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.

中文翻译：

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几何非线性双稳态振动能量采集器性能的估计和改进


本研究旨在从全局动力学的角度研究和改进具有几何非线性的振动能量收集器 （VEH） 的性能。根据 VEH 动力系统的静力分叉分析，选择每根杆与中线之间的初始装配角度作为关键结构参数进行调整，以配置双稳态井和降低潜在障碍。在此基础上，通过扩展平均方法研究了井间和井内谐振响应。基于通过微扰增量法构建同斜轨道，应用 Melnikov 方法分析井间混沌响应的临界条件。此外，数值结果验证了分析的准确性，并进一步研究了丰富的动力学行为，例如高阶周期响应、混沌、隐藏和稀有的吸引子以及分形吸引力盆地。由此可见，用于配置双稳态井的初始组装角度的最大值对于在低频或低强度基极振荡下有效收集能量是最佳的。基极振荡水平的增加可以引起井间谐振响应的整体吸引力，这意味着 VEH 的可靠和高输出。研究结果可为几何非线性振动能量采集器的优化设计和运行提供一定的参考。