Loughborough University
10.1007%2Fs11071-018-4124-2.pdf (1.38 MB)
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On the dynamics of a nonlinear energy harvester with multiple resonant zones

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journal contribution
posted on 2018-02-09, 14:58 authored by Panagiotis Alevras, Stephanos TheodossiadesStephanos Theodossiades, Homer Rahnejat
The dynamics of a nonlinear vibration energy harvester for rotating systems is investigated analytically through harmonic balance, as well as by numerical analysis. The electromagnetic harvester is attached to a spinning shaft at constant speed. Magnetic levitation is used as the system nonlinear restoring force for broadening the resonant range of the oscillator. The system is modelled as a Duffing oscillator with linear frequency variation under static, as well as harmonic excitation. Behaviour charts and backbone curves are extracted for the fundamental harmonic response and validated against frequency response curves for selected cases, using direct numerical integration. It is found that variation in stiffness, together with asymmetric forcing gives rise to a novel structure of multiple resonant zones, incorporating mono-stable and bi-stable dynamics. Contrary to previously considered bi-stable energy harvesters, cross-well oscillations are realised through a transition from single-well potential energy to double-well with forward frequency sweep. Furthermore, in-well oscillations present a hardening behaviour, unlike the well-known softening in-well response of bi-stable Duffing oscillators. The analysis shows that the proposed system has multiple resonant responses to a frequency sweep, influenced by consecutive interacting backbone curves similar to a multimodal system. This combined effect of the transition to bi-stable dynamics and the hardening in-well oscillations induces resonant response of the harvester over multiple distinct frequency ranges. Thus, the system exhibits a broadened frequency response, enhancing its energy harvesting potential.


This work was supported by the Engineering and Physical Sciences Research Council (EPSRC) “Targeted energy transfer in powertrains to reduce vibration-induced energy losses” Grant (EP/L019426/1).



  • Mechanical, Electrical and Manufacturing Engineering

Published in

Nonlinear Dynamics




1271 - 1286


ALEVRAS, P., THEODOSSIADES, S. and RAHNEJAT, H., 2018. On the dynamics of a nonlinear energy harvester with multiple resonant zones. Nonlinear Dynamics, 92 (3), pp.1271–1286.


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This work is made available according to the conditions of the Creative Commons Attribution 4.0 International (CC BY 4.0) licence. Full details of this licence are available at: http://creativecommons.org/licenses/by/4.0/

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This is an Open Access Article. It is published by Springer under the Creative Commons Attribution 4.0 International Licence (CC BY). Full details of this licence are available at: http://creativecommons.org/licenses/by/4.0/




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