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Nonlinear Characterization of a Bistable Energy Harvester Dynamical System

  • Vinicius G. Lopes
  • João Victor L. L. Peterson
  • Americo Cunha Jr.Email author
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 228)

Abstract

This chapter explores the nonlinear dynamics of a bistable piezo-magneto-elastic energy harvester with the objective of determining the influence of external force parameters on the system response. Time series, phase space trajectories, Poincaré maps and bifurcation diagrams are employed in order to reveal system dynamics complexity and nonlinear effects, such as chaos incidence and hysteresis.

Notes

Acknowledgements

The authors acknowledge the support given to this research by the funding agencies Carlos Chagas Filho Research Foundation of Rio de Janeiro State (FAPERJ) under grants E-26/010.002.178/2015 and E-26/010.000.805/2018, and Coordenação de Aperfeiçoamento de Pessoal de Ní­vel Superior–Brasil (CAPES)–Finance Code 001.

References

  1. 1.
    M.A.A. Abdelkareem, L. Xu, M.K.A. Ali, A. Elagouz, J. Mi, S. Guo, Y. Liu, L. Zuo, Vibration energy harvesting in automotive suspension system: a detailed review. Appl. Energy 229, 672–699 (2018)CrossRefGoogle Scholar
  2. 2.
    C.H.C.C. Basqueroto, F.R. Chavarette, S. da Silva, Analysis of bistable and chaotic piezoelectric energy harvesting device coupled with diode bridge rectifier. Int. J. Pure Appl. Math. 98, 275–289 (2015)CrossRefGoogle Scholar
  3. 3.
    M. Belhaq, M. Hamdi, Energy harvesting from quasi-periodic vibrations. Nonlinear Dyn. 86, 2193–2205 (2016)CrossRefGoogle Scholar
  4. 4.
    M. Borowiec, Energy harvesting of cantilever beam system with linear and nonlinear piezoelectric model. Eur. Phys. J. Spec. Top. 224(14), 2771–2785 (2015)CrossRefGoogle Scholar
  5. 5.
    S. Bradai, S. Naifar, C. Viehweger, O. Kanoun, G. Litak, Nonlinear analysis of an electrodynamic broadband energy harvester. Eur. Phys. J. Spec. Top. 224(14), 2919–2927 (2015)CrossRefGoogle Scholar
  6. 6.
    M.A. Clementino, R. Reginatto, S. da Silva, Modeling of piezoeletric energy harvesting considering the dependence of the rectifier circuit. J. Intell. Mater. Syst. Struct. 36, 283–292 (2014)Google Scholar
  7. 7.
    F. Cottone, H. Vocca, L. Gammaitoni, Nonlinear energy harvesting. Phys. Rev. Lett. 102, 080601 (2009)ADSCrossRefGoogle Scholar
  8. 8.
    H.L. Dai, Y.W. Yang, A. Abdelkefi, L. Wang, Nonlinear analysis and characteristics of inductive galloping energy harvesters. Commun. Nonlinear Sci. Numer. Simul. 59, 580–591 (2018)ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    A. Erturk, J. Hoffmann, D.J. Inman, A piezomagnetoelastic structure for broadband vibration energy harvesting. Appl. Phys. Lett. 94, 254102 (2009)ADSCrossRefGoogle Scholar
  10. 10.
    F.M. Foong, C.K. Thein, D. Yurchenko, On mechanical damping of cantilever beam-based electromagnetic resonators. Mech. Syst. Signal Process. 119, 120–137 (2019)ADSCrossRefGoogle Scholar
  11. 11.
    M.I. Friswell, S.F. Ali, O. Bilgen, S. Adhikari, A.W. Lees, G. Litak, Non-linear piezoelectric vibration energy harvesting from a vertical cantilever beam with tip mass. J. Intell. Mater. Syst. Struct. 23(13), 1505–1521 (2012)CrossRefGoogle Scholar
  12. 12.
    Z. Ghouli, M. Hamdi, F. Lakrad, M. Belhaq, Quasiperiodic energy harvesting in a forced and delayed Duffing harvester device. J. Sound Vib. 407, 271–285 (2017)ADSCrossRefGoogle Scholar
  13. 13.
    J.A.B. Gripp, L.C.S. Góes, O. Heuss, F. Scinocca, An adaptive piezoelectric vibration absorber enhanced by a negative capacitance applied to a shell structure. Smart Mater. Struct. 24(12), 125017 (2015)ADSCrossRefGoogle Scholar
  14. 14.
    Z. Hadas, L. Janak, J. Smilek, Virtual prototypes of energy harvesting systems for industrial applications. Mech. Syst. Signal Process. 110, 152–164 (2018)ADSCrossRefGoogle Scholar
  15. 15.
    E. Halvorsen, G. Litak, Statistics of a noise-driven elastic inverted pendulum. Eur. Phys. J. Appl. Phys. 70(1), 10901 (2015)ADSCrossRefGoogle Scholar
  16. 16.
    P. Harris, G. Litak, J. Iwaniec, C.R. Bowen, Recurrence plot and recurrence quantification of the dynamic properties of cross-shaped laminated energy harvester. Appl. Mech. Mater. 849, 95–105 (2016)CrossRefGoogle Scholar
  17. 17.
    P. Holmes, A nonlinear oscillator with a strange attractor. Philos. Trans. R. Soc. A 292, 429–448 (1979)ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    S. Ju, C. Ji, Impact-based piezoelectric vibration energy harvester. Appl. Energy 214, 139–151 (2018)CrossRefGoogle Scholar
  19. 19.
    P. Kamalinejad, C. Mahapatra, Z. Sheng, S. Mirabbasi, V.C.M. Leung, Y.L. Guan, Wireless energy harvesting for the internet of things. IEEE Commun. Mag. 53, 102–108 (2015)CrossRefGoogle Scholar
  20. 20.
    S. Kato, S. Ushiki, A. Masuda, A broadband energy harvester using leaf springs and stoppers with response stabilization control. J. Phys. Conf. Ser. 1052, 012083 (2018)CrossRefGoogle Scholar
  21. 21.
    J.M. Kluger, T.P. Sapsis, A.H. Slocum, Robust energy harvesting from walking vibrations by means of nonlinear cantilever beams. J. Sound Vib. 341, 174–194 (2015)ADSCrossRefGoogle Scholar
  22. 22.
    I. Kovacic, M. Brennan, The Duffing Equation: Nonlinear Oscillators and their Behavior (Wiley, 2011)Google Scholar
  23. 23.
    A. Kumar, R. Kiran, V.S. Chauhan, R. Kumar, R. Vaish, Piezoelectric energy harvester for pacemaker application: a comparative study. Mater. Res. Express 5, 075701 (2018)ADSCrossRefGoogle Scholar
  24. 24.
    Y. Liao, J. Liang, Unified modeling, analysis and comparison of piezoelectric vibration energy harvesters. Mech. Syst. Signal Process. 123, 403–425 (2019)ADSCrossRefGoogle Scholar
  25. 25.
    G. Litak, M.I. Friswell, S. Adhikari, Regular and chaotic vibration in a piezoelectric energy harvester. Meccanica 51(5), 1017–1025 (2016)MathSciNetCrossRefGoogle Scholar
  26. 26.
    G. Litak, A. Rysak, M. Borowiec, M. Scheffler, J. Gier, Vertical beam modal response in a broadband energy harvester. Proc. Inst. Mech. Eng. Part K J. Multi-Body Dyn. 230 (2016)Google Scholar
  27. 27.
    V.G. Lopes, J.V.L.L. Peterson, A. Cunha Jr., Numerical study of parameters influence over the dynamics of a piezo-magneto-elastic energy harvesting device (In XXXVII Congresso Nacional de Matemática Aplicada e Computacional, São José dos Campos, Brazil, 2017)Google Scholar
  28. 28.
    V.G. Lopes, J.V.L.L. Peterson, A. Cunha Jr, On the nonlinear dynamics of a bi-stable piezoelectric energy harvesting device, in 24th ABCM International Congress of Mechanical Engineering (COBEM 2017) (Curitiba, Brazil, 2017)Google Scholar
  29. 29.
    V.G. Lopes, J.V.L.L. Peterson, A. Cunha Jr, Analysis of the nonlinear dynamics of a bistable energy harvesting system with colored noise disturbances, in Conference of Computational Interdisciplinary Science (CCIS 2019) (2019)Google Scholar
  30. 30.
    Q. Lu, L. Liu, F. Scarpa, J. Leng, Y. Liu, A novel composite multi-layer piezoelectric energy harvester. Compos. Struct. 201, 121–130 (2018)CrossRefGoogle Scholar
  31. 31.
    W. Martens, U. von Wagner, G. Litak, Stationary response of nonlinear magneto-piezoelectric energy harvester systems under stochastic excitation. Eur. Phys. J. Spec. Top. 222(7), 1665–1673 (2013)CrossRefGoogle Scholar
  32. 32.
    F.C. Moon, P.J. Holmes, A magnetoelastic strange attractor. J. Sound Vib. 65, 275–296 (1979)ADSCrossRefGoogle Scholar
  33. 33.
    R. Naseer, H.L. Dai, A. Abdelkefi, L. Wang, Piezomagnetoelastic energy harvesting from vortex-induced vibrations using monostable characteristics. Appl. Energy 203, 142–153 (2017)CrossRefGoogle Scholar
  34. 34.
    D. Pan, F. Dai, Design and analysis of a broadband vibratory energy harvester using bi-stable piezoelectric composite laminate. Energy Convers. Manag. 169, 149–160 (2018)CrossRefGoogle Scholar
  35. 35.
    T. Pereira, A. Paula, A. Fabro, M. Savi. Random effects in a nonlinear vibration-based piezoelectric energy harvesting system. Int. J. Bifurc. Chaos, (in press) (2019)Google Scholar
  36. 36.
    J.V.L.L. Peterson, V.G. Lopes, A. Cunha Jr., Dynamic analysis and characterization of a nonlinear bi-stable piezo-magneto-elastic energy harvester, in MATEC Web of Conferences vol. 241 (2018), p. 01001Google Scholar
  37. 37.
    D. Puspitarini, A. Suzianti, H. Al Rasyid, Designing a sustainable energy-harvesting stairway: determining product specifications using triz method. Procedia Soc. Behav. Sci. 216, 938–947, in Urban Planning and Architectural Design for Sustainable Development (UPADSD) (2016)Google Scholar
  38. 38.
    T.M.P. Silva, M.A. Clementino, A. Erturk, C. de Marqui Jr., Equivalent electrical circuit framework for nonlinear and high quality factor piezoelectric structures. Mechatronics 54, 133–143 (2018)CrossRefGoogle Scholar
  39. 39.
    S. Stoykov, G. Litak, E. Manoach, Vibration energy harvesting by a timoshenko beam model and piezoelectric transducer. Eur. Phys. J. Spec. Top. 224(14), 2755–2770 (2015)CrossRefGoogle Scholar
  40. 40.
    M.A. Trindade, C.C. Pagani, L.P.R. Oliveira, Semi-modal active vibration control of plates using discrete piezoelectric modal filters. J. Sound Vib. 351, 17–28 (2015)ADSCrossRefGoogle Scholar
  41. 41.
    K. Vijayan, M.I. Friswell, H. Haddad Khodaparast, S. Adhikari, Non-linear energy harvesting from coupled impacting beams. Int. J. Mech. Sci. 96-97, 101–109 (2015)CrossRefGoogle Scholar
  42. 42.
    C. Wang, Q. Zhang, W. Wang, J. Feng, A low-frequency, wideband quad-stable energy harvester using combined nonlinearity and frequency up-conversion by cantilever-surface contact. Mech. Syst. Signal Process. 112, 305–318 (2018)ADSCrossRefGoogle Scholar
  43. 43.
    C. Wei, X. Jing, A comprehensive review on vibration energy harvesting: modelling and realization. Renew. Sustain. Energy Rev. 74, 1–18 (2017)CrossRefGoogle Scholar
  44. 44.
    X.D. Xie, Q. Wang, S.J. Wang, Energy harvesting from high-rise buildings by a piezoelectric harvester device. Energy 93, 1345–1352 (2015)CrossRefGoogle Scholar
  45. 45.
    Z. Zhou, W. Qin, W. Du, P. Zhu, Q. Liu, Improving energy harvesting from random excitation by nonlinear flexible bi-stable energy harvester with a variable potential energy function. Mech. Syst. Signal Process. 115, 162–172 (2019)ADSCrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Vinicius G. Lopes
    • 1
  • João Victor L. L. Peterson
    • 1
  • Americo Cunha Jr.
    • 1
    Email author
  1. 1.Universidade do Estado do Rio de JaneiroRio de JaneiroBrazil

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