On the fundamental and superharmonic effects in bistable energy harvesting

Abstract

Superharmonic dynamics are characteristic of many nonlinear systems undergoing high levels of excitation. However, what constitutes high levels is relative to the system under study. For instance, bistable oscillators may have very low linearized natural frequency which often becomes a normalization parameter for excitation in analysis. Thus, high excitation levels may be a common operating condition for bistable oscillators. Recent experimental energy harvesting investigations using bistable devices (referred to as bistable energy harvesting) have observed superharmonic spectral and phenomenological effects yielding superior electrical power relative to that achieved by the fundamental harmonic. To provide a thorough analytical framework to probe the collective fundamental and superharmonic effects on bistable energy harvester power harvesting performance, this article employs the method of harmonic balance to predict the resulting electrodynamic responses applicable to piezoelectric and electromagnetic coupling configurations. The analytical results exemplify the relative ease by which significant superharmonic effects are activated and dominate spectral characteristics, potentially to greatly benefit energy harvesting. The conclusions are corroborated by trends observed in previously published investigations and are validated by present numerical results and experimental findings. This study provides new insights and suggests that careful understanding of excitation characteristics is needed for optimum bistable energy harvesting in practice.