Multiple solutions and corresponding power output of a nonlinear bistable piezoelectric energy harvester


We examine multiple responses of a vibrational energy harvester composed of a vertical beam and a tip mass. The beam is excited horizontally by a harmonic inertial force while mechanical vibrational energy is converted to electrical power through a piezoelectric patch. The mechanical resonator can be described by single or double well potentials depending on the gravity force from the tip mass. By changing the tip mass we examine the appearance of various solutions and their basins of attraction. Identification of particular solutions of the energy harvester is important as each solution may provide a different level of power output.


  1. 1.

    P.D. Mitcheson, E.M. Yeatman, G.K. Rao, A.S. Holmes, T.C. Green, Proc. IEEE 96, 1457 (2008)

    Article  Google Scholar 

  2. 2.

    M.F. Daqaq, R. Masana, A. Erturk, D.D. Quinn, Appl. Mech. Rev. 66, 040801 (2014)

    ADS  Article  Google Scholar 

  3. 3.

    R.L. Harne, K.W. Wang, Smart Mat. Struct. 22, 023001 (2013)

    ADS  Article  Google Scholar 

  4. 4.

    S.P. Pellegrini, N. Tolou, M. Schenk, J.L. Herder, J. Intell. Mater. Syst. Struct. 24, 1303 (2013)

    Article  Google Scholar 

  5. 5.

    J. Twiefel, H. Westermann, J. Intell. Mater. Syst. Struct. 24, 1291 (2013)

    Article  Google Scholar 

  6. 6.

    J. Cao, S. Zhou, D.J. Inman, Y. Chen, Nonlinear Dyn. 80, 1705 (2014)

    Article  Google Scholar 

  7. 7.

    J. Cao, A. Syta, G. Litak, S. Zhou, D.J. Inman, Y. Chen, Eur. Phys. J. Plus 130, 103 (2015)

    Article  Google Scholar 

  8. 8.

    A. Syta, C.R. Bowen, H.A. Kim, A. Rysak, G. Litak, Meccanica 50, 1961 (2015)

    Article  Google Scholar 

  9. 9.

    M.I. Friswell, S.F. Ali, O. Bilgen, S. Adhikari, A.W. Lees, G. Litak, J. Intell. Mater. Syst. Struct. 23, 1505 (2012)

    Article  Google Scholar 

  10. 10.

    L. Zavodney, A. Nayfeh, Int. J. Non-Linear Mechanics 24, 105 (1989)

    ADS  Article  Google Scholar 

  11. 11.

    E. Esmailzadeh, G. Nakhaie-Jazar, Int. J. Non-Linear Mechanics 33, 567 (1998)

    ADS  Article  Google Scholar 

  12. 12.

    T.Y. Li, J.A. Yorke, Amer. Math. Monthly 82, 985 (1975)

    MathSciNet  Article  Google Scholar 

  13. 13.

    G. Litak, M. Coccolo, M.I. Friswell, S.F. Ali, S. Adhikari, A.W. Lees, O. Bilgen, in Proceedings of NSC 2012 - 4th IEEE International Conference on Nonlinear Science and Complexity, August 6-11, 2012, Budapest, Hungary, pp. 113–116.

  14. 14.

    J. Aguirre, J.C. Vallejo, M.A.F. Sanjuan, Phys. Rev. E 64, 066208 (2001)

    ADS  Article  Google Scholar 

  15. 15.

    M.V. Zakrzhevsky, in Proceedings of the ASME – IDETC/EIE, August 30-September 2, 2009, San Diego, California, USA, DETC2009-86657, pp. 1411–1418.

  16. 16.

    J. Guckenheimer, P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer, 1983)

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Correspondence to Grzegorz Litak.

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Syta, A., Litak, G., Friswell, M. et al. Multiple solutions and corresponding power output of a nonlinear bistable piezoelectric energy harvester. Eur. Phys. J. B 89, 99 (2016).

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  • Statistical and Nonlinear Physics