Broadband energy harvesting from time-delayed nonlinear oscillations of magnetic levitation

This article investigates quasiperiodic energy harvesting in a nonlinear vibration-based harvester, consisting of delayed nonlinear vibrations from magnetic levitation subjected to harmonic base acceleration, in which time-delay is introduced. For energy harvesting, a coil made up of seven layers of 36 gauges wound around the outer casing is utilized. The first- and second-order perturbation approximations are used to obtain the frequency responses of the power and vibration amplitudes in the vicinity of primary resonance. Numerical results are presented to verify the correctness of the analytical solutions. The results show that there is a good agreement between the second approximation and the numerical method; thus, we used the second-order perturbation to present the results. The impact of several parameters on the power and vibration amplitudes in the absence and presence of delay is studied. It was observed that using the nonlinear vibrations due to magnetic levitation in the absence and presence of the delay enables energy harvesting over broadband frequencies distant from primary resonance, which benefits preventing the instability and hysteresis regions near resonance. Dynamic behaviors of the motion are shown in the form of time histories and phase portraits. The results indicate periodic and quasiperiodic motions for the different values of the delay parameters. Also, the effects of the separation distance between magnets (d0), without and with time-delay, on the vibration and power amplitudes were examined. It was observed that the d0, for both points chosen from stable periodic solution and unstable periodic solution, has a significant influence on the system behavior. Thus, choosing proper values for these parameters enables the device to extract more power in lower and broadband excitation frequencies. Besides, we illustrate that for specific values of d0 and delay time parameters, the maximum system power output is not necessarily accompanied by maximum vibration amplitude.