Nonlinear Dynamics

, Volume 94, Issue 4, pp 2537–2546 | Cite as

Energy harvesting in a Mathieu–van der Pol–Duffing MEMS device using time delay

  • Mohamed BelhaqEmail author
  • Zakaria Ghouli
  • Mustapha Hamdi
Original Paper


This paper investigates quasi-periodic vibration-based energy harvesting in a delayed nonlinear MEMS device consisting of a delayed Mathieu–van der Pol–Duffing type oscillator coupled to a delayed piezoelectric coupling mechanism. We use the multiple scales method to approximate the quasi-periodic response and the related power output near the principal parametric resonance. The effect of time delay on the energy harvesting performance is studied. It is shown that for appropriate combination of time delay parameters, there exists an optimum range of excitation frequency beyond the resonance where quasi-periodic vibration-based energy harvesting is maximum. Numerical simulations are performed to confirm the analytical predictions.


Energy harvesting Delayed Mathieu–van der Pol–Duffing oscillator Quasi-periodic vibrations Delayed piezoelectric coupling 


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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  • Mohamed Belhaq
    • 1
    Email author
  • Zakaria Ghouli
    • 1
  • Mustapha Hamdi
    • 2
  1. 1.Faculty of Sciences Aïn ChockUniversity Hassan II of CasablancaCasablancaMorocco
  2. 2.Faculty of Science and Technology-Al HoceimaUniversity Mohammed IOujdaMorocco

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