Simple analytical models and analysis of bistable vibration energy harvesters

In order to scavenge the energy of ambient vibrations, bistable vibration energy harvesters constitute a promising solution due to their large frequency bandwidth. Because of their complex dynamics, simple models that easily explain and predict the behavior of such harvesters are missing from the literature. To tackle this issue, this paper derives simple analytical closed-form models of the characteristics of bistable energy harvesters (e.g. power-frequency response, displacement response, cut-off frequency of the interwell motion) by mean of truncated harmonic balance methods. Measurements on a bistable piezoelectric energy harvester illustrate that the proposed analytical models allow the prediction of the mechanical displacement and harvested power, with a relative error below 10%. From these models, the influences of various parameters such as the inertial mass, the acceleration amplitude, the electromechanical coupling, and the resistive load, are derived, analyzed and discussed. The proposed models and analysis give an intuitive understanding of the dynamics of bistable vibration energy harvesters, and can be exploited for their design and optimization.