Analytical Model for Electric Power Prediction of Piezoelectric Energy Harvesting

Abstract

Vibration energy can be converted into electrical energy using a piezoelectric energy harvester. An analytical model is of great importance to understand the first principle of piezoelectric energy conversion mechanism. Furthermore, for quick decision-making of the number and location of piezoelectric energy harvesters, harvestable electric power must be analytically quantified under a given vibration condition. In order to develop the analytical model for electric power prediction of the piezoelectric energy harvester, this study aims at advancing two essential research areas: 1) research thrust 1 – stochastic electric power prediction under non-stationary random vibrations, 2) research thrust 2 – the electromechanically coupled analytical model of an energy harvesting skin (EH skin). In research thrust 1, statistical time-frequency analysis, smoothed pseudo Wigner-Ville distribution, was used to estimate a time-varying power spectral density (time-varying PSD) of a non-stationary random vibration signal. The time-varying PSD of the output voltage response was estimated from a linear electromechanical operator. Finally the expected electric power was obtained from the autocorrelation function which is the inverse Fourier transform of the time-varying PSD of the output voltage. In research thrust 2, the electromechanically analytical model of the EH skin was developed using the Kirchhoff plate theory. The Levy solution was used to calculate the natural frequencies and mode shapes. A steady-state output voltage response was obtained by solving the mechanical equation of motion and electrical circuit equation simultaneously. The analytical plate model can be also used for EH skin design to extract the inflection lines for piezoelectric material segmentation to avoid the voltage cancellation.