Cascaded essential nonlinearities for enhanced vibration suppression and energy harvesting

Abstract

The concept of simultaneous energy harvesting and vibration suppression has made tremendous progress in the past few years. However, the energy harvesting and vibration reduction seem to be independent, or even paradox in some scenarios; for example, energy harvesting strategy expects the primary system to maintain large-amplitude vibration as long as possible. In comparison, the vibration suppression strategy aims to suppress the vibration of primary system as soon as possible. In this paper, we aim to demonstrate how to properly design an integrated system, which first ensures the broadband vibration suppression performance, while at the same time, harvests additional energy as much as possible. To achieve this goal, a cascaded essentially nonlinear system is presented for high-sensitive vibration and harvesting energy. The presented device comprises a nonlinear energy sink and a nonlinear energy harvester with cascaded essential nonlinearities. Numerical results show that the presented device is able to simultaneously suppress vibration and harvest vibration energy over a wide frequency range. Moreover, unlike previous research, it is effective for extremely small initial impulses. This work explores possibilities for reducing and harvesting extremely low ambient vibration.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

References

  1. 1.

    Lu, Z.Q., Chen, L.Q., Brennan, M., Yang, T.J., Ding, H., Liu, Z.G.: Stochastic resonance in a nonlinear mechanical vibration isolation system. J. Sound Vib. 370, 221–229 (2016)

    Article  Google Scholar 

  2. 2.

    Virgin, L.N., Santillan, S.T., Plaut, R.H.: Vibration isolation using extreme geometric nonlinearity. J. Sound Vib. 315(3), 21–731 (2008)

    Article  Google Scholar 

  3. 3.

    Sun, X.T., Jing, X.J.: Multi-direction vibration isolation with quasi-zero stiffness by employing geometrical nonlinearity. Mech. Syst. Signal Process. 62–63, 149–163 (2015)

    Article  Google Scholar 

  4. 4.

    Peng, Z.K., Meng, G., Lang, Z.Q., Zhang, W.M., Chu, F.L.: Study of the effects of cubic nonlinear damping on vibration isolations using Harmonic Balance Method. Int. J. Non-Linear Mech. 47(10), 1073–1080 (2012)

    Article  Google Scholar 

  5. 5.

    Gendelman, O., Manevitch, L.I., Vakakis, A.F., M’closkey, R.: Energy pumping in nonlinear mechanical oscillators: part I—dynamics of the underlying Hamiltonian systems. J. Appl. Mech. 68(1), 34–41 (2001)

    MathSciNet  Article  Google Scholar 

  6. 6.

    Vakakis, A.F., Gendelman, O.: Energy pumping in nonlinear mechanical oscillators: part II—resonance capture. J. Appl. Mech. 68(1), 42–48 (2001)

    MathSciNet  Article  Google Scholar 

  7. 7.

    Dai, H.L., Abdelkefi, A., Wang, L.: Vortex-induced vibrations mitigation through a nonlinear energy sink. Commun. Nonlinear Sci. Numer. Simul. 42, 22–36 (2018)

    Article  Google Scholar 

  8. 8.

    Bab, S., Khadem, S.E., Shahgholi, M., Abbasi, A.: Vibration attenuation of a continuous rotor-blisk-journal bearing system employing smooth nonlinear energy sinks. Mech. Syst. Signal Process. 84, 128–157 (2017)

    Article  Google Scholar 

  9. 9.

    Tehrani, G.G., Dardel, M.: Mitigation of nonlinear oscillations of a Jeffcott rotor System with an optimized damper and nonlinear energy sink. Int. J. Non-Linear Mech. 98, 122–136 (2018)

    Article  Google Scholar 

  10. 10.

    Yang, T.Z., Yang, X.D., Li, Y., Fang, B.: Passive and adaptive vibration suppression of pipes conveying fluid with variable velocity. J. Vib. Control 20, 1293–1300 (2014)

    MathSciNet  Article  Google Scholar 

  11. 11.

    Yang, K., Zhang, Y.W., Ding, H., Yang, T.Z., Li, Y., Chen, L.Q.: Nonlinear energy sink for whole-spacecraft vibration reduction. J. Vib. Acoust. 139(2), 021011 (2017)

    Article  Google Scholar 

  12. 12.

    Sun, Y.-H., Zhang, Y.W., Ding, H., Chen, L.Q.: Nonlinear energy sink for a flywheel system vibration reduction. J. Sound Vib. 429, 305–324 (2018)

    Article  Google Scholar 

  13. 13.

    Zhang, Y.W., Zhang, Z., Chen, L.Q., Yang, T.Z., Fang, B., Zang, J.: Impulse-induced vibration suppression of an axially moving beam with parallel nonlinear energy sinks. Nonlinear Dyn. 82(1–2), 61–71 (2015)

    MathSciNet  Article  Google Scholar 

  14. 14.

    Chiacchiari, S., Romeo, F., McFarland, D.M., Bergman, L.A., Vakakis, A.F.: Vibration energy harvesting from impulsive excitations via a bistable nonlinear attachment. Int. J. Non-Linear Mech. 94, 84–97 (2017)

    Article  Google Scholar 

  15. 15.

    Kremer, D., Liu, K.F.: A nonlinear energy sink with an energy harvester: harmonically forced responses. J. Sound Vib. 410, 287–302 (2017)

    Article  Google Scholar 

  16. 16.

    Zhou, S.X., Zuo, L.: Nonlinear dynamic analysis of asymmetric tristable energy harvesters for enhanced energy harvesting. Commun. Nonlinear Sci. Numer. Simul. 61, 271–284 (2018)

    MathSciNet  Article  Google Scholar 

  17. 17.

    Zhou, S.X., Cao, J., Inman, D.J., Lin, J., Liu, S.S., Wang, Z.: Broadband tristable energy harvester: modeling and experiment verification. Appl. Energy 133, 33–39 (2014)

    Article  Google Scholar 

  18. 18.

    Naseer, R., Dai, H.L., Abdelkefi, A., Wang, L.: Piezomagnetoelastic energy harvesting from vortex-induced vibrations using monostable characteristics. Appl. Energy 203, 142–153 (2017)

    Article  Google Scholar 

  19. 19.

    Jiang, W.A., Chen, L.Q.: Snap-through piezoelectric energy harvesting. J. Sound Vib. 333(18), 4314–4325 (2014)

    Article  Google Scholar 

  20. 20.

    Zhang, Y., Tang, L.H., Liu, K.F.: Piezoelectric energy harvesting with a nonlinear energy sink. J. Intell. Mater. Syst. Struct. 28, 307–322 (2016)

    Google Scholar 

  21. 21.

    Izadgoshasb, I., Lim, Y.Y., Lake, N., Tang, L.H., Padilla, R.V., Kashiwao, T.: Optimizing orientation of piezoelectric cantilever beam for harvesting energy from human walking. Energy Convers. Manag. 161, 66–73 (2019)

    Article  Google Scholar 

  22. 22.

    Wang, H.Y., Tang, L.H.: Modeling and experiment of bistable two-degree-of-freedom energy harvester with magnetic coupling. Mech. Syst. Signal Process. 86, 29–39 (2017)

    Article  Google Scholar 

  23. 23.

    Gendelman, O.V., Sapsis, T., Vakakis, A.F., Bergman, L.A.: Enhanced passive targeted energy transfer in strongly nonlinear mechanical oscillators. J. Sound Vib. 330, 1–8 (2011)

    Article  Google Scholar 

  24. 24.

    AL-Shudeifat, M.A.: Highly efficient nonlinear energy sink. Nonlinear Dyn. 76, 1905 (2014)

    MathSciNet  Article  Google Scholar 

  25. 25.

    Wei, Y.M., Peng, Z.K., Dong, X.J., Zhang, W.M., Meng, G.G.: Mechanism of optimal targeted energy transfer. ASME J. Appl. Mech. 84(1), 011007-1–011007-9 (2016)

    Google Scholar 

  26. 26.

    Fang, Z.W., Zhang, Y.W., Li, X., Ding, H., Chen, L.Q.: Integration of a nonlinear energy sink and a giant magnetostrictive energy harvester. J. Sound Vib. 391, 35–49 (2017)

    Article  Google Scholar 

  27. 27.

    Li, X., Zhang, Y.W., Ding, H., Chen, L.Q.: Integration of a nonlinear energy sink and a piezoelectric energy harvester. Appl. Math. Mech. 38, 1019–1030 (2017)

    MathSciNet  Article  Google Scholar 

  28. 28.

    Fang, Z.W., Zhang, Y.W., Li, X., Ding, H., Chen, L.Q.: Complexification-averaging analysis on a giant magnetostrictive harvester integrated with a nonlinear energy sink. ASME J. Vib. Acoust. 140, 021009 (2018)

    Article  Google Scholar 

  29. 29.

    Wheeler, H.: Simple inductance formulas for radio coils. Proc. IRE 16, 1398–1400 (1928)

    Article  Google Scholar 

  30. 30.

    Remick, K., Dane, Quinn D., Michael, McFarland D., Bergman, L., Vakakis, A.: High-frequency vibration energy harvesting from impulsive excitation utilizing intentional dynamic instability caused by strong nonlinearity. J. Sound Vib. 370, 259–279 (2016)

    Article  Google Scholar 

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China (No. 12072221, 11672187) and Scientific Research Project of Tianjin Education Commission (No. 2019KJ121).

Author information

Affiliations

Authors

Corresponding author

Correspondence to Tianzhi Yang.

Ethics declarations

Conflict 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.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Jin, Y., Hou, S. & Yang, T. Cascaded essential nonlinearities for enhanced vibration suppression and energy harvesting. Nonlinear Dyn 103, 1427–1438 (2021). https://doi.org/10.1007/s11071-020-06165-6

Download citation

Keywords

  • Nonlinear energy sink
  • Energy harvesting
  • Vibration suppression