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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.

This paper presents a model suited for the design of mechanically bistable beams used in Piezoelectric EnergyHarvesters (PEHs). The proposed model accounts for the bending and compression of post-buckled beams used in the PEH. The effect of the beam's geometry on the generated power and frequency bandwidth is evaluated with a performance criterion. It is concluded that a low beam compression stiffness can have a negative impact on the performance of the PEH and that the bending stiffness solely implies a prestress on the piezoelectric transducer.

This paper introduces an optimized orbit jump strategy for nonlinear Vibration Energy Harvesters (VEHs). Nonlinear VEHs are a promising alternative to linear VEHs due to their broadband characteristics. However, they exhibit complex dynamical behaviors, including not only high-power inter-well orbits but also low-power intra-well orbits and chaos. The existence of low-power orbits in their dynamics can restrict their energy harvesting performance. In order to overcome this issue, this study investigates an orbit jump strategy that allows the VEH to transition from low-power intra-well orbits to high-power inter-well orbits. This strategy, based on varying the buckling level of a bistable VEH, has been previously studied but not yet optimized. In this study, we define an optimization criterion that maximizes both the effectiveness and robustness of the orbit jump strategy. We developed a Python CUDA code using GPU parallel computing to handle the large number of numerical resolutions of the nonlinear VEH model. Experimental tests were performed on a bistable VEH over a frequency range of 30 Hz, validating the numerical results obtained with the optimized orbit jump strategy. The results indicate that the energy consumption required for a successful orbit jump ranges between 0.2 mJ and 1 mJ, and can be restored within 0.2 s in the worst case. Experimental results show an average success rate of 48%, despite a variation of ±15% in the starting and ending times of the jump, leading to a robust and optimized orbit jump strategy. The proposed optimization procedure can be applied to other orbit jump strategies, and other types of nonlinear VEHs.