Benjamin Ducharne

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 k2 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 harvesters 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.

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 harvesters 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.

Fractional derivative operators for modeling the dynamic polarization behavior as a function of frequency and electric field amplitude

Polarization phenomena in ferroelectric materials are frequency-dependent, and the present article describes the use of a fractional derivative for the understanding of these phenomena as well as modeling them as functions of frequency and electric field amplitude. The focus was first directed toward the definition and validation of the proposed model through comparisons between simulations and measurements for high electrical field excitation amplitudes on a large frequency bandwidth (major hysteresis loops, measured over 4 decades). Subsequently, the same comparisons were made under ultra-weak as well as weak electric fields. Large frequency bandwidths were tested in each case, and it was shown that the fractional term provided a very accurate modeling of the dynamic behavior of the ferroelectrics. The dielectric permittivity coefficient along the polarization direction epsiv33 is a major parameter in ferroelectrics, and the frequency dependence of epsiv33 is correctly reproduced by the model. The time-dependence of the polarization reversal/variation was accurately simulated by a fractional derivation (a 0.5 order derivative), however, the use of a first-order derivation term (i.e., viscous losses) was in poor agreement with experimental results. It was found that the model was valid for large excitation field amplitudes as well as for large frequency bandwidths.

High nonlinearities in Langevin transducer: a comprehensive model.

The design and simulation of power transducers are difficult since piezoelectric, dielectric and elastic properties of ferroelectric materials differ from linear behavior when driven at large levels. This paper is devoted to modeling of a resonant power transducer at a high level of dynamic mechanical stress. The power transducer is subjected to a sine electrical field E of varying frequency which was considered as the excitation of the transducer. The mechanical equation of the piezoelectric element is written using electrostriction. The dielectric part is written as a nonlinear function of an equivalent electric field including stress influence (scaling relationship between electric field and mechanical stress). Using various simulations, we show then that typical resonance nonlinearities are obtained, such as jump phenomenon of transducer speed amplitude and phase, resonance peak that become asymmetric, and diminution of mechanical quality factor. As a consequence, we state that those typical nonlinearities are only due to dielectric nonlinearities, in good correlation with typical ferroelectric behavior. Moreover, this demonstrates the usefulness of scaling relationships in ferroelectrics, which explain static depoling under stress and butterfly strain hysteresis loop. The same scaling law gives here several nonlinearities for resonant transducers as well.

Modeling energy losses in power ultrasound transducers

Most power ultrasonic applications use Langevin transducers to generate power ultrasounds. In this chapter, we focus on a model for resonant power transducers under extreme excitation conditions. The challenge here is to correctly consider the usual resonance nonlinearities, such as jump phenomenon of transducer, asymmetric resonance peaks, and diminution of mechanical quality factor. The mechanical equation of the piezoelectric element is written using electrostriction. The dielectric part is written as a nonlinear function of an equivalent electric field including stress influence. Good simulation results allow concluding that in an ultrasonic transducer nonlinearities are only due to dielectric nonlinearities.

Strain in ferroelectric polymers under low-frequency electric fields: Experiments and modeling

The study of the electric field–induced thickness strain of ferroelectric polymers is very interesting because of the high actuating capabilities and various applications of these materials, such as electroactive materials for artificial muscles or as the active materials of membranes, due to their flexibility. This article reports on the effect on the strain properties of uniaxially and biaxially stretched β-form polyvinylidene fluoride when applying a low quasi-static triangular electric field E (100 mHz, E < 16 MV/m). For an applied electrical field at this level, the strain was proportional to the square of the electric field. The strain depended mainly on the electrostriction effect, linked to the induced reversal polarization and to interlaminar charges. The dielectric constant of the biaxially stretched polyvinylidene fluoride at 100 mHz was higher than for its uniaxially stretched counterpart. As a consequence, the induced charges and microscopic polarization for the first film exceeded those of the second one, and the electroactive strain for the biaxially stretched sample was more significant than for the uniaxially stretched film. This article first offers a description of the strain phenomenon through the polyvinylidene fluoride material during electrical excitation, after which a new model is presented. This model was developed to evaluate the induced electric current and strain phenomenon. A good agreement between simulations and experimental results was obtained.