Abstract
This paper explores a 2:1 internal resonance of a bistable vibration energy harvester (BVEH) to enhance the harvesting performance. Two linear natural frequencies are tuned to meet the nearly commensurate ratio, i.e., 1:2. Thus, the 2:1 internal resonance could be activated when the first mode is directly excited under the same vibration frequency as the first linear natural frequency. The amplitude-frequency responses under small vibration amplitudes are obtained through the multi-scale method. The analytic results reveal the double-jumping characteristics, which could expand the bandwidth of the BVEH. Among them, an intriguing “flower pattern” amplitude-frequency curve is observed. Besides, the frequency spectrums are introduced to demonstrate the mode coupling and energy exchange between the first two modes. With small vibration amplitude, only intra-well responses could be obtained, and the energy exchange between modes obeys strict commensurate relation, i.e., 2:1. However, it does not obey the 2:1 ratio when the inter-well responses are activated, and the energy transfers to several low-frequency modes which results in a chaotic inter-well response. Afterward, the bifurcation diagrams and basin-of-attraction maps are explored by the numerical method to develop insights into the nonlinear responses of the BVEH. The results quantitatively prove the enhancement of the inter-well responses by internal resonance, and the chaotic inter-well response dominates the nonlinear behaviors.
Electron-vibration energy exchange models in nitrogen-containing plasma flows
