Abstract
In the first part of the chapter, we present some results on quasi-periodic (QP) vibration-based energy harvesting (EH) in a delayed van der Pol oscillator with modulated delay amplitude. Two examples are considered which include a delayed van der Pol harvester coupled either to a delayed or undelayed electromagnetic sub- system. The influence of delay parameters on the performance of the harvester has been examined. It is shown that a maximum amplitude of the response does not induce necessarily a maximum output power. In the second part, we investigate QP vibration-based EH in the case where the van der Pol oscillator is subjected to external harmonic excitation and coupled to a delayed piezoelectric component. Perturbation method is applied near a resonance to obtain approximation of the periodic and QP responses as well as the amplitude of the harvested powers. To guarantee the robustness of the QP vibration during energy extraction operation, a stability anal- ysis is performed and the QP stability chart is determined. Results show that in the presence of time delay in the electrical circuit of the excited van der Pol oscillator, it is possible to harvest energy from QP vibrations with a good performance over a broadband of system parameters away from the resonance. Numerical simulations are conducted to support the analytical predictions.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
N.G. Stephen, On energy harvesting from ambient vibration. J. Sound Vib. 293, 409–425 (2006)
G.A. Lesieutre, G.K. Ottman, H.F. Hofmann, Damping as a result of piezoelectric energy harvesting. J. Sound Vib. 269, 991–1001 (2004)
H.A. Sodano, D.J. Inman, G. Park, Generation and storage of electricity from power harvesting devices. J. Intell. Mater. Syst. 16, 67–75 (2005)
H.A. Sodano, D.J. Inman, G. Park, Comparison of piezoelectric energy harvesting devices for recharging batteries. J. Intell. Mater. Syst. 16, 799–807 (2005)
D.D. Quinn, A.L. Triplett, A.F. Vakakis, L.A. Bergman, Energy harvesting from impulsive loads using intestinal essential nonlinearities. J. Vib. Acoust. 133, 011004 (2011)
A. Abdelkefi, A.H. Nayfeh, M.R. Hajj, Modeling and analysis of piezoaeroelastic energy harvesters. Nonlinear Dyn. 67, 925–939 (2011)
A. Abdelkefi, A.H. Nayfeh, M.R. Hajj, Design of piezoaeroelastic energy harvesters. Nonlinear Dyn. 68, 519–530 (2012)
B.P. Mann, N.D. Sims, Energy harvesting from the nonlinear oscillations of magnetic levitation. J. Sound Vib. 319, 515–530 (2009)
A. Bibo, M.F. Daqaq, Energy harvesting under combined aerodynamic and base excitations. J. Sound Vib. 332, 5086–5102 (2013)
M. Hamdi, M. Belhaq, Quasi-periodic vibrations in a delayed van der Pol oscillator with time-periodic delay amplitude. J. Vib. Control (2015). https://doi.org/10.1177/1077546315597821
M. Belhaq, M. Hamdi, Energy harversting from quasi-periodic vibrations. Nonlinear Dyn. 86, 2193–2205 (2016)
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)
Z. Ghouli, M. Hamdi, M. Belhaq, Energy harvesting from quasi-periodic vibrations using electromagnetic coupling with delay. Nonlinear Dyn. 89, 1625–1636 (2017)
M. Belhaq, Z. Ghouli, M. Hamdi, Energy harvesting in a Mathieu-van der Pol-Duffing MEMS device using time delay. Nonlinear Dyn. 94, 2537–2546 (2018)
Z. Ghouli, M. Hamdi, M. Belhaq, Improving energy harvesting in excited Duffing harvester device using a delayed piezoelectric coupling, in MATEC Web of Conferences, vol. 241 (2018), pp. 01010
I. Kirrou, A. Bichri, M. Belhaq, Energy harvesting in a delayed Rayleigh harvester device, in MATEC Web of Conferences, vol. 241 (2018), pp. 01026
G. Stepan, T. Kalmr-Nagy, Nonlinear regenerative machine tool vibrations, in Proceedings of the 1997 ASME Design Engineering Technical Conferences, 16th ASME Biennial Conference on Mechanical Vibration and Noise (Sacramento, 1997), DETC97/VIB-4021 (1997), pp. 1–11
T. Kalmr-Nagy, G. Stepan, F.C. Moon, Subcritical Hopf bifurcation in the delay equation model for machine tool vibrations. Nonlinear Dyn. 26, 121–142 (2001)
R. Rusinek, A. Weremczuk, J. Warminski, Regenerative model of cutting process with nonlinear Duffing oscillator. Mech. Mech. Eng. 15, 129–143 (2011)
A.H. Nayfeh, D.T. Mook, Nonlinear Oscillations (Wiley, New York, 1979)
L.E. Shampine, S. Thompson, Solving delay differential equations with dde23 (2000). http://www.radford.edu/~thompson/webddes/tutorial.pdf
M. Belhaq, M. Houssni, Quasi-periodic oscillations, chaos and suppression of chaos in a nonlinear oscillator driven by parametric and external excitations. Nonlinear Dyn. 18, 1–24 (1999)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Ghouli, Z., Hamdi, M., Belhaq, M. (2019). The Delayed van der Pol Oscillator and Energy Harvesting. In: Belhaq, M. (eds) Topics in Nonlinear Mechanics and Physics. Springer Proceedings in Physics, vol 228. Springer, Singapore. https://doi.org/10.1007/978-981-13-9463-8_4
Download citation
DOI: https://doi.org/10.1007/978-981-13-9463-8_4
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-13-9462-1
Online ISBN: 978-981-13-9463-8
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)