Nonlinear Dynamics

, Volume 96, Issue 4, pp 2369–2392 | Cite as

Investigation of coupled lever-bistable nonlinear energy harvesters for enhancement of inter-well dynamic response

  • Kai YangEmail author
  • Fei Fei
  • Haichao An
Original Paper


This paper proposes two new coupled lever-bistable nonlinear energy harvesters to enhance the inter-well dynamic response for improvement of vibration energy harvesting. For the first harvester, the oscillator mass and lever-supporting mass are on different sides of the lever pivot; for the second, both the masses are on the same side. The fundamental-periodic inter-well dynamics of both the lever-bistable energy harvesters are analytically, numerically and experimentally investigated in this study. Their variation trends are firstly studied analytically with respect to different lever parameters, which are also mathematically interpreted afterward. Subsequently, experiments are conducted to validate the theoretically predicted variation trends. The analytical and experimental results show that both the lever-bistable energy harvesters with appropriate lever parameters can significantly outperform the conventional bistable energy harvester. Finally, through numerical investigations, this paper reveals that different initial conditions of the lever-bistable energy harvesters can lead to other different types of inter-well responses apart from the fundamental-periodic responses, e.g., subharmonic response. The numerical results show that the fundamental-periodic inter-well response is more beneficial to energy harvesting than other inter-well responses. The basin-of-attraction map corresponding to each type of inter-well response is drawn to describe the distributions of each type’s initial condition. Based on the basin-of-attraction maps, both the lever-bistable energy harvesters’ occurring probabilities of exhibiting fundamental-periodic inter-well response are evaluated, which can quantitatively illustrate the lever structural benefit to stabilization of this favorable inter-well response.


Bistable energy harvester Lever structure Inter-well response Basin of attraction 



This work is supported by National Natural Science Foundation of China (Grant Nos. 11802097, 51506063).

Compliance with ethical standards

Conflict of interest

All authors declare that they have no conflict of interest.

Research involving human participants and/or animals

This work is about the mechanical engineering. This research does not involve any human participants or animals.

Informed consent

Only the authors listed in the manuscript are involved into this work. The submission of this research is agreed by all the authors listed in the manuscript and is permitted by both the affiliations of the authors.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.School of Aerospace EngineeringHuazhong University of Science and TechnologyWuhanChina
  2. 2.Department of Mechanical EngineeringMcGill UniversityMontrealCanada

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