Chaotic responses across the potential barrier of bistable vortex-induced vibration energy harvesters

Large-amplitude interwell limit cycle oscillations (LCOs) are regarded as an ideal high-output state of multistable vibration energy harvesters. However, chaotic responses, which result in lower output voltages than interwell LCOs, can be observed in bistable vortex-induced vibration energy harvesters (VIVEHs). In this paper, the chaos in bistable VIVEHs is investigated through numerical simulation, theoretical analyses, and experimental validation. The distribution of the periodic solutions obtained by the incremental harmonic balance (IHB) method and chaos judgment using Lyapunov exponents are elucidated. It is found that the bistable VIVEH shows intrawell periodic solutions at high reduced wind speeds (RWSs) and period-doubling bifurcation appears with the periodic solutions turning into chaos with decreasing RWS. Analyses of the influence of nonlinear parameters on the chaotic responses identify the nonlinear stiffness as the dominant factor contributing to the chaos. Meanwhile, the chaotic responses and interwell LCOs would exist at the same RWS with different initial states. Finally, wind tunnel experiments confirm the occurrence of homologous chaotic responses of the bistable VIVEH which feature aperiodic jumping back and forth motion between two potential wells, in agreement with numerical simulations. Overall, this paper provides a framework for analyzing the chaotic responses of bistable VIVEHs, offering valuable insights for complex response mechanism understanding.