SpringerLink
Log in

Dynamic phononic crystals with spatially and temporally modulated circuit networks

受时空调制电网控制的动态声子晶体

  • Research Paper
  • Published:
Acta Mechanica Sinica Aims and scope Submit manuscript

Abstract

Elastic wave mitigation covering multiple broad bands is highly demanded for modern applications in wave control. Here, we report both theoretically and experimentally on the complete investigation of a series of dynamic phononic crystal beams integrated with circuit networks decorated with both spatial and temporal modulation. They are capable of practicing multi-band flexural wave mitigation with convenient tunability and broadband operability. The electromechanical interaction through piezoelectric shunts allows for energy exchange between electrical and mechanical modes and gives rise to Bragg forbidden bands. The key contribution of this work lies in the inclusion of spatial and temporal modulation that is applied solely in circuit networks and improves wave mitigation abilities in terms of operable frequency range. Specifically, the spatial modulation of circuit network effectively broadens the wave attenuation band by creating space-Bragg forbidden bands for electrical modes and thus extending the electromechanical coupling range. The temporal modulation, on the other hand, generates time-Bragg band gaps by linearly translating the fundamental electromechanical mode in terms of frequency. More importantly, both seemingly complicated approaches are simply based on the convenient tuning of a single resistor in the circuit network. This advantage later facilitates the experimental evidences of the transmission characteristics of the spatially and temporally modulated configurations. We believe the dynamic phononic crystals are highly promising for the next-generation applications such as tunable multi-band filters.

摘要

宽频弹性波衰减技术在现代工程应用中有不可或缺的地位. 本文提出了一种基于时间/空间调制电网和压电材料的动态声子 晶体并进行了实验验证. 该动态声子晶体可以在多频带上实现对弯曲波传输的衰减, 并对衰减频带进行调控. 压电分流电路为机械模 态和电模态提供了能 量 交换的同时也产生了布拉格带隙. 该动态声子晶体仅需对电网进行时间/空间调制以实现可调制的宽频带弯曲 波衰减. 其中, 通过对电网进行空间调制可实现两条布拉格带隙从而扩大了机电耦合以及弯曲波衰减的频率范围. 另一方面, 时间调制 使机电耦合的模态频率产生线性**移从而生成了多条时间-布拉格带隙. 更重要的是, 本文提供了一种简易的弯曲波带隙调谐方式, 即 只对单一电阻进行控制. 相关实验也进一步验证了时间/空间调制对弯曲波传输的影响. 该动态声子晶体可以为下一代可调谐的多频带 滤波器等设备提供新思路.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Institutional subscriptions

References

  1. J. J. Hollkamp, Multimodal passive vibration suppression with piezoelectric materials and resonant shunts, J. Intell. Mater. Syst. Struct. 5, 49 (1994).

    Article  Google Scholar 

  2. B. S. Beck, K. A. Cunefare, M. Ruzzene, and M. Collet, Experimental analysis of a cantilever beam with a shunted piezoelectric periodic array, J. Intell. Mater. Syst. Struct. 22, 1177 (2011).

    Article  Google Scholar 

  3. A. Spadoni, M. Ruzzene, and K. Cunefare, Vibration and wave propagation control of plates with periodic arrays of shunted piezoelectric patches, J. Intell. Mater. Syst. Struct. 20, 979 (2009).

    Article  Google Scholar 

  4. L. Brillouin, Wave Propagation in Periodic Structures: Electric Filters and Crystal Lattices, 2nd ed. (McGraw-Hill Book Company, Dover, 1946).

    MATH  Google Scholar 

  5. X. Zhou, and G. Hu, Analytic model of elastic metamaterials with local resonances, Phys. Rev. B 79, 195109 (2009).

    Article  Google Scholar 

  6. G. Ma, and P. Sheng, Acoustic metamaterials: From local resonances to broad horizons, Sci. Adv. 2, e1501595 (2016).

    Article  Google Scholar 

  7. Z. Liu, X. Zhang, Y. Mao, Y. Y. Zhu, Z. Yang, C. T. Chan, and P. Sheng, Locally resonant sonic materials, Science 289, 1734 (2000).

    Article  Google Scholar 

  8. M. Nouh, O. Aldraihem, and A. Baz, Wave propagation in metamaterial plates with periodic local resonances, J. Sound Vib. 341, 53 (2015).

    Article  Google Scholar 

  9. Y. Lai, Y. Wu, P. Sheng, and Z. Q. Zhang, Hybrid elastic solids, Nat. Mater 10, 620 (2011).

    Article  Google Scholar 

  10. V. Laude, Phononic Crystals: Artificial Crystals for Sonic, Acoustic, and Elastic Waves (Walter de Gruyter GmbH & Co KG, Berlin, 2015).

    Book  MATH  Google Scholar 

  11. H. Zhao, Y. Liu, G. Wang, J. Wen, D. Yu, X. Han, and X. Wen, Resonance modes and gap formation in a two-dimensional solid phononic crystal, Phys. Rev. B 72, 012301 (2005).

    Article  Google Scholar 

  12. Y. **, N. Fernez, Y. Pennec, B. Bonello, R. P. Moiseyenko, S. Hémon, Y. Pan, and B. Djafari-Rouhani, Tunable waveguide and cavity in a phononic crystal plate by controlling whispering-gallery modes in hollow pillars, Phys. Rev. B 93, 054109 (2016).

    Article  Google Scholar 

  13. D. Yu, J. Wen, H. Zhao, Y. Liu, and X. Wen, Vibration reduction by using the idea of phononic crystals in a pipe-conveying fluid, J. Sound Vib. 318, 193 (2008).

    Article  Google Scholar 

  14. M. H. Lu, L. Feng, and Y. F. Chen, Phononic crystals and acoustic metamaterials, Mater. Today 12, 34 (2009).

    Article  Google Scholar 

  15. C. P. Wei, and C. X. Xue, Bending waves of a rectangular piezoelectric laminated beam, Acta Mech. Sin. 36, 1099 (2020).

    Article  MathSciNet  Google Scholar 

  16. G. Wang, S. Chen, and J. Wen, Low-frequency locally resonant band gaps induced by arrays of resonant shunts with Antoniou’s circuit: Experimental investigation on beams, Smart Mater. Struct. 20, 015026 (2010).

    Article  Google Scholar 

  17. J. A. B. Gripp, and D. A. Rade, Vibration and noise control using shunted piezoelectric transducers: A review, Mech. Syst. Signal Process. 112, 359 (2018).

    Article  Google Scholar 

  18. Y. Wang, C. Zhang, W. Chen, Z. Li, M. V. Golub, and S. I. Fomenko, Precise and target-oriented control of the low-frequency Lamb wave bandgaps, J. Sound Vib. 511, 116367 (2021).

    Article  Google Scholar 

  19. B. Hu, J. Liu, Y. Wang, B. Zhang, and H. Shen, Wave propagation in graphene reinforced piezoelectric sandwich nanoplates via high-order nonlocal strain gradient theory, Acta Mech. Sin. 37, 1446 (2021).

    Article  MathSciNet  Google Scholar 

  20. Y. Wang, Z. Li, W. Chen, C. Zhang, and J. Zhu, Free vibration and active control of pre-stretched multilayered electroactive plates, Int. J. Solids Struct. 180–181, 108 (2019).

    Article  Google Scholar 

  21. Z. Y. Li, Y. Z. Wang, T. X. Ma, Y. F. Zheng, C. Zhang, and F. M. Li, A self-sensing and self-actuating metamaterial sandwich structure for the low-frequency vibration mitigation and isolation, Compos. Struct. 297, 115894 (2022).

    Article  Google Scholar 

  22. R. **a, J. Yi, Z. Chen, and Z. Li, In situ steering of shear horizontal waves in a plate by a tunable electromechanical resonant elastic meta-surface, J. Phys. D-Appl. Phys. 53, 095302 (2019).

    Article  Google Scholar 

  23. Q. Wu, X. Zhang, P. Shivashankar, Y. Chen, and G. Huang, Independent flexural wave frequency conversion by a linear active metalayer, Phys. Rev. Lett. 128, 244301 (2022).

    Article  Google Scholar 

  24. R. **a, S. Shao, J. Yi, K. Zheng, M. Negahban, and Z. Li, Tunable asymmetric transmission of Lamb waves in piezoelectric bimorph plates by electric boundary design, Compos. Struct. 300, 116111 (2022).

    Article  Google Scholar 

  25. Q. Wu, Y. Chen, and G. Huang, Asymmetric scattering of flexural waves in a parity-time symmetric metamaterial beam, J. Acoust. Soc. Am. 146, 850 (2019).

    Article  Google Scholar 

  26. D. Braghini, L. G. G. Villani, M. I. N. Rosa, and J. R. de F Arruda, Non-Hermitian elastic waveguides with piezoelectric feedback actuation: Non-reciprocal bands and skin modes, J. Phys. D-Appl. Phys. 54, 285302 (2021), ar**v: 2102.07172.

    Article  Google Scholar 

  27. C. Maurini, F. dell’Isola, and D. Del Vescovo, Comparison of piezo-electronic networks acting as distributed vibration absorbers, Mech. Syst. Signal Process. 18, 1243 (2004).

    Article  Google Scholar 

  28. H. Yu, and K. W. Wang, Piezoelectric Networks for vibration suppression of mistuned bladed disks, J. Vib. Acoust. 129, 559 (2007).

    Article  Google Scholar 

  29. A. E. Bergamini, M. Zündel, E. A. Flores Parra, T. Delpero, M. Ruzzene, and P. Ermanni, Hybrid dispersive media with controllable wave propagation: A new take on smart materials, J. Appl. Phys. 118, 154310 (2015).

    Article  Google Scholar 

  30. B. R. Mace, and E. Manconi, Wave motion and dispersion phenomena: Veering, locking and strong coupling effects, J. Acoust. Soc. Am. 131, 1015 (2012).

    Article  Google Scholar 

  31. E. A. Flores Parra, A. Bergamini, L. Kamm, P. Zbinden, and P. Ermanni, Implementation of integrated 1D hybrid phononic crystal through miniaturized programmable virtual inductances, Smart Mater. Struct. 26, 067001 (2017).

    Article  Google Scholar 

  32. E. A. Flores Parra, A. Bergamini, B. Van Damme, and P. Ermanni, Controllable wave propagation of hybrid dispersive media with LC high-pass and band-pass networks, Appl. Phys. Lett. 110, 184103 (2017).

    Article  Google Scholar 

  33. E. A. Flores Parra, A. Bergamini, B. Lossouarn, B. Van Damme, M. Cenedese, and P. Ermanni, Bandgap control with local and interconnected LC piezoelectric shunts, Appl. Phys. Lett. 111, 111902 (2017).

    Article  Google Scholar 

  34. Y. Zheng, J. Zhang, Y. Qu, and G. Meng, Adaptive nonreciprocal wave attenuation in linear piezoelectric metastructures shunted with one-way electrical transmission lines, J. Sound Vib. 503, 116113 (2021).

    Article  Google Scholar 

  35. Q. Wu, H. Chen, H. Nassar, and G. Huang, Non-reciprocal Rayleigh wave propagation in space-time modulated surface, J. Mech. Phys. Solids 146, 104196 (2021).

    Article  MathSciNet  Google Scholar 

  36. X. Xu, Q. Wu, H. Chen, H. Nassar, Y. Chen, A. Norris, M. R. Haber-man, and G. Huang, Physical observation of a robust acoustic pum** in waveguides with dynamic boundary, Phys. Rev. Lett. 125, 253901 (2020), ar**v: 2006.07348.

    Article  Google Scholar 

  37. J. Marconi, E. Riva, M. Di Ronco, G. Cazzulani, F. Braghin, and M. Ruzzene, Experimental observation of nonreciprocal band gaps in a space-time-modulated beam using a shunted piezoelectric array, Phys. Rev. Appl. 13, 031001 (2020), ar**v: 1909.13224.

    Article  Google Scholar 

  38. G. Trainiti, Y. **a, J. Marconi, G. Cazzulani, A. Erturk, and M. Ruzzene, Time-periodic stiffness modulation in elastic metamaterials for selective wave filtering: Theory and experiment, Phys. Rev. Lett. 122, 124301 (2019), ar**v: 1804.09209.

    Article  Google Scholar 

  39. N. W. Hagood, and A. von Flotow, Dam** of structural vibrations with piezoelectric materials and passive electrical networks, J. Sound Vib. 146, 243 (1991).

    Article  Google Scholar 

  40. Q. Wu, P. Shivashankar, X. Xu, Y. Chen, and G. Huang, Engineering nonreciprocal wave dispersion in a nonlocal micropolar metabeam, J. Compos. Mater. 57, 771 (2023).

    Article  Google Scholar 

  41. Y. Chen, X. Li, C. Scheibner, V. Vitelli, and G. Huang, Realization of active metamaterials with odd micropolar elasticity, Nat. Commun. 12, 5935 (2021), ar**v: 2009.07329.

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the Air Force Office of Scientific Research (Grant No. 9550-20-1-0279) with Program Manager Dr. Byung-Lip (Les) Lee and NSF CMMI, USA (Grant No. 1930873).

Author information

Author notes

  1. These authors contributed equally to this work.

Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, Missouri, 65211, USA

    Qian Wu  (吴谦), Honghua Qian  (钱泓桦) & Guoliang Huang  (黄国良)

  2. Department of Mechanical and Aerospace Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, 999077, China

    Yangyang Chen  (陈洋洋)

Authors
  1. Qian Wu  (吴谦)
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Honghua Qian  (钱泓桦)
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yangyang Chen  (陈洋洋)
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Guoliang Huang  (黄国良)
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Guoliang Huang and Yangyang Chen designed the research. Qian Wu, Yangyang Chen and Honghua Qian carried out the numerical simulation, set up the experiment set-up and processed the experimental data. Guoliang Huang supervised the research.

Corresponding authors

Correspondence to Yangyang Chen  (陈洋洋) or Guoliang Huang  (黄国良).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wu, Q., Qian, H., Chen, Y. et al. Dynamic phononic crystals with spatially and temporally modulated circuit networks. Acta Mech. Sin. 39, 723007 (2023). https://doi.org/10.1007/s10409-023-23007-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10409-023-23007-x

Keywords

Search

Navigation