Simulation of a Duffing oscillator for broadband piezoelectric energy harvesting

Vibration energy harvesters are usually resonant mechanical systems working at resonance. The subsequent mechanical amplification results in output powers multiplied by the mechanical quality factor when compared to non-resonant systems. The main drawback is the difficulty of matching a given vibration frequency range to the energy harvester's resonance frequency. Among several techniques, the use of nonlinear mechanical resonators was proposed in several studies for enlarging energy harvester power bandwidth. In addition, microelectromechanical systems become nonlinear when driven even at moderate levels due to their small size. This paper is devoted to a theoretical study of a Duffing oscillator exhibiting piezoelectric electromechanical coupling. After presenting the dimensionless model, it is solved both in the frequency domain and in the time domain. The frequency-domain simulations show that a huge gain in bandwidth is possible when the resonator is highly nonlinear. Special attention has been paid to the influence of electromechanical coupling. However, this encouraging result is counterbalanced by the difficulty to make the resonator reach high level vibration. Indeed, the Duffing oscillator exhibits a frequency range where two harmonic solutions are possible. When excited with sine bursts or colored noise, the oscillator remains most of the time on the lowest solution. From simulations in the time domain, it is shown that fast burst perturbation (FBP) applied to the piezoelectric voltage may induce the jump from lowest solution to highest solution. Consequently a huge gain may be expected in output power. Finally, the resonator is excited with colored noise and the previously developed strategy is applied. Once again, the mean output power may be greatly enhanced.