Stochastic analysis of a time-delayed viscoelastic energy harvester subjected to narrow-band noise

Vibration energy harvester (VEH) has proven to be a favorable potential device to supply continuous energy for electric components. Researchers have done a lot of investigations on VEH in recent years. However, there are few studies on delayed VEH with viscoelastic property under random excitation. A new viscoelastic energy harvester with time delay subjected to narrow-band random excitation is investigated in this paper. Firstly, we utilize the multiple scales method to obtain the analytical approximations of the steady-state amplitude close to the primary resonance. Secondly, Monte Carlo simulations are applied to verify the correctness of the proposed method. Results demonstrate the satisfactory accuracy of the method presented in this paper. Then, the phenomena of stochastic jump, stochastic bifurcation, and the extension of the effective bandwidth of VEH can be found. Finally, the influence of system parameters on the mean square voltage and mean output power are discussed. It is shown that a negative feedback gain is profitable to the enhancement of the performance of VEH, and we find that the piezoelectric coupling term has a positive effect on the mean square voltage and mean output power. The mean square voltage and mean output power can reach the maximum at an appropriate time delay and feedback gain. These results indicate that the narrow-band random excitation has an important effect on the dynamics of the delayed vibration energy harvester with viscoelastic property, namely a large dose of noise intensity can decline the responses in the energy harvester.