On the dynamics and optimization of a non-smooth bistable oscillator - Application to energy harvesting

Bistable nonlinear oscillators can transform slow sinusoidal excitations into higher frequency periodic or quasi-periodic oscillations. This behaviour can be exploited to efficiently convert mechanical oscillations into electrical power, but being nonlinear, their dynamical behaviour is relatively complicated. In order to better understand the dynamics of bistable oscillators, an approximate bilinear analytical model, which is valid for narrow potential barriers, is developed. This model is expanded to the case of wider potential with experimental verification. Indeed, the model is verified by numerical simulations and a suitable Poincaré section that the analytical model captures most of bifurcations for large amplitude vibrations and can be used to optimize the harvested power of such devices. The method of Shaw and Holmes [1] is enhanced by exploiting symmetry to obtain closed form expressions of the Poincaré section and mapping. The approximate non-smooth model proves useful in the study of orbital stability, large amplitude oscillations and in explaining most of the period doubling and symmetry breaking bifurcations arising when such an oscillator is subjected to sinusoidal excitation. The proposed model is successfully verified through analytical numerical analysis and some experimental results.