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Vibration attenuation and energy harvesting in metastructures with nonlinear absorbers conserving mass and strain energy

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Abstract

In this work, we explore the performance of vibration attenuation and energy harvesting of a metastructure with vibration absorbers with nonlinear stiffness under harmonic excitation. We devise the metastructure with two main concepts: conservation of total mass, by designing the metastructure with the same mass as a structure without absorbers; conservation of strain energy, by designing the nonlinear absorbers with the same strain energy as a linear one. The use of metastructures for vibration attenuation and energy harvesting is attracting increasing attention from many engineering applications, as they have interesting wave filtering characteristics. The use of vibration absorbers allows band gaps in low frequencies, and nonlinear characteristics have been explored in different ways to increase the bandwidth of vibration attenuation in such metastructures. Modal analysis is used to determine eigenfrequencies, eigenmodes and frequency response (FRF) of the base structure and the metastructure with linear and nonlinear absorbers, both with five elements. The dissipated power by the absorbers’ dampers and the electric power in the piezoelectric harvester devices are analysed. The metastructure has slightly smaller attenuation at the tuned frequency while the total harvested power increases considerably near the first resonance.

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References

  1. D. Beli, J.R.F. Arruda, M. Ruzzene, Wave propagation in elastic metamaterial beams and plates with interconnected resonators. Int. J. Solids Struct. 139–140, 105–120 (2018)

    Article  Google Scholar 

  2. M. Bukhari, O. Barry, Simultaneous energy harvesting and vibration control in a nonlinear metastructure: A spectro-spatial analysis. J. Sound Vib. 473, 115215 (2020)

    Article  Google Scholar 

  3. G. Chakraborty, A.K. Mallik, Dynamics of a weakly non-linear periodic chain. Int. J. Non-Linear Mech. 36(2), 375–389 (2001)

    Article  Google Scholar 

  4. Z. Chen, B. Guo, Y. Yang, C. Cheng, Metamaterials-based enhanced energy harvesting: a review. Phys. B 438, 1–8 (2014)

    Article  ADS  Google Scholar 

  5. L. Cveticanin, M. Zukovic, D. Cveticanin, Influence of nonlinear subunits on the resonance frequency band gaps of acoustic metamaterial. Nonlinear Dyn. 93, 1–11 (2018)

    Article  Google Scholar 

  6. M.F. Daqaq, R. Masana, A. Erturk, D.D. Quinn, On the role of nonlinearities in vibratory energy harvesting: a critical review and discussion. Appl. Mech. Rev. 66, 040801–1 (2014)

    Article  ADS  Google Scholar 

  7. J.P. den Hartog, Mechanical Vibrations, 4th edn. (McGraw-Hill, New York, 1956)

    MATH  Google Scholar 

  8. A. Erturk, D.J. Inman, Broadband piezoelectric power generation on high-energy orbits of the bistable dufng oscillator with electromechanical coupling. J. Sound Vib. 330, 2339–2353 (2011)

    Article  ADS  Google Scholar 

  9. P.J.P. Gonçalves, M.J. Brennan, V.G. Cleante, Predicting the stop-band behaviour of finite mono-coupled periodic structures from the transmissibility of a single element. Mech. Syst. Signal Process. 154, 107512 (2021)

    Article  Google Scholar 

  10. G. Hu, L. Tang, R. Das, Internally coupled metamaterial beam for simultaneous vibration suppression and low frequency energy harvesting. J. Appl. Phys. 123, 055107 (2018)

    Article  ADS  Google Scholar 

  11. H.H. Huang, C.T. Sun, G.L. Huang, On the negative effective mass density in acoustic metamaterials. Int. J. Eng. Sci. 47, 610–617 (2009)

    Article  Google Scholar 

  12. C.H. Lamarque, A. Ture Savadkoohi, S. Charlemagne, Experimental results on the vibratory energy exchanges between a linear system and a chain of nonlinear oscillators. J. Sound Vib. 437, 97–109 (2018)

    Article  ADS  Google Scholar 

  13. B.S. Lazarov, J.S. Jensen, Low-frequency band gaps in chains with attached non-linear oscillators. Int. J. Non-Linear Mech. 42, 1186–1193 (2007)

    Article  ADS  Google Scholar 

  14. A. Marathe, A. Chatterjee, Wave attenuation in nonlinear periodic structures using harmonic balance and multiple scales. J. Sound Vib. 289(4–5), 871–888 (2006)

    Article  ADS  Google Scholar 

  15. D.J. Mead, Wave propagation and natural modes in periodic systems: I. Mono-coupled systems. J. Sound Vib. 40, 1–18 (1975)

    Article  ADS  Google Scholar 

  16. A.H. Nayfeh, B. Balachandran, Applied Nonlinear Dynamics: Analytical, Computational, and Experimental Methods (Wiley, Hoboken, 2008)

    MATH  Google Scholar 

  17. K.K. Reichl, D.J. Inman, Lumped mass model of a 1d metastructure for vibration suppression with no additional mass. J. Sound Vib. 403, 75–89 (2017)

    Article  ADS  Google Scholar 

  18. S.C. Stanton, C.C. McGehee, B.P. Mann, Nonlinear dynamics for broadband energy harvesting: investigation of a bistable piezoelectric inertial generator. Phys. D 239, 640–653 (2010)

    Article  Google Scholar 

  19. C. Sugino, A. Erturk, Analysis of multifunctional piezoelectric metastructures for low-frequency bandgap formation and energy harvesting. J. Phys. D Appl. Phys. 51(21), 215103 (2018)

  20. C. Sugino, Y. Xia, S. Leadenham, M. Ruzzene, A. Erturk, A general theory for bandgap estimation in locally resonant metastructures. J. Sound Vib. 406, 104–123 (2017)

  21. A.F. Vakakis, M.E. King, Resonant oscillations of a weakly coupled, nonlinear layered system. Acta Mech. 128(1–2), 59–80 (1998)

  22. D.P. Vasconcellos, M. Silveira, Optimization of axial vibration attenuation of periodic structure with nonlinear stiffness without addition of mass. J. Vib. Acoust. 142, 061009 (2020). https://doi.org/10.1115/1.4047197

    Article  Google Scholar 

  23. S. Yao, X. Zhou, G. Hu, Experimental study on negative effective mass in a 1D mass-spring system. New J. Phys. 10(4), 043020 (2008)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

DPV and RSC received funding from the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brazil (CAPES) (#88887.487915/2020-00 and #88882.432818/2019-01). MS received funding from CNPq (#309860/2020-2) and FAPESP (#2018/15894-0).

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Authors and Affiliations

  1. School of Engineering, State University of São Paulo (UNESP), Bauru, São Paulo, Brazil

    D. P. Vasconcellos, R. S. Cruz, J. C. M. Fernandes & M. Silveira

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  1. D. P. Vasconcellos
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  2. R. S. Cruz
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  3. J. C. M. Fernandes
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  4. M. Silveira
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Correspondence to M. Silveira.

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Vasconcellos, D.P., Cruz, R.S., Fernandes, J.C.M. et al. Vibration attenuation and energy harvesting in metastructures with nonlinear absorbers conserving mass and strain energy. Eur. Phys. J. Spec. Top. 231, 1393–1401 (2022). https://doi.org/10.1140/epjs/s11734-022-00489-7

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  • DOI: https://doi.org/10.1140/epjs/s11734-022-00489-7

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