Stochastic Thermodynamics of a Piezoelectric Energy Harvester Model

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.

Stochastic Thermodynamics of an Electromagnetic Energy Harvester

“…[ 32 , 33 ] for a similar linear model, the contribution of the medium entropy production takes the form , where T is related to the noise amplitude and is obtained from a projection over the current distribution probability [ 33 ] and explicitly involves the variables x and v . We plan to address the study of entropy production in future works, in particular for a piezoelectric energy harvester [ 27 ], where direct access to all the dynamical variables is possible, and therefore, an experimental measurement of entropy production can be compared to theory and simulations.…”

“…Both piezoelectric and electromagnetic vibration harvesters are typically operated in resonant structures and can efficiently operate only near resonance, even if electromagnetic harvesters are characterized by higher powers with respect to piezoelectric ones. In the literature, the study of vibration harvesters forced by non-sinusoidal or random vibrations has been deeply carried out in case of piezoelectric technology [ 25 , 26 , 27 ], and in case of hybrid electromagnetic-piezoelectric systems [ 28 , 29 ]. On the other hand, electromagnetic vibration harvesters are typically studied under purely sinusoidal vibrations tuned to their resonance frequency.…”

“…The model is, by construction, out of equilibrium, since detailed balance is broken by the coupling with the current variable. This can also be interpreted as a feedback mechanism acting on the mass and introducing a memory effect in the system [ 32 , 33 ]; see also [ 27 ] where we performed a similar analysis on a piezoelectric energy harvester. We first fit the effective model parameters to the characteristic curve of the system, namely the extracted power versus the load resistance, and then analyze the time correlation functions of the current and the fluctuations of the extracted work over finite time intervals.…”

Uniqueness of Solutions in Thermopiezoelectricity of Nonsimple Materials

“…To deepen the concept of thermodynamic entropy, the reader can refer to the review article [ 39 ]. In addition, for an application to piezoelectric phenomena see [ 40 ], where the authors study a piezoelectric energy harvester driven by random broadband vibrations and propose an analytical and numerical analysis of the linear model compatible with the experiments.…”

Thermodynamic bounds for diffusion in non-equilibrium systems with multiple timescales

“…The first variable represents the main observable, eventually subject to a constant external force, while the other n variables are auxiliary variables, representing memory terms. This kind of model can describe the underdamped dynamics of a tracer in a fluid, when a separation of timescales allows one to obtain an effective generalized Langevin equation (GLE) for the slow variable [25], or systems with feedback control [26][27][28]. Defining the vectors X = {ω, Ω 1 , .…”