Dynamics of a Tri-Stable Energy Harvesting System With Time-Delay Feedback Under Narrow-Band Random Excitation

A tri-stable energy harvester with time-delay feedback control under narrow-band random excitation was proposed. The steady-state responses of the energy harvesting system near the main resonance were obtained with the multi-scale method. Moreover, the Ist-order and 2nd-order nontrivial steady-state moments of the system were derived with the moment method, and their accuracy was also verified through the Monte Carlo simulations. Based on the above steady-state response moments, the effects of system parameters on the performances of the energy harvester were discussed in detail. The results show that, increasing the nonlinear stiffness coefficient can enlarge the working bandwidth of the energy harvester system, while increasing the narrowband random excitation intensity can enhance the output voltage of the energy harvester. The 2nd-order steady-state moments visibly decrease with the piezoelectric coupling term, which indicates that a larger piezoelectric coupling term is beneficial to the miniaturization of energy harvesters. Furthermore, a negative control feedback gain is beneficial to realize the miniaturization design of the energy harvester and increase the power output of the system effectively. The findings provide a theoretical basis for further exploration and optimization of energy harvesting systems.