Skip to main content
SpringerLink
Log in

An improved method for unidirectional mechanical wave propagation in a metamaterial beam

  • Published:
Applied Physics A Aims and scope Submit manuscript

Abstract

Recent attention has been drawn to breaking reciprocity due to its astounding applications. Metamaterials can be utilized to break the time-reversal symmetry of a system. This paper investigates the theoretical propagation of waves in a space–time modulating medium and presents a novel Fourier series expansion for avoiding flat wave method barriers. The acquired results are validated by comparing them to those reported in the literature and the simulation results in COMSOL commercial software. Additionally, a theoretical function is created to discuss the effect of various parameters on the position and bandwidth of bandgaps. The plane wave expansion (PWE) approach is incapable of predicting the higher-mode bandgaps. In contrast, the proposed technique accurately detects a bandgap, as demonstrated by FEM results. On the other hand, it is demonstrated that the convergence rate of the presented method is significantly higher than that of the PWE method and decreases the computation time appropriately, indicating that this method is more accurate and reliable than the traditional PWE method, particularly in predicting the higher-mode bandgaps. The findings of this study could be utilized for intelligent periodic structures that use piezoelectricity to regulate wave propagation.

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

Similar content being viewed by others

References

  1. S. Deep, V. Sharma, Love wave propagation in viscoelastic layer sandwiched between fiber-reinforced layer and consistent couple stress substrate. Iran J. Sci. Technol. Trans. Mech. Eng. 46, 225–235 (2022). https://doi.org/10.1007/s40997-020-00411-3

    Article  Google Scholar 

  2. A. Yavari, M.H. Abolbashari, Generalized thermoelastic waves propagation in non-uniform rational B-spline rods under quadratic thermal shock loading using isogeometric approach. Iran J. Sci. Technol. Trans. Mech. Eng. 46, 43–59 (2022). https://doi.org/10.1007/s40997-020-00391-4

    Article  Google Scholar 

  3. S.A. Faghidian, A. Tounsi, Dynamic characteristics of mixture unified gradient elastic nanobeams. Facta Univ. Ser. Mech. Eng. 20(3), 539–552 (2022)

    Google Scholar 

  4. P.A. Radchenko, S.P. Batuev, A.V. Radchenko, Numerical analysis of concrete fracture under shock wave loading. Phys. Mesomech. 24, 40–45 (2021). https://doi.org/10.1134/S1029959921010069

    Article  MATH  Google Scholar 

  5. D. Kurhan, S. Fischer, Modeling of the dynamic rail deflection using elastic wave propagation. J. Appl. Comput. Mech. 8(1), 379–387 (2022). https://doi.org/10.22055/jacm.2021.38826.3290

    Article  Google Scholar 

  6. A. Singhal, S.A. Sahu, S. Chaudhary, M. Sultana, Scattering and backscattering study of mechanical plane wave in composite materials plates (Earth model 1066B and LiNbO3). J. Appl. Comput. Mech. 8(2), 518–527 (2022). https://doi.org/10.22055/jacm.2020.30804.1784

    Article  Google Scholar 

  7. A.H. Shirazi, H.M. Sedighi, Physics of rack-and-pinion-inspired metamaterials with rotational resonators for broadband vibration suppression. Eur. Phys. J. Plus 135, 1–23 (2020)

    Article  Google Scholar 

  8. C. Rasmussen, L. Quan, A. Alù, Acoustic nonreciprocity. J. Appl. Phys. 129(21), 1–12 (2021)

    Article  Google Scholar 

  9. X. Zhang, M. Xiao, Y. Cheng et al., Topological sound. Commun. Phys. 1, 97 (2018)

    Article  Google Scholar 

  10. R. Fleury, D.L. Sounas, C.F. Sieck, M.R. Haberman, A. Alù, Sound isolation and giant linear nonreciprocity in an acoustic circulator. Science 343(6170), 516–519 (2014)

    Article  ADS  Google Scholar 

  11. X. Xu, M.V. Barnhart, X. Fang, J. Wen, Y. Chen, G. Huang, A nonlinear dissipative elastic metamaterial for broadband wave mitigation. Int. J. Mech. Sci. 164(July), 105159 (2019)

    Article  Google Scholar 

  12. Y. Xia, M. Ruzzene, A. Erturk, Dramatic bandwidth enhancement in nonlinear metastructures via bistable attachments. Appl. Phys. Lett. 114(9), 093501 (2019)

    Article  ADS  Google Scholar 

  13. Y. Chen, X. Li, H. Nassar, A.N. Norris, C. Daraio, G. Huang, Nonreciprocal wave propagation in a continuum-based metamaterial with space-time modulated resonators. Phys. Rev. Appl. 11(6), 1 (2019)

    Article  Google Scholar 

  14. H. Nassar, X.C. Xu, A.N. Norris, G.L. Huang, Modulated phononic crystals: nonreciprocal wave propagation and Willis materials. J. Mech. Phys. Solids 101, 10–29 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  15. K. Yi, S. Karkar, M. Collet, K. Yi, S. Karkar, M. Collet, One-way energy insulation using time-space modulated structures 0–22 (2021).

  16. Cellulose nanocrystal-derived hollow mesoporous carbon spheres and their application as a metal-free catalyst. Nanotechnology 0–22 (2019).

  17. A. Valipour, M.H. Kargozarfard, M. Rakhshi, A. Yaghootian, H.M. Sedighi, Metamaterials and their applications: an overview. Proc. Inst. Mech. Eng. Part L J. Mater. Des. Appl. 236, 2171–2210 (2021)

    Google Scholar 

  18. C. Croënne, J.O. Vasseur, O. BouMatar, M.F. Ponge, P.A. Deymier, A.C. Hladky-Hennion, B. Dubus, Brillouin scattering-like effect and nonreciprocal propagation of elastic waves due to spatio-temporal modulation of electrical boundary conditions in piezoelectric media. Appl. Phys. Lett. 110(6), 061901 (2017)

    Article  ADS  Google Scholar 

  19. M. Brandenbourger, X. Locsin, E. Lerner, C. Coulais, Non-reciprocal robotic metamaterials. Nat. Commun. 10(1), 4608 (2019)

    Article  ADS  Google Scholar 

  20. Y. Xia, E. Riva, M.I.N. Rosa, G. Cazzulani, A. Erturk, F. Braghin, M. Ruzzene, Experimental observation of temporal pumping in electromechanical wave-guides. Phys. Rev. Lett. (2021). https://doi.org/10.1103/PhysRevLett.126.095501

    Article  Google Scholar 

  21. B.M. Goldsberry, S.P. Wallen, M.R. Haberman, Nonreciprocal Longitudinal vibrations of finite elastic structures with spatiotemporally modulated properties, in 2020 Fourteenth International Congress on Artificial Materials for Novel Wave Phenomena (Metamaterials) (IEEE, 2020). p. 391–393.

  22. C. Sugino, M. Ruzzene, A. Erturk, Nonreciprocal piezoelectric metamaterial framework and circuit strategies. Phys. Rev. B 102(1), 014304 (2020)

    Article  ADS  Google Scholar 

  23. M. Zanjani, A. Davoyan, N. Engheta, NEMS with broken t symmetry: graphene based unidirectional acoustic transmission lines. Sci. Rep. 5, 9926 (2015)

    Article  ADS  Google Scholar 

  24. C. Olivier, A. Maddi, G. Poignand, G. Penelet, Asymmetric transmission and coherent perfect absorption in a periodic array of thermoacoustic cells. J. Appl. Phys. 131(24), 244701 (2022)

    Article  ADS  Google Scholar 

  25. H. Nassar, H. Chen, A.N. Norris, G.L. Huang, Nonreciprocal flexural wave propagation in a modulated metabeam. Extreme Mech. Lett. 15, 97–102 (2017)

    Article  Google Scholar 

  26. H. Nassar, H. Chen, A.N. Norris, M.R. Haberman, G.L. Huang, Nonreciprocal wave propagation in modulated elastic metamaterials. Proc. R. Soc. A Math. Phys. Eng. Sci. 473(2202), 20170188 (2017)

    ADS  MATH  Google Scholar 

  27. G. Trainiti, Y. Xia, J. Marconi, G. Cazzulani, A. Erturk, M. Ruzzene, Time-periodic stiffness modulation in elastic metamaterials for selective wave filtering: theory and experiment. Phys. Rev. Lett. 122(12), 1–6 (2019)

    Article  Google Scholar 

  28. G. Trainiti, M. Ruzzene, Nonreciprocal elastic wave propagation in spatiotemporal periodic structures. New J. Phys. 18(8), 1–22 (2016)

    Article  Google Scholar 

  29. Y. Wang, B. Yousefzadeh, H. Chen, H. Nassar, G. Huang, C. Daraio, Observation of nonreciprocal wave propagation in a dynamic phononic lattice. Phys. Rev. Lett. 121(19), 194301 (2018)

    Article  ADS  Google Scholar 

  30. J. Li, C. Shen, X. Zhu, Y. Xie, S.A. Cummer, Nonreciprocal sound propagation in space-time modulated media. Phys. Rev. B 99(14), 144311 (2019)

    Article  ADS  Google Scholar 

  31. M.A. Attarzadeh, M. Nouh, Elastic wave propagation in moving phononic crystals and correlations with stationary spatiotemporally modulated systems. AIP Adv. 8(10), 105302 (2018)

    Article  ADS  Google Scholar 

  32. B.M. Goldsberry, S.P. Wallen, M.R. Haberman, Nonreciprocal vibrations of finite elastic structures with spatiotemporally modulated material properties. Phys. Rev. B 102(1), 1–9 (2020)

    Article  Google Scholar 

  33. E. Riva, J. Marconi, G. Cazzulani, F. Braghin, Generalized plane wave expansion method for nonreciprocal discretely modulated wave-guides. J. Sound Vib. 449, 172–181 (2019)

    Article  ADS  Google Scholar 

  34. V.F.D. Poggetto, A.L. Serpa, Elastic wave band gaps in a three-dimensional periodic metamaterial using the plane wave expansion method. Int. J. Mech. Sci. 184(April), 105841 (2020)

    Article  Google Scholar 

  35. M. Oudich, N. J. Gerard, Y. Deng, Y. Jing, Tailoring Structure-borne sound through bandgap engineering in phononic crystals and metamaterials: a comprehensive review. 1–57 (2022).

  36. P. Wang, H. Liu, Voltage-dependent modulation of effective Young’ s modulus and shape in piezoelectric composite metamaterials. 306 (2023)

  37. J. Xu, H. Lu, W. Qin, P. Wang, J. Bian, Mechanical shunt resonators-based piezoelectric metamaterial for elastic wave attenuation. Materials 15(3), 891 (2022)

    Article  ADS  Google Scholar 

  38. F. Aloschi, A. Marzani, A. Palermo, Dispersion analysis of periodic structure performing experimental floqute-bloch condition to the unit-cell. 1–4 (2020).

  39. S. Soni, N. Aggarwal, A. Doegar, A review on acoustic metamaterial (2019).

  40. A. Ben, S. Brugiapaglia, C.G. Webster, Methods in computational science. Chapter 10, Section 8, p. 259 (2022).

  41. A. Yadav, G. Burak, A. Ahmadivand, A. Kaushik, G.J. Cheng, Z. Ouyang, Q. Wang, V.S. Yadav, Y.K. Mishra, Y. Wu, Y. Liu, S. RamaKrishna, Controlled self-assembly of plasmon-based photonic nanocrystals for high performance photonic technologies. Nano Today 37, 101072 (2021)

    Article  Google Scholar 

Download references

Funding

H.M. Sedighi is grateful to the Research Council of Shahid Chamran University of Ahvaz for its financial support (Grant no. SCU.EM1401.98).

Author information

Authors and Affiliations

  1. Mechanical Engineering Department, Faculty of Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran

    Mohammad Hassan Kargozarfard, Hamid M. Sedighi, Amin Yaghootian & Ali Valipour

  2. Drilling Center of Excellence and Research Center, Shahid Chamran University of Ahvaz, Ahvaz, Iran

    Hamid M. Sedighi

Authors
  1. Mohammad Hassan Kargozarfard
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hamid M. Sedighi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Amin Yaghootian
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ali Valipour
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hamid M. Sedighi.

Ethics declarations

Conflict of interest

The authors declared no potential conflicts of interest concerning the research, authorship, and publication of this article.

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 (e.g. a society or other partner) 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

Kargozarfard, M.H., Sedighi, H.M., Yaghootian, A. et al. An improved method for unidirectional mechanical wave propagation in a metamaterial beam. Appl. Phys. A 129, 296 (2023). https://doi.org/10.1007/s00339-023-06567-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00339-023-06567-4

Keywords

Search

Navigation