窄带随机激励下具有时滞反馈的三稳态能量采集系统动力学分析

肖玉柱; 王若涵; 孙中奎; 赵楠楠

doi:10.21656/1000-0887.450237

窄带随机激励下具有时滞反馈的三稳态能量采集系统动力学分析

doi: 10.21656/1000-0887.450237

1.
长安大学理学院，西安 710064
2.
西北工业大学数学与统计学院，西安 710129

(我刊青年编委孙中奎来稿)

基金项目:

国家自然科学基金 12302033

详细信息

作者简介:
肖玉柱(1980—)，男，副教授，博士，硕士生导师(E-mail: yuzhuxiao@chd.edu.cn)

通讯作者:
赵楠楠(1991—)，男，副教授，博士，硕士生导师(通讯作者. E-mail: nzhao@chd.edu.cn)

中图分类号: O322;O324
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出版历程
- 收稿日期: 2024-08-29
- 修回日期: 2024-10-16
- 刊出日期: 2025-06-01

Dynamics of a Tri-Stable Energy Harvesting System With Time-Delay Feedback Under Narrow-Band Random Excitation

1.
School of Sciences, Chang'an University, Xi'an 710064, P.R.China
2.
School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an 710129, P.R.China

(Contributed by SUN Zhongkui, M.AMM Youth Editorial Board)

摘要

摘要: 提出了一种窄带随机激励下具有时滞反馈控制的三稳态能量采集器. 首先，利用多尺度方法得到了能量采集系统在主共振附近的稳态响应. 然后, 采用矩方法推导出了系统的一阶与二阶非平凡稳态矩, 并通过Monte-Carlo仿真验证了其准确性. 最后, 基于上述稳态响应矩, 探讨了系统参数对能量采集性能的影响. 研究结果表明：非线性刚度系数的增加可以扩大能量采集系统的工作带宽, 窄带随机激励强度的增加可以使能量采集系统的输出电压增大, 压电耦合项的增加将导致振幅的二阶稳态矩减小, 进而有利于实现能量采集器的小型化设计. 此外, 当控制反馈增益为负值时，既有利于实现能量采集器的小型化设计，又能有效地增大系统的功率输出. 相关结果可为进一步探索和优化能量采集系统提供一定的理论参考.
- 非线性动力学 /
- 三稳态压电能量采集 /
- 时滞反馈 /
- 随机激励
Abstract: A tri-stable energy harvester with time-delay feedback control under narrow-band random excitation was proposed. The steady-state responses of the energy harvesting system near the main resonance were obtained with the multi-scale method. Moreover, the 1st-order and 2nd-order nontrivial steady-state moments of the system were derived with the moment method, and their accuracy was also verified through the Monte Carlo simulations. Based on the above steady-state response moments, the effects of system parameters on the performances of the energy harvester were discussed in detail. The results show that, increasing the nonlinear stiffness coefficient can enlarge the working bandwidth of the energy harvester system, while increasing the narrowband random excitation intensity can enhance the output voltage of the energy harvester. The 2nd-order steady-state moments visibly decrease with the piezoelectric coupling term, which indicates that a larger piezoelectric coupling term is beneficial to the miniaturization of energy harvesters. Furthermore, a negative control feedback gain is beneficial to realize the miniaturization design of the energy harvester and increase the power output of the system effectively. The findings provide a theoretical basis for further exploration and optimization of energy harvesting systems.
- nonlinear dynamics /
- tri-stable piezoelectric energy harvester /
- time delay feedback /
- random excitation
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1) (我刊青年编委孙中奎来稿)

HTML全文

图 1 三稳态能量采集系统的模型

Figure 1. The model for the tri-stable energy harvesting system

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图 2 F=2.5, Ω=2.5时，随机激励的功率S(ω)

Figure 2. Power spectrum S(ω) of random excitation for fixed F=2.5, Ω=2.5

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图 3 振幅的一阶和二阶稳态矩与失谐频率σ的关系

Figure 3. The 1st-order and the 2nd-order steady-state moments of the vibration amplitudes as functions of detuning frequency σ

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图 4 振幅与电压的一阶稳态矩随失谐参数σ变化的函数

Figure 4. The functions of the 1st-order steady-state moments of the vibration amplitude and the voltage with the detuning parameter

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图 5 图 4中所选用的势能函数图

Figure 5. Potential energy function curves selected in fig. 4

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图 6 二阶稳态矩Ea²，Ev²和平均输出功率EP随失谐频率σ的变化

Figure 6. The 2nd-order steady-state moments Ea², Ev² and average output power EP changing with detuning frequency excitation σ

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图 7 不同噪声强度与时滞下的时间历程

Figure 7. Time histories with different noise intensities and time delays

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图 8 不同失谐频率下的随机响应和不同噪声强度下的相位轨迹

Figure 8. Random responses with different detuning frequencies and phase trajectories with different noise intensities

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图 9 Ea²与EP随噪声强度和激励幅值变化的三维图

Figure 9. The 3D curves of Ea² and EP with noise intensities and excitation amplitudes

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图 10 Ea²和EP随压电耦合项k与时间常数比λ变化的三维图

Figure 10. The 3D curves of Ea²and EP with piezoelectric coupling term kand time constant ratio λ

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图 11 Ea²和EP随反馈增益β和时间延迟τ变化的三维图

Figure 11. The 3D curves of Ea² and EP with feedback gain β and time delay τ

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图 12 不同的反馈增益下, 振幅的二阶稳态矩Ea²和平均输出功率EP随时间常数比λ的变化

Figure 12. The 2nd-order steady-state moments of vibration amplitude Ea² and mean output power EP as functions of time constant ratio λ with different feedback gains

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图 13 双稳态能量采集系统的时间历程

Figure 13. The output voltage time histories of the bistable energy system

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