Abstract

Vibration energy, which is widely available, can be converted into electric energy using a piezoelectric energy harvester that generates alternating current in response to applied mechanical strain. For the last decade, there has been a strong surge of interest in developing an electromechanically-coupled analytical model of a piezoelectric energy harvester. Such a model is of great importance to enable understanding of the first principle of the piezoelectric transduction and to quantify harvestable electric power under a given vibration condition. However, existing analytical models that operate under an assumption of deterministic excitations cannot deal with the random nature present in realistic vibrations, even though this randomness considerably affects the variation in harvestable electric power. Furthermore, even when random vibrations are taken into account, existing stochastic analytical models can only be applied to stationary excitations, such as in the case of white Gaussian noise. This paper thus proposes a three-step framework for stochastic quantification of the electric power generated by a piezoelectric energy harvester under non-stationary random vibrations. First, we propose estimation of the time-varying power spectral density (PSD) of the input non-stationary random vibration using a statistical time–frequency analysis. The second step is to employ an existing electromechanical model as the linear operator for calculating the output voltage response. The final step is to estimate the time-varying PSD of the output voltage response. Following this three-step process, the expected electric power can be estimated from the autocorrelation function which is the inverse Fourier transform of the time-varying PSD of the output voltage response. The merits of the proposed framework are two-fold in that it enables: (i) quantification of the time-varying electric power generated under non-stationary random vibrations and (ii) consideration of the randomness in the design process of the energy harvester. Four case studies are used to demonstrate the effectiveness of the proposed framework.