Slow-fast response decomposition of a bi-stable energy harvester

A bi-stable vibration-based energy harvester excited by low frequency base motions exhibits vibrations characterised by a combination of slow and non-stationary fast components. The conversion of slow into fast oscillations by a nonlinear potential barrier can increase the amount of harvested power as has been shown before. In this paper the dynamical behaviour leading to the conversion of low-frequency oscillations into high frequency ones is discussed and explained. A non-parametric response decomposition approach able to separate the slow and fast parts is employed. This decomposition provides deeper insight into the effect of the nonlinear potential barrier by identifying the local evolution of instantaneous amplitude and frequency near the potential barrier and far from it. The slow and fast components are utilised to identify the backbone-curves of the two asymmetric potential wells and the nonlinear stiffness of the system. The proposed decomposition and analysis allow one to examine the repetitive transient dynamics near the potential barrier without resorting to averaging or perturbation based methods. The proposed approach and the subsequent analysis are demonstrated and explained via numerical and experiment results.

Graphical AbstractFigure optionsDownload full-size imageDownload as PowerPoint slideHighlights► Highlights the importance of nonlinearity in vibration based energy harvesters. ► Introduces a new non-parametric method for the investigation of bistable oscillators. ► Presents graphically the frequency up-conversion property in nonlinear energy harvesters. ► Compute the double backbone of asymmetric potentials and potential force functions. ► New three-dimensional diagram: instantaneous amplitude and frequency vs. time.