Subharmonic orbits and their stability robustness to greatly enhance the bandwidth of bistable vibration energy harvesters

International audienceThis research work focuses on vibration energy harvesting in order to design an alternative to batteries for stand-alone, left-behind wireless devices. This study brings a new vision on bistable generators featuring nonlinear stiffness, presenting a wide operating frequency bandwidth compared to linear generators for a better adaptation to complex excitations. In this study, original behaviors of bistable oscillators are considered and analyzed for vibration energy harvesting, consisting in subharmonic motions for which the mass oscillates at a frequency N times lower than the excitation. First, experimental analysis is conducted with a generator integrating buckled beams for the bistability feature. It is shown that, in addition to the well-known first harmonic behavior, the third subharmonic orbit widens the bistable microgenerator useful operating frequency band by 180% compared to the sole exploitation of the first harmonic motion. A second part of this study analytically investigates those subharmonic orbits for the optimized design of future generator. The different orbits are obtained with the harmonic balance method and their stability is calculated for small disturbances. Stable orbits being more or less easy to reach and maintain, a new criterion is introduced, namely the stability robustness, indicating the stable orbit sensitivity to disturbances of different levels. For low stability robustness, the orbit will be considered as non-suitable for energy harvesting leading to a new definition of bistable generators frequency bandwidth. Analytical results following this method show good agreement with previous experimental results validating the relevance of stability robustness criterion