doi.org/10.1016/j.ymssp.2020.106982

    Article  Google Scholar 

  25. Guo, J.C., Li, J.R., Zhang, Z.: Interface design of low-frequency band gap characteristics in stepped hybrid phononic crystals. Appl. Acoust. (2021). https://doi.org/10.1016/j.apacoust.2021.108209

    Article  Google Scholar 

  26. Hosseinkhani, A., Younesian, D., Ranjbar, M., Scarpa, F.: Enhancement of the vibro-acoustic performance of anti-tetra-chiral auxetic sandwich panels using topologically optimized local resonators. Appl. Acoust. (2021). https://doi.org/10.1016/j.apacoust.2021.107930

    Article  Google Scholar 

  27. Krushynska, A.O., Miniaci, M., Bosia, F., Pugno, N.M.: Coupling local resonance with Bragg band gaps in single-phase mechanical metamaterials. Extrem. Mech. Lett. (2017). https://doi.org/10.1016/j.eml.2016.10.004

    Article  Google Scholar 

  28. Sigalas, M., Economou, E.N.: Band structure of elastic waves in two dimensional systems. Solid State Commun. (1993). https://doi.org/10.1016/0038-1098(93)90888-T

    Article  Google Scholar 

  29. Martínez-Sala, R., Sancho, J., Sánchez, J.V., Gómez, V., Llinares, J., Meseguer, F.: Sound attenuation by sculpture. Nature (1995). https://doi.org/10.1038/378241a0

    Article  Google Scholar 

  30. Ruzzene, M., Scarpa, F., Soranna, F.: Wave beaming effects in two-dimensional cellular structures, (2003)

  31. Liu, X.N., Hu, G.K., Sun, C.T., Huang, G.L.: Wave propagation characterization and design of two-dimensional elastic chiral metacomposite. J. Sound Vib. (2011). https://doi.org/10.1016/j.jsv.2010.12.014

    Article  Google Scholar 

  32. Dong, H.W., Su, X.X., Wang, Y.S., Zhang, C.: Topological optimization of two-dimensional phononic crystals based on the finite element method and genetic algorithm. Struct. Multidiscip. Optim. (2014). https://doi.org/10.1007/s00158-014-1070-6

    Article  MathSciNet  Google Scholar 

  33. Chen, L., Guo, Y., Yi, H.: Optimization study of bandgaps properties for two-dimensional chiral phononic crystals based on lightweight design. Phys Lett. Sect. A Gen. At. Solid State Phys (2021). https://doi.org/10.1016/j.physleta.2020.127054

    Article  Google Scholar 

  34. Valencia, C., Restrepo, D., Mankame, N.D., Zavattieri, P.D., Gomez, J.: Computational characterization of the wave propagation behavior of multi-stable periodic cellular materials. Extrem. Mech. Lett. (2019). https://doi.org/10.1016/j.eml.2019.100565

    Article  Google Scholar 

  35. Yao, Z., Zhao, R., Zega, V., Corigliano, A.: A metaplate for complete 3D vibration isolation. Eur. J. Mech. A/Solids. (2020). https://doi.org/10.1016/j.euromechsol.2020.104016

    Article  MATH  Google Scholar 

  36. Zhao, P., Zhang, K., Deng, Z.: Elastic wave propagation in lattice metamaterials with Koch fractal. Acta Mech. Solida Sin. (2020). https://doi.org/10.1007/s10338-020-00177-w

    Article  Google Scholar 

  37. Yi, G., Youn, B.D.: A comprehensive survey on topology optimization of phononic crystals. Struct. Multidiscip. Optim. (2016). https://doi.org/10.1007/s00158-016-1520-4

    Article  MathSciNet  Google Scholar 

  38. Tang, H.W., Chou, W.D., Chen, L.W.: Wave propagation in the polymer-filled star-shaped honeycomb periodic structure. Appl. Phys. A Mater. Sci. Process. (2017). https://doi.org/10.1007/s00339-017-1124-x

    Article  Google Scholar 

  39. Meng, J., Deng, Z., Zhang, K., Xu, X., Wen, F.: Band gap analysis of star-shaped honeycombs with varied Poisson’s ratio. Smart Mater. Struct. (2015). https://doi.org/10.1088/0964-1726/24/9/095011

    Article  Google Scholar 

  40. Li, Y., Chen, T., Wang, X., Yu, K., Song, R.: Band structures in two-dimensional phononic crystals with periodic Jerusalem cross slot. Phys. B Condens. Matter. (2015). https://doi.org/10.1016/j.physb.2014.08.035

    Article  Google Scholar 

  41. Kumar, N., Pal, S.: Low frequency and wide band gap metamaterial with divergent shaped star units: Numerical and experimental investigations. Appl. Phys. Lett. (2019). https://doi.org/10.1063/1.5119754

    Article  Google Scholar 

  42. Kumar, N., Pal, S.: Unraveling interactions of resonances for tunable low frequency bandgap in multiphase metamaterials under applied deformation. Int. J. Solids Struct. (2021). https://doi.org/10.1016/j.ijsolstr.2020.11.032

    Article  Google Scholar 

  43. Timorian, S., Ouisse, M., Bouhaddi, N., De Rosa, S., Franco, F.: Numerical investigations and experimental measurements on the structural dynamic behaviour of quasi-periodic meta-materials. Mech. Syst. Signal Process. (2020). https://doi.org/10.1016/j.ymssp.2019.106516

    Article  Google Scholar 

  44. Chen, M., Xu, W., Liu, Y., Yan, K., Jiang, H., Wang, Y.: Band gap and double-negative properties of a star-structured sonic metamaterial. Appl. Acoust. (2018). https://doi.org/10.1016/j.apacoust.2018.04.035

    Article  Google Scholar 

  45. Qi, D., Yu, H., Hu, W., He, C., Wu, W., Ma, Y.: Bandgap and wave attenuation mechanisms of innovative reentrant and anti-chiral hybrid auxetic metastructure. Extrem. Mech. Lett. (2019). https://doi.org/10.1016/j.eml.2019.02.005

    Article  Google Scholar 

  46. Vadalà, F., Bacigalupo, A., Lepidi, M., Gambarotta, L.: Bloch wave filtering in tetrachiral materials via mechanical tuning. Compos. Struct. (2018). https://doi.org/10.1016/j.compstruct.2018.05.117

    Article  Google Scholar 

  47. Lepidi, M., Bacigalupo, A.: Multi-parametric sensitivity analysis of the band structure for tetrachiral acoustic metamaterials. Int. J. Solids Struct. (2018). https://doi.org/10.1016/j.ijsolstr.2017.12.014

    Article  MATH  Google Scholar 

  48. Gonella, S., Ruzzene, M.: Analysis of in-plane wave propagation in hexagonal and re-entrant lattices. J. Sound Vib. (2008). https://doi.org/10.1016/j.jsv.2007.10.033

    Article  MATH  Google Scholar 

  49. Koutsianitis, P.I., Tairidis, G.K., Drosopoulos, G.A., Stavroulakis, G.E.: Conventional and star-shaped auxetic materials for the creation of band gaps. Arch. Appl. Mech. (2019). https://doi.org/10.1007/s00419-019-01594-1

    Article  Google Scholar 

  50. Xiao, S.H., Zhang, C., Qin, Q.H., Wang, H.: A novel planar auxetic phononic crystal with periodic cookie-shaped cellular microstructures. Mech. Adv. Mater. Struct. (2021). https://doi.org/10.1080/15376494.2021.1896057

    Article  Google Scholar 

  51. Jiang, S., Hu, H., Laude, V.: Ultra-Wide Band Gap in Two-Dimensional Phononic Crystal with Combined Convex and Concave Holes, (2018)

  52. Gao, N., Qu, S., Si, L., Wang, J., Chen, W.: Broadband topological valley transport of elastic wave in reconfigurable phononic crystal plate. Appl. Phys. Lett. (2021). https://doi.org/10.1063/5.0036840

    Article  Google Scholar 

  53. De Pascalis, R., Donateo, T., Ficarella, A., Parnell, W.J.: Optimal design of phononic media through genetic algorithm-informed pre-stress for the control of antiplane wave propagation. Extrem. Mech. Lett. (2020). https://doi.org/10.1016/j.eml.2020.100896

    Article  Google Scholar 

  54. Muhammad, Lim, C.W., Li, J.T.H., Zhao, Z.: Lightweight architected lattice phononic crystals with broadband and multiband vibration mitigation characteristics. Extrem. Mech. Lett. (2020). https://doi.org/10.1016/j.eml.2020.100994

    Article  Google Scholar 

  55. Panahi, E., Hosseinkhani, A., Khansanami, M.F., Younesian, D., Ranjbar, M.: Novel cross shape phononic crystals with broadband vibration wave attenuation characteristic: design, modeling and testing. Thin-Walled Struct. (2021). https://doi.org/10.1016/j.tws.2021.107665

    Article  Google Scholar 

  56. Gasparetto, V.E.L., ElSayed, M.S.A.: Shape transformers for phononic band gaps tuning in two-dimensional Bloch-periodic lattice structures. Eur. J. Mech. A/Solids. (2021). https://doi.org/10.1016/j.euromechsol.2021.104278

    Article  MathSciNet  MATH  Google Scholar 

  57. Ruan, Y., Liang, X., Hua, X., Zhang, C., Xia, H., Li, C.: Isolating low-frequency vibration from power systems on a ship using spiral phononic crystals. Ocean Eng. (2021). https://doi.org/10.1016/j.oceaneng.2021.108804

    Article  Google Scholar 

  58. Cranford, S.W., Tarakanova, A., Pugno, N.M., Buehler, M.J.: Nonlinear material behaviour of spider silk yields robust webs, (2012)

  59. Aoyanagi, Y., Okumura, K.: Simple model for the mechanics of spider webs. Phys. Rev. Lett. 104, (2010). https://doi.org/10.1103/PhysRevLett.104.038102

  60. Miniaci, M., Krushynska, A., Movchan, A.B., Bosia, F., Pugno, N.M.: Spider web-inspired acoustic metamaterials. Appl. Phys. Lett. (2016). https://doi.org/10.1063/1.4961307

    Article  Google Scholar 

  61. Mironov, M.A.: Propagation of a flexural wave in a plate whose thickness decreases smoothly to zero in a finite interval. Sov. Phys. Acoust. 34, (1988)

  62. Laude, V.: Phononic Crystals. De Gruyter (2020)

  63. Genetic algorithms in search, optimization, and machine learning. Choice Rev. Online. 27, (1989). https://doi.org/10.5860/choice.27-0936

  64. Hedayatrasa, S.: Design Optimisation and Validation of Phononic Crystal Plates for Manipulation of Elastodynamic Guided Waves. (2018)

Download references

Author information

Authors and Affiliations

  1. School of Railway Engineering, Iran University of Science and Technology, Tehran, 16846-13114, Iran

    Emad Panahi, Ali Hosseinkhani, Davood Younesian & Armin Moayedizadeh

Authors
  1. Emad Panahi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ali Hosseinkhani
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Davood Younesian
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Armin Moayedizadeh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Davood Younesian.

Additional information

Publisher's Note

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

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Panahi, E., Hosseinkhani, A., Younesian, D. et al. A new circular-maze-shaped phononic crystal with multiband and broadband vibration filtration feature: design and experiment. Acta Mech 233, 4961–4983 (2022). https://doi.org/10.1007/s00707-022-03357-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-022-03357-6

Search

Navigation