Efficiency of energy harvesting out of colored Lévy fluctuations by a harmonic oscillator with piezoelectric transducer

Abstract

The efficiency of a linear kinetic energy harvester by piezoelectric transduction—when driven by colored α−stable Lévy noise—is the focus of this study. Analytical results are obtained for the harvested power (in the adiabatic approximation x¨ ∼= 0 and for very large load circuit’s time constant τp), which are accurately validated by numerical simulations. In addition, an analytical expression is obtained for the characteristic time the system takes to reach a stationary regime; this information is crucial to calculate averaged quantities through simulations, given the large dispersion between realizations due to the infinite variance of the Lévy noise.