Dynamics of a delayed Duffing-type energy harvester under narrow-band random excitation

In this paper, a Duffing-type energy harvester with time delay circuit under narrow-band random excitation is studied by using the method of multiple scales. The analytical expressions of the steady-state responses near the principal resonance and their stable conditions are derived. Results show that the phenomenon of stochastic jump is found, and the operational bandwidth of the nonlinear energy harvester can be extended. The effects of frequency detuning, noise intensity, time delay, piezoelectric coupling, and time constant ratio on the dynamical behaviors are discussed. From the viewpoint of improving system performance and optimizing harvester design, a proper choose of time delay and feedback gain is proposed by the power conversion efficiency and the RMS voltage. It indicates that the negative feedback gain is favorable for an energy harvester to provide more electrical output power and miniaturize design. Moreover, the Monte Carlo simulations are given to verify the validity of the theoretical method.