Abstract
We experimentally study a piezoelectric energy harvester driven by broadband random vibrations. We show that a linear model, consisting of an underdamped Langevin equation for the dynamics of the tip mass, electromechanically coupled with a capacitor and a load resistor, can accurately describe the experimental data. In particular, the theoretical model allows us to define fluctuating currents and to study the stochastic thermodynamics of the system, with focus on the distribution of the extracted work over different time intervals. Our analytical and numerical analysis of the linear model is succesfully compared to the experiments.
Highlights
From microscopic organisms in the biosphere, life in general and human activities in particular critically depend on the conversion of different forms of energy into useful work.Harvesting energy from the environment is a central task in many applications, where random fluctuations possibly arising from disparate sources at different scales, from the microscopic thermal Brownian motion in a fluid, to the macroscopic vibrations in means of transport, can be converted into work.The well established rules of thermodynamics for macroscopic systems become blurred when fluctuations are relevant and have to be taken into account [1]
General relations have pushed the range of validity of standard thermodynamics into the realm of non-equilibrium regimes [2,3,4]: from the Fluctuation Relations [5,6,7,8,9] and the generalized fluctuation-dissipation relations [10,11], to the general results ruling work and heat exchanged in non-equilibrium transformations, such as the Jarzinski relation [12], the Crooks fluctuation theorem [13], or the Hatano–Sasa relation [14]
We have studied experimentally a piezoelectric energy harvester driven by random broadband vibrations, focusing on the behavior of the extracted power as a function of the load resistance and of the vibration amplitude
Summary
From microscopic organisms in the biosphere, life in general and human activities in particular critically depend on the conversion of different forms of energy into useful work. The study of fluctuations is addressed within the theory of stochastic thermodynamics, where the standard concepts of energy, heat, work and entropy, are extended to non-equilibrium systems, driven by external forces or coupled to different reservoirs. Very well studied examples are the Brownian (or molecular) motors [33], known as ratchet models, where a probe is in contact with a thermal bath and the presence of a spatial asymmetry coupled to some non-equilibrium source allows to rectify the motion of the probe, with extraction of useful work These systems have been studied theoretically and experimentally for instance in the context of granular media [34,35], where the dissipative interactions among grains induce the non-equilibrium behavior, or in biological motors [36], where active internal forces are at play. Our analysis shows that a simplified linear model, which allows for analytical computations, is able to accurately reproduce the experimental results, even at the fine level of fluctuations
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