On the dynamics of a nonlinear energy harvester with multiple resonant zones

Research output: Contribution to journalArticlepeer-review


  • P Alevras
  • Stephanos Theodossiades
  • Homer Rahnejat

Colleges, School and Institutes

External organisations

  • Loughborough University


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 realized 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 multi-modal 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.


Original languageEnglish
Pages (from-to)1271-1286
Number of pages16
JournalNonlinear Dynamics
Issue number3
Early online date23 Feb 2018
Publication statusPublished - 1 May 2018


  • Backbone curve, Bi-stable dynamics, Duffing oscillator, Energy harvesting, In-well oscillations