Stochastic dynamics of a piezoelectric energy harvester with correlated colored noises from rotational environment

The energy harvesting from rotational automotive tire is studied through an electromechanical-coupled system which is a harmonically driven bi-stable potential with correlated additive and multiplicative colored noises. By integrating the voltage equation and introducing generalized harmonic transformation, the equivalent uncoupled system based on energy-dependent frequency is derived. The improved stochastic averaging of energy envelope is then carried out to obtain the stationary probability density (SPD) of the equivalent uncoupled system. The effects of correlated colored noises and other system parameters on SPD and mean output power are discussed theoretically and numerically. Besides, signal-to-noise ratio (SNR) is obtained analytically to measure stochastic resonance (SR). It is found that the curve of SNR has a single peak versus noise intensity and system parameters. That is, the appropriate choice of system parameters, such as noise intensity, electromechanical coupling coefficient and time constant ratio, can enhance power conversion efficiency greatly and produce more mean output power from the viewpoint of parameter-optimized SR. Especially, with a large periodic rotational angular velocity, the RMS voltage can be significantly enhanced by increasing the magnetic end mass gravity. Finally, the proposed stochastic averaging is well verified by numerical simulations.