Probabilistic maps on bistable vibration energy harvesters

This paper analyzes the impact of parametric uncertainties on the dynamics of bistable energy harvesters, focusing on obtaining statistical information about how each parameter's variability affects the energy harvesting process. To model the parametric uncertainties, we use a probability distribution derived from the maximum entropy principle, while polynomial chaos is employed to propagate uncertainty. Conditional probabilities and probability maps are obtained to investigate the effect of uncertainty on harvesting energy. We consider different models of bistable energy harvesters that account for nonlinear piezoelectric coupling and asymmetries. Our findings suggest a higher probability of increasing harvested power in the intrawell motion regime as the excitation frequency increases. In contrast, increasing the excitation amplitude and piezoelectric coupling are more likely to increase power in the chaotic and interwell motion regimes, respectively. An illustrative example is presented to emphasize the importance of investigating the influence when all parameters vary simultaneously.

Automated summary

This paper analyzes the impact of parametric uncertainties on the dynamics of bistable energy harvesters and investigates how each parameter's variability affects the energy harvesting process. The study uses probability distributions and polynomial chaos to model and propagate uncertainty. Different models of bistable energy harvesters with nonlinear piezoelectric coupling and asymmetries are considered. The findings suggest that increasing the excitation frequency leads to a higher probability of increasing harvested power in the intrawell motion regime, while increasing the excitation amplitude and piezoelectric coupling are more likely to increase power in the chaotic and interwell motion regimes, respectively. The importance of investigating the influence of simultaneous parameter variations is emphasized through an illustrative example.