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

Larissa Serdukova*, Rachel Kuske, Daniil Yurchenko

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

21 Citations (Scopus)
67 Downloads (Pure)


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 β, 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 β≥ 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.

Original languageEnglish
Pages (from-to)1807–1819
Number of pages13
JournalNonlinear Dynamics
Issue number3
Early online date26 Oct 2019
Publication statusPublished - Nov 2019


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

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Aerospace Engineering
  • Ocean Engineering
  • Mechanical Engineering
  • Applied Mathematics
  • Electrical and Electronic Engineering


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