Analytical solution and optimal design for the output performance of Galfenol cantilever energy harvester considering electromechanical coupling effect.
Analytical solution and optimal design for the output performance of Galfenol cantilever energy harvester considering electromechanical coupling effect.
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DOI：
10.1038/s41598-023-40111-x
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发表时间：
2023-08-08
影响因子：
4.6
通讯作者：
Nie, Xiaochun
中科院分区：
文献类型：
--
作者：
Wang, Lingzhi;Lian, Chengling;Shu, Dalin;Yan, Zhitao;Nie, Xiaochun
研究了Galfenol悬臂梁振动能量采集器的理论模型。与数值解相比，解析解能更好地反映物理参数对收割机性能的内在影响。基于汉密尔顿原理、磁致伸缩材料的线性本构方程和法拉第电磁感应定律，建立了Galfenol悬臂梁能量采集器的机电耦合分布参数模型。由于机电耦合，提出了电阻尼和修正频率的定义和表达式。利用Galliakin分解和机电解耦方法，推导了Galfenol能量采集模型在负载电阻和尖端振动位移下的平均采集功率的显式解析表达式。实验数据和数值解验证了解析结果的准确性。通过改变激励频率、外电阻和激励加速度幅值，研究了Galfenol能量收集模型的振动响应和能量收集性能。分析结果表明，随着外负载电阻和激励频率的增加，系统的功率采集量先增加后减小，存在最佳电阻和激励频率。从平均收获功率的显式解析表达式，可以很容易地找到最佳外部负载电阻或激励频率，以实现任何固定的激励频率或外部负载电阻的最大收获功率。提出了Galfenol悬臂梁能量采集器的电阻尼和修正频率的概念，简化了输出性能的求解过程，受益于本文导出的输出性能与机电耦合参数之间的精确关系。
The theoretical model of a Galfenol cantilever energy harvester is investigated for vibration energy harvesting. Compared with the numerical solution, the analytical solution can better capture the intrinsic effects of the physical parameters on the performance of the harvester. In this work, an electromechanical coupled distributed-parameter model of the Galfenol cantilever energy harvester is established based on Hamilton’s principle, linear constitutive equations of magnetostrictive material, and Faraday’s law of electromagnetic induction. The definitions and expressions of the electric damping and modified frequency are proposed due to the electromechanical coupling. The explicit analytical expressions of the average harvested power across the load resistance and tip vibration displacement of the Galfenol energy harvesting model are derived using the methods of Galliakin decomposition and electromechanical decoupling. The accuracy of the derived analytical results is verified by the experimental data and numerical solutions. The vibration response and energy harvesting performance of the Galfenol energy harvesting model are investigated by varying the excitation frequency, external resistance, and excitation acceleration amplitude. The analytical results show that, with the increase of the external load resistance and excitation frequency, the harvested power increases first and then decreases, indicating the existence of the optimal resistance and excitation frequency. From the explicit analytical expressions of the average harvested power, the optimal external load resistance or excitation frequency could be easily found to achieve the maximum harvested power for any fixed excitation frequency or external load resistance. The concept of proposing the electric damping and modified frequency for the Galfenol cantilever energy harvester simplifies the solution process for the output performances benefiting from the exact relationship between the output performances and the electromechanical coupling parameter derived in this work.