Skip to main content
SpringerLink
Log in

Bistable attachments for wideband nonlinear vibration attenuation in a metamaterial beam

  • Original paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

This work investigates the amplitude-dependent dynamics of a locally resonant metamaterial beam with bistable attachments. The concept that was previously demonstrated for a discrete chain is extended to a continuous system, and the enhancement in vibration attenuation bandwidth is investigated through a cantilever beam under base excitation. The analysis approach combines the harmonic balance method and time-domain numerical integration to capture periodic and aperiodic responses for up-sweep and down-sweep harmonic excitation. The bistable attachments are shown to exhibit linear intrawell, nonlinear intrawell and nonlinear interwell oscillations for low, moderate, and high base acceleration levels. As a result, the metastructure leverages linear locally resonant bandgap under low excitation intensity, and nonlinear wideband attenuation due to chaotic vibrations of the bistable attachments under high excitation intensity. This is first demonstrated through frequency sweep numerical simulations for a broad range of excitation amplitudes. Experimental validations are then presented for a base-excited cantilever beam hosting seven magnetoelastic beam attachments. For moderate-to-high amplitude excitation levels, the interwell oscillations of the attachments produce an attenuation frequency range that is 350% wider than the corresponding linear locally resonant bandgap (observed for low-amplitude excitation levels), yielding the suppression of modes outside the bandgap with increased excitation intensity.

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. Liu, Z., Zhang, X., Mao, Y., Zhu, Y., Yang, Z., Chan, C.T., Sheng, P.: Locally resonant sonic materials. Science 289(5485), 1734 (2000)

    Article  Google Scholar 

  2. Li, J., Chan, C.T.: Double-negative acoustic metamaterial. Phys. Rev. E 70(5), 055602 (2004)

    Article  Google Scholar 

  3. Yu, D., Liu, Y., Wang, G., Zhao, H., Qiu, J.: Flexural vibration band gaps in Timoshenko beams with locally resonant structures. J. Appl. Phys. 100(12), 124901 (2006)

    Article  Google Scholar 

  4. Sun, H., Du, X., Pai, P.F.: Theory of metamaterial beams for broadband vibration absorption. J. Intell. Mater. Syst. Struct. 21(11), 1085 (2010)

    Article  Google Scholar 

  5. Oudich, M., Senesi, M., Assouar, M.B., Ruzenne, M., Sun, J.H., Vincent, B., Hou, Z., Wu, T.T.: Experimental evidence of locally resonant sonic band gap in two-dimensional phononic stubbed plates. Phys. Rev. B 84(16), 165136 (2011)

    Article  Google Scholar 

  6. Assouar, M.B., Senesi, M., Oudich, M., Ruzzene, M., Hou, Z.: Broadband plate-type acoustic metamaterial for low-frequency sound attenuation. Appl. Phys. Lett. 101(17), 173505 (2012)

    Article  Google Scholar 

  7. Zhu, R., Liu, X., Hu, G., Sun, C., Huang, G.: A chiral elastic metamaterial beam for broadband vibration suppression. J. Sound Vib. 333(10), 2759 (2014)

    Article  Google Scholar 

  8. Sugino, C., Leadenham, S., Ruzzene, M., Erturk, A.: On the mechanism of bandgap formation in locally resonant finite elastic metamaterials. J. Appl. Phys. 120(13), 134501 (2016)

    Article  Google Scholar 

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

    Article  Google Scholar 

  10. Daqaq, M.F., Masana, R., Erturk, A., Quinn, D.D.: On the role of nonlinearities in vibratory energy harvesting: a critical review and discussion. Appl. Mech. Rev. 66(4), 040801 (2014)

    Article  Google Scholar 

  11. Erturk, A., Hoffmann, J., Inman, D.: A piezomagnetoelastic structure for broadband vibration energy harvesting. Appl. Phys. Lett. 94(25), 254102 (2009)

    Article  Google Scholar 

  12. Cottone, F., Vocca, H., Gammaitoni, L.: Nonlinear energy harvesting. Phys. Rev. Lett. 102(8), 080601 (2009)

    Article  Google Scholar 

  13. Stanton, S.C., McGehee, C.C., Mann, B.P.: Nonlinear dynamics for broadband energy harvesting: investigation of a bistable piezoelectric inertial generator. Phys. D Nonlinear Phenom. 239(10), 640 (2010)

    Article  Google Scholar 

  14. Harne, R.L., Wang, K.: A review of the recent research on vibration energy harvesting via bistable systems. Smart Mater. Struct. 22(2), 023001 (2013)

    Article  Google Scholar 

  15. Gendelman, O.V.: Bifurcations of nonlinear normal modes of linear oscillator with strongly nonlinear damped attachment. Nonlinear Dyn. 37(2), 115 (2004)

    Article  MathSciNet  Google Scholar 

  16. Starosvetsky, Y., Gendelman, O.: Vibration absorption in systems with a nonlinear energy sink: nonlinear damping. J. Sound Vib. 324(3–5), 916 (2009)

    Article  Google Scholar 

  17. Starosvetsky, Y., Gendelman, O.: Attractors of harmonically forced linear oscillator with attached nonlinear energy sink. II: optimization of a nonlinear vibration absorber. Nonlinear Dyn. 51(1–2), 47 (2008)

    MATH  Google Scholar 

  18. Parseh, M., Dardel, M., Ghasemi, M.H.: Performance comparison of nonlinear energy sink and linear tuned mass damper in steady-state dynamics of a linear beam. Nonlinear Dyn. 81(4), 1981 (2015)

    Article  MathSciNet  Google Scholar 

  19. Kani, M., Khadem, S., Pashaei, M., Dardel, M.: Vibration control of a nonlinear beam with a nonlinear energy sink. Nonlinear Dyn. 83(1–2), 1 (2016)

    Article  MathSciNet  Google Scholar 

  20. Silva, T.M., Clementino, M.A., De Marqui Jr, C., Erturk, A.: An experimentally validated piezoelectric nonlinear energy sink for wideband vibration attenuation. J. Sound Vib. 437, 68 (2018)

    Article  Google Scholar 

  21. Yang, K., Harne, R., Wang, K., Huang, H.: Investigation of a bistable dual-stage vibration isolator under harmonic excitation. Smart Mater. Struct. 23(4), 045033 (2014)

    Article  Google Scholar 

  22. Manevitch, L., Sigalov, G., Romeo, F., Bergman, L., Vakakis, A.: Dynamics of a linear oscillator coupled to a bistable light attachment: analytical study. J. Appl. Mech. 81(4), 041011 (2014)

    Article  Google Scholar 

  23. Romeo, F., Sigalov, G., Bergman, L.A., Vakakis, A.F.: Dynamics of a linear oscillator coupled to a bistable light attachment: numerical study. J. Comput. Nonlinear Dyn. 10(1), 011007 (2015)

    Article  Google Scholar 

  24. Johnson, D.R., Harne, R., Wang, K.: A disturbance cancellation perspective on vibration control using a bistable snap-through attachment. J. Vib. Acoust. 136(3), 031006 (2014)

    Article  Google Scholar 

  25. Banerjee, A., Das, R., Calius, E.P.: Waves in structured mediums or metamaterials: a review. Arch. Comput. Methods Eng. 26(4), 1029 (2019)

    Article  MathSciNet  Google Scholar 

  26. Lazarov, B.S., Jensen, J.S.: Low-frequency band gaps in chains with attached non-linear oscillators. Int. J. Non-Linear Mech. 42(10), 1186 (2007)

    Article  Google Scholar 

  27. Banerjee, A., Calius, E.P., Das, R.: The effects of cubic stiffness nonlinearity on the attenuation bandwidth of 1D elasto-dynamic metamaterials. In: ASME 2016 International Mechanical Engineering Congress and Exposition (American Society of Mechanical Engineers Digital Collection, 2016)

  28. Casalotti, A., El-Borgi, S., Lacarbonara, W.: Metamaterial beam with embedded nonlinear vibration absorbers. Int. J. Non-Linear Mech. 98, 32 (2018)

    Article  Google Scholar 

  29. Nadkarni, N., Daraio, C., Kochmann, D.M.: Dynamics of periodic mechanical structures containing bistable elastic elements: from elastic to solitary wave propagation. Phys. Rev. E 90(2), 023204 (2014)

    Article  Google Scholar 

  30. Nadkarni, N., Arrieta, A.F., Chong, C., Kochmann, D.M., Daraio, C.: Unidirectional transition waves in bistable lattices. Phys. Rev. Lett. 116(24), 244501 (2016)

    Article  Google Scholar 

  31. Hwang, M., Arrieta, A.F.: Solitary waves in bistable lattices with stiffness grading: augmenting propagation control. Phys. Rev. E 98(4), 042205 (2018)

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  33. Leadenham, S., Erturk, A.: Nonlinear M-shaped broadband piezoelectric energy harvester for very low base accelerations: primary and secondary resonances. Smart Mater. Struct. 24(5), 055021 (2015)

    Article  Google Scholar 

  34. He, Q., Daqaq, M.F.: Influence of potential function asymmetries on the performance of nonlinear energy harvesters under white noise. J. Sound Vib. 333(15), 3479 (2014)

    Article  Google Scholar 

  35. Wang, W., Cao, J., Bowen, C.R., Inman, D.J., Lin, J.: Performance enhancement of nonlinear asymmetric bistable energy harvesting from harmonic, random and human motion excitations. Appl. Phys. Lett. 112(21), 213903 (2018)

    Article  Google Scholar 

Download references

Acknowledgements

The authors acknowledge the partial support of grant W911NF-18-1-0036 from the Army Research Office.

Author information

Authors and Affiliations

  1. George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, 30332, USA

    Yiwei Xia & Alper Erturk

  2. Department of Mechanical Engineering, University of Colorado Boulder, Boulder, 80309, USA

    Massimo Ruzzene

Authors
  1. Yiwei Xia
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Massimo Ruzzene
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Alper Erturk
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yiwei Xia.

Ethics declarations

Conflicts of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

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

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (mp4 26510 KB)

Supplementary material 2 (mp4 29669 KB)

Supplementary material 3 (mp4 24004 KB)

Supplementary material 4 (mp4 27036 KB)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xia, Y., Ruzzene, M. & Erturk, A. Bistable attachments for wideband nonlinear vibration attenuation in a metamaterial beam. Nonlinear Dyn 102, 1285–1296 (2020). https://doi.org/10.1007/s11071-020-06008-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-020-06008-4

Keywords

Search

Navigation