Skip Navigation Links
Journal of Vibration Testing and System Dynamics

C. Steve Suh (editor), Pawel Olejnik (editor),

Xianguo Tuo (editor)

Pawel Olejnik (editor)

Lodz University of Technology, Poland


C. Steve Suh (editor)

Texas A&M University, USA


Xiangguo Tuo (editor)

Sichuan University of Science and Engineering, China


Energy Harvesting from Quasiperiodic Vibrations in a Delayed Rayleigh-Duffing Harvester Device

Journal of Vcibration Testing and System Dynamics 4(2) (2020) 191--200 | DOI:10.5890/JVTSD.2020.06.006

Amine Bichri$^{1}$, Ilham Kirrou$^{2}$, Mohamed Belhaq$^{3}$

$^{1}$ Departement of physics, Laboratory of MMESA FSTE, University Moulay Ismail, Morocco

$^{2}$ MMGC Group ENSA-Agadir, University Ibn Zohr, Morocco

$^{3}$ FSAC, University Hassan II Casablanca, Morocco

Download Full Text PDF



This paper studies quasiperiodic vibration-based energy harvesting in a delayed Rayleigh-Dung oscillator coupled to a piezoelectric harvester device. Analytical investigation is performed using the multiple scales method to obtain approximation of periodic and quasiperiodic responses as well as the corresponding output power. The influence of different parameters of the harvester on the amplitude of solutions and powers is examined. Results show that for appropriate values of the delay parameters, quasiperiodic vibration-based energy harvesting is significantly improved far from the resonance while the periodic vibration-based one is almost absent near the resonance.


  1. [1]  Belhaq, M. and Hamdi, M. (2016), Energy harvesting from quasiperiodic vibrations, Nonlinear Dyn., 86, 2193-2205.
  2. [2]  Kammer, A.S. and Olgac, N., (2016), Delayed feedback vibration absorbers to enhance energy harvesting, J. Sound Vib., 363, 54-67.
  3. [3]  Ghouli, Z., Hamdi, M., Lakrad, F., and Belhaq, M., (2017), Quasiperiodic energy harvesting in a forced and delayed Duffing harvester device, J. Sound Vib., 407, 271-285.
  4. [4]  Ghouli, Z., Hamdi, M., and Belhaq, M. (2017), Energy harvesting from quasi-periodic vibrations using electromagnetic coupling with delay, Nonlinear Dyn., 89, 1625-1636.
  5. [5]  Belhaq, M., Ghouli, Z., and Hamdi, M., (2018), Energy harvesting in a Mathieu-van der Pol-Duffing MEMS device using time delay, Nonlinear Dyn., 94, 2537-2546.
  6. [6]  Felix, J.L.P., Balthazar, J.M., and Brasil, R.M.L.R.F., (2009), Comments on nonlinear dynamics of a non-ideal Duffing-Rayleigh oscillator: numerical and analytical approaches, J. Sound Vib., 319, 1136-1149.
  7. [7]  Kanai, Y. and Yabuno, H., (2012), Creation-annihilation process of limit cycles in the Rayleigh-Duffing oscillator, Nonlinear Dyn., 70, 1007-1016.
  8. [8]  Qriouet, M.T. and Mira, C. (2000), Reducible fractional harmonics generated by the non-autonomous Duffing-Rayleigh equation. Pockets of reducible harmonics and Arnold's tongues, Int. J. Bif. and Chaos, 10, 1345- 1366.
  9. [9]  Siewe, S.M., Tchawoua, C., and Rajasekar S. (2012), Parametric resonance in the Rayleigh-Duffing oscillator with time-delayed feedback, Comm. Nonl. Sc. Numerical Sim., 17, 4485-4493.
  10. [10]  Mihara, T. and Kawakami, H. (1996), Synchronization and chaos of coupled Duffing-Rayleigh oscillators, IEEE Transactions on Fundamentals of Electronics, Comm. Comp. Sciences, E79-A, 1581-1586.
  11. [11]  Miwadinou, C.H., Monwanou, A.V., and Chabi Orou, J.B., (2013), Active Control of the Parametric Resonance in the Modified Rayleigh-Duffing Oscillator, arXiv:1303.0536 [physics. u-dyn]
  12. [12]  Guin, A., Dandapathak, M., Sarkar, S., and Sarkar, B.C., (2017), Birth of oscillation in coupled non-oscillatory Rayleigh-Duffing oscillators, Comm. Nonl. Sc. Numerical Sim., 42, 420-436.
  13. [13]  Zhou, L., Liu, S., and Chen, F. (2016), Chaotic dynamics of a Rayleigh-Duffing oscillator with periodically external and parametric excitations, Proceedings of the 6th International Conference on Mechatronics, Materials, Biotechnology and Environment (ICMMBE 2016), Series:Advances in Engineering Research,
  14. [14]  Belhaq, M. and Houssni, M. (1999), Quasi-periodic oscillations, chaos and suppression of chaos in a nonlinear oscillator driven by parametric and external excitations, Nonlinear Dyn., 18, 1-24.
  15. [15]  Nayfeh, A.H. and Mook, D.T. (1979), Nonlinear Oscillations, Wiley, New York.
  16. [16]  Nayfeh, A.H. (1981), Introduction to Perturbation Techniques, New York: Wiley.