The European Physical Journal Special Topics

, Volume 222, Issue 7, pp 1575–1586 | Cite as

A non-ideal portal frame energy harvester controlled using a pendulum

  • I. IliukEmail author
  • J.M. BalthazarEmail author
  • A.M. TussetEmail author
  • J.R.C. PiqueiraEmail author
  • B. Rodrigues de PontesEmail author
  • J.L.P. FelixEmail author
  • Á.M. BuenoEmail author
Regular Article


A model of energy harvester based on a simple portal frame structure is presented. The system is considered to be non-ideal system (NIS) due to interaction with the energy source, a DC motor with limited power supply and the system structure. The nonlinearities present in the piezoelectric material are considered in the piezoelectric coupling mathematical model. The system is a bi-stable Duffing oscillator presenting a chaotic behavior. Analyzing the average power variation, and bifurcation diagrams, the value of the control variable that optimizes power or average value that stabilizes the chaotic system in the periodic orbit is determined. The control sensitivity is determined to parametric errors in the damping and stiffness parameters of the portal frame. The proposed passive control technique uses a simple pendulum to tuned to the vibration of the structure to improve the energy harvesting. The results show that with the implementation of the control strategy it is possible to eliminate the need for active or semi active control, usually more complex. The control also provides a way to regulate the energy captured to a desired operating frequency.


Average Power European Physical Journal Special Topic Bifurcation Diagram Energy Harvester Passive Control 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    S.F. Ali, S. Adhikari, M.I. Friswell, S. Narayanan, J. Appl. Phys. 109, 074904 (2011)ADSCrossRefGoogle Scholar
  2. 2.
    J.M. Balthazar, D.T. Mook, H.I. Weber, R.M.L.R.F. Brasil, A. Fenili, D. Belato, J.L.P. Felix, Meccanica 38, 613 (2003)zbMATHCrossRefGoogle Scholar
  3. 3.
    D. Belato, J.M. Balthazar, H.I. Weber, D.T. Mook, Nonlinear Dynamics, Chaos, Control and Their Applications to Engineering Sciences 2, Vibrations with Measurements and Control, edited by J.M. Balthazar, P.B. Gonçalvez, J. Clayssen, 222 (1999)Google Scholar
  4. 4.
    D.A.W. Barton, S.G. Burrow, L.R. Clare, J. Vibr. Acoust. 132, 021009 (2010)CrossRefGoogle Scholar
  5. 5.
    F. Cottone, H. Vocca, L. Gammaitoni, Phys. Rev. Lett. 102, 080601 (2009)ADSCrossRefGoogle Scholar
  6. 6.
    A. Erturk, D.J. Inman, Piezoelectric Energy Harvesting (John Wiley & Sons, Ltd., 2011)Google Scholar
  7. 7.
    A. Erturk, J. Hoffmann, D.J. Inman, Appl. Phys. Lett. 94, 254102 (2009)ADSCrossRefGoogle Scholar
  8. 8.
    A. Erturk, D.J. Inman, J. Sound Vibr. 330, 2339 (2011)ADSCrossRefGoogle Scholar
  9. 9.
    M. Ferrari, V. Ferrari, M. Guizzetti, B. Andò, S. Baglio, C. Trigona, Sensors Actuators A 162, 425 (2010)CrossRefGoogle Scholar
  10. 10.
    M.I. Friswell, S.F. Ali, S. Adhikari, A.W. Lees, O. Bilgen, G. Litak, J. Intell. Material Syst. Struct. 23, 1505 (2012)CrossRefGoogle Scholar
  11. 11.
    W. Heywang, K. Lubitz, W. Wersing, Piezoelectricity Evolution and Future of a Technology (Springer Series in Materials Science ISSN 0933-033x, Springer-Verlag Berlin Heidelberg, 2008)Google Scholar
  12. 12.
    I. Iliuk, J.M. Balthazar, A.M. Tusset, B.R. Pontes Jr, J.L.P. Felix, J. Differential Equations Dyn. Sys. 21, 93 (2013)zbMATHCrossRefGoogle Scholar
  13. 13.
    I. Iliuk, J.M. Balthazar, A.M. Tusset, B.R. Pontes Jr., J.L.P. Felix, MATEC Web of Conferences, 08003 (2012)Google Scholar
  14. 14.
    N. Jalili, Piezoelectric-Based Vibration Control, From Macro to Micro/Nano Scale Systems (Springer Science Business Media, LLC., 2010)Google Scholar
  15. 15.
    M.A. Karami, D.J. Inman, J. Sound Vibr. 330, 5583 (2011)ADSCrossRefGoogle Scholar
  16. 16.
    G. Litak, M.I. Friswell, S. Adhikari, Appl. Phys. Lett. 96, 214103 (2010)ADSCrossRefGoogle Scholar
  17. 17.
    G. Litak, M.I. Friswell, C.A. Kitio Kwuimy, S. Adhikari, B. Borowiec, Theoretical Appl. Mech. Lett. 2, 043009 (2012)CrossRefGoogle Scholar
  18. 18.
    B.P. Mann, N.D. Sims, J. Sound Vibr. 319, 515 (2009)ADSCrossRefGoogle Scholar
  19. 19.
    C. McInnes, D. Gorman, M. Cartmell, J. Sound Vibr. 318, 655 (2010)ADSCrossRefGoogle Scholar
  20. 20.
    S. Priya, D.J. Inman, Energy Harvesting Technologies (Springer Science Business Media, LLC., 2009)Google Scholar
  21. 21.
    D. Sado, M. Kot, J. Theoretical Appl. Mech. 45, 119 (2007)Google Scholar
  22. 22.
    J. Scruggs, J. Sound Vibr. 320, 707 (2009)ADSCrossRefGoogle Scholar
  23. 23.
    S.C. Stanton, C.C. McGehee, B.P. Mann, Physica D: Nonlinear Phenomena 239, 640 (2010)zbMATHADSCrossRefGoogle Scholar
  24. 24.
    A. Triplett, D.D. Quinn, J. Intell. Material Syst. Struct. 20, 1959 (2009)CrossRefGoogle Scholar
  25. 25.
    A.M. Tusset, J.M. Balthazar, F.R Chavarette, J.L.P. Felix, Nonlinear Dyn. 69, 1859 (2012)zbMATHMathSciNetCrossRefGoogle Scholar
  26. 26.
    A.M. Tusset, J.M. Balthazar, J.L.P. Felix, J. Vibr. Control, 1 (2012)Google Scholar
  27. 27.
    A.M. Tusset, J.M. Balthazar, Differential Equations Dyn. Syst. 21, 105 (2013)zbMATHMathSciNetCrossRefGoogle Scholar
  28. 28.
    U. Von Wagner, P. Hagedorn, J. Sound Vibr. 256, 861 (2002)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences and Springer 2013

Authors and Affiliations

  1. 1.Escola Politécnica da Universidade de São Paulo, Av. Prof. Luciano GualbertoSão PauloBrazil
  2. 2.UNESP–Rio Claro, Department of Statistics, Applied Mathematics and Computation (DEMAC)Bela VistaRio ClaroBrazil
  3. 3.UTFPR – Ponta Grossa, PR, Department of Engineering Scienc, Av. Monteiro LobatoePonta GrossaBrazil
  4. 4.Escola Politécnica da Universidade de São Paulo, Department of Telecommunications and Control, Av. Prof. Luciano GualbertoSão PauloBrazil
  5. 5.UNESP – Bauru – SP, Department of Engineering Mechanics (FEB) Av. Engenheiro Luiz Edmundo Carrijo CoubeBauru-SPBrazil
  6. 6.UNIPAMPA – BagéBagéBrazil
  7. 7.UNESP – Campus experimental de Sorocaba Av. Três de março 511, Alto da boa vistaSorocabaBrazil

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