基于等效线性化方法的非线性振动能量采集器功率分析

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摘要输出功率分析是振动能量采集器结构设计、参数选择的重要依据。有鉴于传统功率分析方法比较复杂，本文以一类电磁式振动能量采集器为对象，提出了一种新的非线性振动能量采集器功率分析方法，其核心是将非线性振动方程进行等效线性化处理，并借助传递函数开展功率优化分析。首先，考虑非线性磁力以及基尔霍夫电流定律，建立了通用化的采集器1.5自由度七次非线性机电耦合模型；其次，将动态频率法用于求解该系统控制方程，采用高阶谐波成分替代方程中的非线性项，实现了原有系统控制方程的等效线性化；最后，利用传递函数推导了输出功率表达式，分析等效线性化系统负载，机电耦合系数等因素对于输出功率的影响。研究结果表明：以等效线性化为基础的功率分析，可以有效地克服传统非线性能量采集器系统功率分析方法复杂的问题，具有良好的适用性。

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	李佳诚1
	王志霞1
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	王炜1
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	王辰3

关键词 ：非线性, 动态频率法, 能量采集, 等效线性化

Abstract：Output power analysis is an important basis for the structural design and parameter selection of vibration energy harvester. Due to the complex traditional power analysis method, a novel power analysis method is proposed based on a kind of electromagnetic vibration energy harvester, in which the nonlinear vibration equation turns into an equivalent linear system and the power optimization is carried out by transfer function in the linear system. Firstly, a 1.5-degree and 7-order nonlinear electromechanical coupling generalized model of the harvester is established with nonlinear magnetic force and Kirchhoff's current law. Secondly, the dynamic frequency method is employed to solve the steady-state response of the system, in which the high-order harmonic term replaces the nonlinear component to achieve the equivalent linearization of the nonlinear governing equation. Finally, the transfer function is used to derive the power expression, and the influence of key parameters such as system load and electromechanical coupling coefficient on the output power are analyzed. The research results show that the power analysis method based on equivalent linearization can effectively overcome the complexity of the traditional power analysis approach and has good applicability.

Key words： nonlinear dynamical frequency method energy harvester equivalent linearization

收稿日期: 2020-07-15 出版日期: 2022-01-15

引用本文:

李佳诚1，王志霞1, 2，王炜1, 2，王辰3. 基于等效线性化方法的非线性振动能量采集器功率分析[J]. 振动与冲击, 2022, 41(1): 196-205.
LI Jiacheng1, WANG Zhixia1, 2, WANG Wei1, 2, WANG Chen3. Power analysis of nonlinear vibration energy harvester based on equivalent linearization method. JOURNAL OF VIBRATION AND SHOCK, 2022, 41(1): 196-205.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2022/V41/I1/196

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