Skip to main content

Advertisement

SpringerLink
Log in

A Comparison of Time-Frequency Methods for Nonlinear Dynamics and Chaos Analysis in an Energy Harvesting Model

  • General and Applied Physics
  • Published:
Brazilian Journal of Physics Aims and scope Submit manuscript

Abstract

In this paper, an energy harvesting model based on a portal frame structure, modeled as a duffing system, with a non-ideal excitation force, DC motor with an unbalanced mass, is presented and the piezoelectric coupling is designed to exhibit nonlinear characteristics. Nonlinearity included provides higher power output over a wide frequency range. This analysis was carried out by numerical simulation of the proposed mathematical formulation. Thus, the bifurcation diagram and the largest Lyapunov exponents are plotted to investigate the dynamic behavior by ranging the voltage applied to the DC motor. In this way, power harvesting is analyzed for two different dynamic responses: periodic and chaotic behavior. Furthermore, this work exhibits an application of frequency-domain techniques, such as short-time Fourier transform, continuous wavelet transform, synchrosqueezed wavelet transform, and Wigner-Ville distribution methods. These methods are often used to analyze non-stationary signals, allowing the verification of dynamic behavior and power harvesting. Therefore, this paper aims to apply the time-frequency methods, mentioned previously, to analyze the mechanical system response in different behaviors.

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. R. Bogue, Energy harvesting and wireless sensors: A review of recent developments. Sens. Rev. 29, 194–199 (2009)

    Article  Google Scholar 

  2. K. Uchino, Piezoelectric energy harvesting systems. J. Phys. Conf. Ser., 1052 (2018)

  3. J. Siang, M.H. Lim, M.S. Leong, Review of vibration-based energy harvesting technology: mechanism and architectural approach. Int. J. Energy Res., 42 (2018)

  4. M.F. Lumentut, I.M. Howard, Analytical and experimental comparisons of electromechanical vibration response of a piezoelectric bimorph beam for power harvesting. Mech Syst Signal Process. 36, 66–86 (2013)

    Article  ADS  Google Scholar 

  5. H. Wang, Q. Meng, Analytical modeling and experimental verification of vibration-based piezoelectric bimorph beam with a tip-mass for power harvesting. Mech Syst Signal Process. 36, 193–209 (2013)

    Article  ADS  Google Scholar 

  6. Z. Chen, Y. Yang, Z. Lu, Y. Luo, Broadband characteristics of vibration energy harvesting using onedimensional phononic piezoelectric cantilever beams. Physica B: Condens Matter. 410, 5–12 (2013)

    Article  ADS  Google Scholar 

  7. C. Wei, X. Jing, A comprehensive review on vibration energy harvesting: Modelling and realization. J. Renew. Sustain. Energy Rev. 74, 1–18 (2017)

    Article  MathSciNet  Google Scholar 

  8. F. Cottone, Nonlinear piezoelectric generators for vibration energy harvesting. Universita’ Degli Studi Di Perugia, Dottorato Di Ricerca In Fisica, XX Ciclo (2007)

  9. A. Erturk, D.J. Inman. Piezoelectric Energy Harvesting (Wiley, USA, 2011)

    Book  Google Scholar 

  10. L. Cveticanin, M. Zukovic, J.M. Balthazar. Dynamic of Mechanical System with Non-Ideal Excitation (Springer, Berlin, 2018)

    Book  Google Scholar 

  11. J.M. Balthazar, R.M.L.R.F. Brasil, F. Garzeri, On non-ideal simple portal frame structural model: Experimental results under a non-ideal excitation. Appl. Mech. Mater. 1, 51–58 (2004)

    Article  ADS  Google Scholar 

  12. L. Cveticanin, M. Zukovic, D. Cveticanin, Non-ideal source and energy harvesting. Acta Mech. 228, 3369–3379 (2017)

    Article  MathSciNet  Google Scholar 

  13. L. Cveticanin, M. Zukovic, Motion of a motor-structure non-ideal system. Europ. J. Mech. 53, 229–240 (2015)

    Article  MathSciNet  Google Scholar 

  14. J.L.P. Felix, J.M. Balthazar, R.T. Rocha, A.M. Tusset, F.C. Janzen, On vibration mitigation and energy harvesting of a non-ideal system with autoparametric vibration absorber system. Meccanica. 53, 1–12 (2018)

    Article  MathSciNet  Google Scholar 

  15. J.P.C.V. Norenberg, M. Varanis, J.M. Balthazar, A.M. Tusset, in Dynamics analysis of the portal frame model with non-ideal drive as an energy harvester. 10th National Congress of Mechanical Engineering (ABCM, Salvador, 2018)

  16. E.F. Crawley, E.H. Anderson, Detailed models of piezoceramic actuation of beams. J. Intll. Mat. Sys. Struct. 1, 4–25 (1990)

    Article  Google Scholar 

  17. A. Triplett, D.D. Quinn, The effect of non-linear piezoelectric coupling on vibration-based energy harvesting. J. Intell. Mat. Syst. Struct. 20, 1959–1967 (2009)

    Article  Google Scholar 

  18. N.E. du Toit, B.L. Wardle, Experimental verification of models for microfabricated piezoelectric vibration energy harvesters. AIAA J. 45, 1126–1137 (2007)

    Article  ADS  Google Scholar 

  19. J. Twiefel, B. Richter, T. Sattel, J. Wallaschek, Power output estimation and experimental validation for piezoelectric energy harvesting systems. J. Electroceram. 20, 203–208 (2008)

    Article  Google Scholar 

  20. J.B. Allen, L.R. Rabiner, A unified approach to short-time Fourier analysis and synthesis. Proc. IEEE. 65, 1558–1564 (1977)

    Article  ADS  Google Scholar 

  21. M. Varanis, J.M. Balthazar, A. Silva, A.A.G. Mereles, R. Pederiva, Remarks on the Som-merfeld effect characterization in the wavelet domain. J. Vib. Cont. 25, 98–108 (2018)

    Article  Google Scholar 

  22. R.W. Schafer, L.R. Rabiner, Design and analysis of a speech analysis- synthesis system based on short time Fourier analysis. IEEE Trans. Audio Electroacoust. 21, 165–174 (1973)

    Article  Google Scholar 

  23. D. Griffin, J. Lim, Signal estimation from modified short-time Fourier transform. IEEE Trans. Acoust. Speech Signal Process. 32, 236–243 (1984)

    Article  ADS  Google Scholar 

  24. I. Daubechies. Ten Lectures on Wavelets (SIAM, Philadelphia, 1992)

    Book  Google Scholar 

  25. S. Mallat. A Wavelet Tour of Signal Processing: The Sparse Way (Academic Press, Burlington, 2008)

    MATH  Google Scholar 

  26. P.S. Addison. The Illustrated Wavelet Transform Handbook: Introductory Theory and Applications in Science, Engineering, Medicine and Finance (CRC Press, USA, 2017)

    MATH  Google Scholar 

  27. I. Daubechies, J. Lu, H.T. Wu, Synchrosqueezed wavelet transforms: An empirical mode decomposition-like tool. App. Comp. Harm. Anal. 30, 243–261 (2011)

    Article  MathSciNet  Google Scholar 

  28. M.H. Rafiei, H. Adeli, A novel unsupervised deep learning model for global and local health condition assessment of structures. Eng. Struct. 156, 598–607 (2017)

    Article  Google Scholar 

  29. Y. Lei, J. Lin, Z. He, M.J. Zuo, A review on empirical mode decomposition in fault diagnosis of rotating machinery. Mech. Syst. Signal Process. 35, 108–126 (2013)

    Article  ADS  Google Scholar 

  30. Y. Chen, T. Liu, X. Chen, J. Li, E. Wange, Time-frequency analysis of seismic data using synchrosqueezing wavelet transform. J. Seism. Explor. 23, 303–312 (2014)

    Google Scholar 

  31. L. Cohen, Time-frequency distributions-A review. Proc. IEE. 77, 941–981 (1989)

    Article  ADS  Google Scholar 

  32. G. Matz, F. Hlawatsch, Wigner distributions (nearly) everywhere: Time-frequency analysis of signals, systems, random processes, signal spaces, and frames. Signal Process. 83, 1355–1378 (2003)

    Article  Google Scholar 

  33. F. Peyrin, R. Prost, A unified definition for the discrete-time, discrete-frequency and discrete-time/frequency Wigner distributions. Signal Process. 34, 858–867 (1986)

    Google Scholar 

  34. L. Debnath, The Wigner-Ville distribution and time-frequency signal analysis. Wavelet Transf. Appl., 307–360 (2002)

  35. M.A. Karami, D.J. Inman, Equivalent damping and frequency change for linear and nonlinear hybrid vibrational energy harvesting systems. J. Sound Vib. 330, 5583–5597 (2011)

    Article  ADS  Google Scholar 

  36. G. Sebald, H. Kuwano, D. Guyomar, B. Ducharne, Experimental Duffing oscillator for broadband piezoelectric energy harvesting. Smart Mat. Struct. 20, 102001 (2011)

    Article  ADS  Google Scholar 

  37. J.S.A.E. Fouda, B. Bodo, G.M.D. Djeufa, S.L. Sabat, . Experimental chaos detection in the Duffing oscillator. 33, 259–269 (2016)

    Google Scholar 

  38. I. Iliuk, J.M. Balthazar, A.M. Tusset, J.R.C. Piqueira, B.R. Pontes, J.L.P. Felix, A.́M. Bueno, Application of passive control to energy harvester efficiency using a nonideal portal frame structural support system. J. Intell. Mat. Syst. Struct. 25, 417–429 (2014)

    Article  Google Scholar 

  39. I. Iliuk, J.M. Balthazar, A.M. Tusset, J.L.P. Felix, JrB. R. Pontes, On non-ideal and chaotic energy harvester behavior. Diff. Eq. Dyn. Syst. 21, 93–104 (2013)

    Article  MathSciNet  Google Scholar 

  40. R. Benítez, V. Bolós, M. Ramírez, A wavelet-based tool for studying non-periodicity. Comput. Math. Appl. 60, 634–641 (2010)

    Article  MathSciNet  Google Scholar 

  41. B. Boashash, P. Black, An efficient real-time implementation of the Wigner-Ville distribution. IEEE Trans. Acous. 35, 1611–1618 (1987)

    Article  Google Scholar 

  42. S. Qian, D. Chen, Decomposition of the Wigner-Ville distribution and time-frequency distribution series. IEEE Trans. Signal Process. 42, 2836–2842 (1994)

    Article  ADS  Google Scholar 

  43. P. Flandrin. Explorations in Time-frequency Analysis (Cambridge University Press, Cambridge, 2018)

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Engineering, Federal University of Grande Dourados, Dourados, 79825070, MS, Brazil

    Marcus Varanis, João Pedro C. V. Norenberg & Clivaldo Oliveira

  2. King Abdullah University of Science and Technology, Jeddah, 23955, Saudi Arabia

    Rodrigo T. Rocha

  3. Federal University Technology of Paraná, Ponta Grossa, PR, 84016-210, Brazil

    José Manoel Balthazar & Ângelo Marcelo Tusset

Authors
  1. Marcus Varanis
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. João Pedro C. V. Norenberg
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Rodrigo T. Rocha
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Clivaldo Oliveira
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. José Manoel Balthazar
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Ângelo Marcelo Tusset
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Marcus Varanis.

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

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Varanis, M., Norenberg, J.P.C.V., Rocha, R.T. et al. A Comparison of Time-Frequency Methods for Nonlinear Dynamics and Chaos Analysis in an Energy Harvesting Model. Braz J Phys 50, 235–244 (2020). https://doi.org/10.1007/s13538-019-00733-x

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13538-019-00733-x

Keywords

Search

Navigation