Experimental Duffing oscillator for broadband piezoelectric energy harvesting

This paper presents an experimental piezoelectric energy harvester exhibiting strong mechanical nonlinear behavior. Vibration energy harvesters are usually resonant mechanical systems working at resonance. The resulting mechanical amplification gives an output power multiplied by the mechanical quality factor Q when compared to non-resonant systems, provided that the electromechanical coupling k(2) is high as well as the mechanical quality factor Q. However, increasing the Q value results in a narrowband energy harvester, and the main drawback is the difficulty of matching a given vibration frequency range to the energy harvester's resonance frequency. Mechanical nonlinear stiffness results in a distortion of the resonance peak that may lead to a broadband energy harvesting capability while keeping a large output power as for high Q systems. This paper is devoted to an experimental study of a Duffing oscillator exhibiting piezoelectric electromechanical coupling. A nonlinear electromechanical model is first presented including piezoelectric coupling, a nonlinear stiffness as for a Duffing oscillator, and an additional nonlinear loss term. Under harmonic excitation, it is shown that for a particular excitation range, the power frequency bandwidth is multiplied by a factor of 5.45 whereas the output power is decreased by a factor of 2.4. In addition, when compared to a linear system exhibiting the same power bandwidth as for the nonlinear one (which is here 7.75%), the output power is increased by a factor of 16.5. Harmonic study is, however, partially irrelevant, because Duffing oscillators exhibit a frequency range where two stable harmonic solutions are possible. When excited with sine bursts or colored noise, the oscillator remains most of the time at the lowest solution. In this paper, we present a technique-called fast burst perturbation-which consists of a fast voltage burst applied to the piezoelectric element. It is then shown that the resonator may jump from the low solution to the high solution at a very small energy cost. Time-domain solution of the model is presented to support experimental data.