Dynamical analysis of an asymmetric tri-stable hybrid energy harvesting system driven by colored noise

The piezoelectric–electromagnetic hybrid vibration energy harvester (HVEH) has proven to be a favorable option to overcome the low-power generation issue of individual energy conversion mechanism. Considering the inevitable asymmetry and the ubiquitous ambient noise in engineering, the stochastic dynamics of an asymmetric tri-stable HVEH driven by colored noise is investigated in this paper. Facing such difficult challenges as multiple couplings, strong nonlinearity, multiple attractors, asymmetry and noise in the system, a novel stochastic averaging technique is developed to explore the dynamics. The energy-dependent frequency is first established according to the operation mechanism of the asymmetric triple-well potential function. Then, the stochastic averaging is extended to obtain the analytical expressions of the stationary probability density, the mean-square voltage, the mean-square current and the mean output power. Finally, the influences of the asymmetric parameter and colored noise on the steady-state response, the mean output power and the stochastic resonance are mainly analyzed. Results show that the energy harvesting performance can be effectively enhanced by reducing asymmetry and correlation time, adopting hybrid design and choosing appropriate electromechanical coupling coefficient and time constants ratio. The developed stochastic averaging technique is well validated by Monte Carlo numerical simulation.