Transient Dynamics and Electric Power Estimation of Bistable Energy Harvesters Under Impulsive Excitations

Bistable vibration energy harvesters are sensitive to impulsive excitations widely existed in environments, and the favorable large-orbit snap-through oscillation possesses high energy conversion efficiency and output voltage. The enhanced averaging method (EA) with Jacobian elliptic functions provides an analytical, efficient tool of guiding the structural design and parameters optimization of bistable harvesters excited in impulsive environments. However, the EA method still suffers some limitations: the predicted transient dynamics undergo undesired sudden jump at the end moment of the snap-through regime, and; phase error occurs during the intrawell regime when large initial velocity is applied. To address these limitations, an improved EA method is proposed in this paper. The transient dynamics in the snap-through and intrawell regimes are separately approximated via two-piecewise expressions, leading to high-fidelity estimation of the vibration amplitude and critical moment dividing the snap-through from intrawell dynamics which occur later in the time. A novel, more accurate estimation of the vibration phase is derived. The prediction performance of the improved EA method is validated via numerous comparisons with the EA method and numerical simulations. It shows that the improved EA method effectively eliminates the aforementioned limitations induced by EA method, providing high-fidelity reconstruction of the transient dynamics of the bistable harvesters excited in impulsive environments.