具有粘弹性的三稳态能量采集系统的动力学分析
Kinetics Analysis of a Tri-Stable Energy Harvesting System with Viscoelastic Properties
摘要: 本文提出了一种具有粘弹性项的三稳态能量采集系统，并深入研究了该系统的主共振响应特性。首先，利用多尺度法得到了主共振附近稳态振幅的解析解，并通过矩方法得到了系统的稳态响应矩。其次，通过蒙特卡罗仿真验证了所用方法的正确性。进一步通过数值分析研究随机跳变、随机分岔和有效带宽扩展等现象，最后分析了系统参数对振幅的二阶矩和平均输出功率的影响，发现对于每个时间延迟都存在一个最佳的反馈增益值使能量采集系统的平均输出功率最大，能量采集效果最佳。这些研究结果为优化三稳态能量采集系统的性能提供了理论支持。
Abstract: In this paper, a tri-stable energy harvesting system with viscoelastic term is proposed, and the main resonance response characteristics of the system are studied in depth. Firstly, the analytical solution of the steady-state amplitude near the principal resonance is obtained by using the multi-scale method, and the steady-state response moment of the system is obtained by the moment method. Secondly, the correctness of the proposed method is verified by Monte Carlo simulation. Further, the phenomena of random jumps, random bifurcations and effective bandwidth expansion are investigated by numerical analysis, and finally, the influence of system parameters on the second-order moment of the amplitude and the average output power is analyzed, and it is found that there is an optimal feedback gain value for each time delay, so that the average output power of the energy harvesting system is the largest and the energy harvesting effect is the best. These results provide theoretical support for optimizing the performance of tri-stable energy harvesting systems.
文章引用：王若涵. 具有粘弹性的三稳态能量采集系统的动力学分析[J]. 应用数学进展, 2025, 14(5): 61-71. https://doi.org/10.12677/aam.2025.145233

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