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.

Bistable piezoelectric energy harvesters are prominent solutions in the field of vibration energy harvesting due to their broadband behavior. However, the impact of the electrical interface and especially the load impedance needs to be addressed. In this study, the impact of the electrical load resistance on the dynamic of the bistable piezoelectric energy harvester has been studied. Through a parametric study, the present paper shows that the load resistance impacts both the harvested power and the bandwidth of the harvester. The analytical expression of the mass displacement, critical angular frequency and harvested power have been obtained, based on a truncated harmonic balance method. A comparison between the analytical model and experimental measurement on a custom bistable energy harvester is then presented. The experimental results are in good agreement with the analytical model, which proves the validity of the proposed model and analysis. The results presented in this study should be considered in the development of maximum power point tracking algorithms and orbit jump strategies.

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Piezoelectric energy harvesters (PEH) require an electronic circuit to rectify their AC voltage in order to supply wireless sensors. In the literature, it has been shown that such electronic circuit can be tuned and optimized in order to enhance the bandwidth and power of linear PEH. However, to date, few works have explored the electrical optimization of non-linear bistable PEH. The present work reports the optimization of the harvested power and bandwidth of bistable PEH by mean of a non-linear energy extraction circuit: the parallel synchronized switch harvesting on inductor (P-SSHI). A simple model of the bistable PEH connected to the P-SSHI circuit has been derived and the closed-form expression of the harvested power has been obtained. The experimental tests, conducted on a custom-made bistable PEH showed that the results are in good agreement with the model, proving its validity. Based on the model, it is shown that the P-SSHI circuit allows to increase the bandwidth (1.6 times) and the harvested power (up to 7.5 times) compared to the standard energy harvesting (SEH) circuit.