Nonlinear Dynamics

, Volume 98, Issue 3, pp 1807–1819 | Cite as

Stability and bifurcation analysis of the period-T motion of a vibroimpact energy harvester

  • Larissa SerdukovaEmail author
  • Rachel Kuske
  • Daniil Yurchenko
Original paper


Stability and bifurcation conditions for a vibroimpact motion in an inclined energy harvester with T-periodic forcing are determined analytically and numerically. This investigation provides a better understanding of impact velocity and its influence on energy harvesting efficiency and can be used to optimally design the device. The numerical and analytical results of periodic motions are in excellent agreement. The stability conditions are developed in non-dimensional parameter space through two basic nonlinear maps based on switching manifolds that correspond to impacts with the top and bottom membranes of the energy harvesting device. The range for stable simple T-periodic behavior is reduced with increasing angle of incline \(\beta \), since the influence of gravity increases the asymmetry of dynamics following impacts at the bottom and top. These asymmetric T-periodic solutions lose stability to period doubling solutions for \(\beta \ge 0\), which appear through increased asymmetry. The period doubling, symmetric and asymmetric periodic motion are illustrated by bifurcation diagrams, phase portraits and velocity time series.


Energy harvesting Vibroimpact system Output voltage Period doubling and saddle-node bifurcations Periodic solutions Non-smooth dynamics 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA
  2. 2.IMPEEHeriot-Watt UniversityEdinburghUK

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