Simulation of a Duffing oscillator for broadband piezoelectric energy harvesting

Abstract

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.

Nonlinear Hybrid Piezoelectric and Electromagnetic Energy Harvesting Driven by Colored Excitation

“…In general, different from previous studies for PE or EM energy harvester [32,35,37], nonlinearities generated by additional magnet interactions could be beneficial for hybrid PE and EM As shown in Figure 6, output performances based on analytical expressions of nonlinear hybrid piezoelectric and electromagnetic energy harvester are consistent with theoretical results through Energies 2018, 11, 498 13 of 23 solving 45 linearly coupled equations, the difference between modeling values obtained by two theoretical models is rather small. As a consequence, it demonstrates that it is feasible to predict output characteristics of nonlinear hybrid PE and EM energy harvester under colored excitation using the presented theoretical model again.…”

“…Daqaq et al [32] demonstrated that the expected value of the output power will decrease with the stiffness-type nonlinearity. After verification through numerical and experimental methods, Sebald et al [35,37] reached a similar conclusion for a Duffing-type PE oscillator under colored excitation. Nevertheless, the effects of introducing nonlinear stiffness into a randomly excited hybrid PE and EM energy harvester on output characteristics could be quite different.…”

“…In general, different from previous studies for PE or EM energy harvester [32,35,37], nonlinearities generated by additional magnet interactions could be beneficial for hybrid PE and EM energy harvesting because it lowers the natural frequency and provides more efficient transduction under colored excitation.…”

“…Daqaq et al [32][33][34] analyzed that a white Gaussian excited Duffing-type PE or EM energy harvester cannot improve the power generation over linear harvesters. Sebald et al [35] and Green et al [36] corroborated these findings and showed that linear and nonlinear energy harvesters will produce exactly the same power levels when both are excited with white noise. Under (band-limited) colored excitation, generating nonlinear stiffness in a PE or EM energy harvester will even hinder power output.…”

Statistics of a noise-driven elastic inverted pendulum

“…This is so either because design constraints make linear response unattainable, or because nonlinearities are believed useful in tailoring the device behaviour to the vibration of the environment. Examples of strongly nonlinear devices are found among harvesters of all the three main transducer types, i.e., electromagnetic [2][3][4], piezoelectric [5][6][7][8][9] and electrostatic [10][11][12][13][14] generators.…”