Estimation and improvement of the performance of a bistable vibration energy harvester with geometric nonlinearities

This study aims to investigate and improve the performance of a vibration energy harvester (VEH) with geometric nonlinearities from a global-dynamics point of view. According to static bifurcation analysis of the VEH dynamic system, the initial assembly angle between each rod and the midline is selected as a key structural parameter to be adjusted for configuring bistable wells and lowering the potential barrier. On this basis, inter-well and intra-well resonant responses are studied via the extended averaging method. Based upon the construction of homoclinic orbits via the perturbation-incremental method, the Melnikov method is applied to analyze the critical conditions for the inter-well chaotic response. Moreover, numerical results validate the accuracy of the analysis and further investigate rich dynamic behaviors such as higher-order periodic responses, chaos, hidden and rare attractors, and fractal basins of attraction. It follows that the largest value of the initial assembly angle for configuring bistable wells is optimal for efficiently energy harvesting under the low-frequency or low-intensity base oscillation. And the increase in the level of the base oscillation can induce the global attraction of an inter-well resonant response, implying reliable and high output of the VEH. The results may provide some reference in the optimal design and operations of geometrically nonlinear vibration energy harvesters.