The dynamics of a BI-stable energy harvester: Exploration via slow-fast decomposition and analytical modeling

The paper discusses the advantages of the bi-stable energy harvester over linear oscillators in the low frequency excitation regime. When excited by low-frequency base motions, a bistable vibration-based energy harvester's response is characterized by a combination of a slow, and a non-stationary fast component. By decomposing the response of the bi-stable system into fast and slow components, some new physical insights into the dynamical properties of the system are obtained. Properties such as mechanical frequency up-conversion, asymmetry in the bi-stable potential of the system and extraction of the backbone curve are explored. The proposed decomposition is demonstrated and explained via numerical and experimental results. A simple, approximate analytical model, for the bi-stable oscillator is proposed and its ability to detect migration towards different vibration regimes is illustrated. An expression for the power output of the harvester is derived from the analytical solution allowing us to tune the bi-stable potential towards optimum performance. The analytical model sheds light on the occurrences of bifurcations in the response of such nonlinear systems and on the optimal values of potential barrier vs. excitation levels.