Nonlinear Dynamics

, Volume 98, Issue 3, pp 2053–2066 | Cite as

Two-step approximation procedure for random analyses of tristable vibration energy harvesting systems

  • Ming XuEmail author
  • Xiaoya Li
Original paper


Vibration energy harvesters have been of great interest for self-power sources. Various harvester designs have been developed to achieve high performance, i.e., considerable output power. The tristable energy harvester is among the best designs due to its large-amplitude oscillation and low threshold excitation intensities under some conditions. However, the theory and analysis of tristable vibration harvesters under random excitations have not been considered. Therefore, an approximate procedure, which includes two successive steps, is established to predict the performance of the tristable energy harvester under Gaussian white noise excitation. In the first step, the interaction between the auxiliary circuit and the mechanical system is decoupled with harmonic functions, and the mechanical–electrical system becomes a modified mechanical system with additional dissipative and conservative terms. In the second step, an equivalent mechanical system associated with the modified mechanical system is established through an unconventional equivalent nonlinearization technique. The statistical quantities of the tristable harvesting system are approximately equal to those of the equivalent mechanical system. The numerical results illustrate the prediction accuracy of the approximation procedure in terms of the mean output power.


Random response Tristable vibration energy harvesting system Modified mechanical system Equivalent nonlinearization technique 



M. Xu acknowledges the National Natural Science Foundation of China under Grant Nos. 11402258, 11872061.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.College of Metrology and Measurement EngineeringChina Jiliang UniversityHangzhouChina

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