Uncertainty in performance for linear and nonlinear energy harvesting strategies

Vibrational energy harvesters are often linear mass-spring-damper-type devices, which have their resonant frequency tuned to the dominant vibration frequency of their host environment. As such, they can be highly sensitive to uncertainties, which may arise from the imprecise characterization of the host environment or, alternatively, from manufacturing defects and tolerances. It has previously been claimed that the use of nonlinear energy harvesters may be one way to alleviate the problems of these uncertainties. This article presents a systematic uncertainty propagation study of a prototypical electromagnetic energy harvester. More specifically, the response of a linear harvester in the presence of parametric uncertainty is compared to the response of harvesters containing some common forms of nonlinearity, that is, hardening, softening, or bistability. Analytical solutions are used in combination with presumed levels of parametric uncertainty to quantify the resulting uncertainty in the power output. Consequently, these studies can determine the regions in the parameter space where a nonlinear strategy may outperform a more traditional linear approach.