Dynamics of a tri-stable hybrid energy harvester under narrow-band random excitation

This paper aims to reveal the stochastic dynamics of a tri-stable piezoelectric–electromagnetic hybrid vibration energy harvester (HVEH) driven by narrow-band random excitation for purpose of enhancing the energy harvesting performance. The steady-state solutions of the electromechanical coupling tri-stable HVEH in the symmetric case are derived by the method of multiple scales, which are verified by Monte Carlo simulations. Results show that the stochastic jump phenomenon exists and the operational bandwidth of HVEH can be extended. The effects of narrow-band random excitation, critical system parameters and asymmetric potential function on stochastic dynamics are discussed. It is found that the miniaturization design of the HVEH can be optimized and the mean output power can be improved by selecting appropriate system parameters. Moreover, compared with the symmetric structure, in the case of the same highest potential-well depth, the asymmetric structure with a smaller potential-well distance is beneficial for HVEH to achieve high-energy inter-well oscillation under low-level excitation. Meanwhile, the power conversion efficiency reaches the maximum in the high-energy inter-well oscillations triggered at the critical excitation amplitude.