研究了通过添加线性振子的磁悬浮非线性能量器采集系统在多频激励下的非线性动力学。通过结合运用谐波平衡法和弧长延伸法,近似解析分析能量采集系统在多频激励下中间磁铁的平均功率辐频响应。并通过直接数值方法验证解析结果。研究结果表明,这种磁悬浮能量采集器在质量比增大时,中间磁铁的平均功率幅频响应的共振峰由两个变为四个共振峰,振幅变小,但共振峰的带宽变宽。另外,通过系统参数分析发现,调节系统参数阻尼比和耦合系数,可以优化共振峰的强度和带宽的宽度,以达到增强振动能量采集效果的目的。
Abstract
Here,nonlinear dynamic behaviors of a magnetic levitation energy harvesting system attaching a linear oscillator were studied under multi-frequency excitation. The nonlinear dynamic equations of this electromagnetic-mechanical coupled model were approximately solved using the harmonic balance method and the arc-length extension method. In addition,the approximate analytical results were verified with a direct numerical simulation. The results showed that with increase in the mass ratio of this energy harvesting system,resonance peaks of its middle magnet’s average power amplitude-frequency response under multi-frequency excitation increase from two peaks to four ones,the resonance peaks’amplitudes decrease,but their bandwidths are wider; adjusting the system’s parametric damping ratio and coupling coefficient can optimize intensities and bandwidths of resonance peaks to enhance the vibration energy harvesting effect.
关键词
非线性 /
多频激励 /
磁悬浮 /
能量采集 /
谐波平衡
{{custom_keyword}} /
Key words
nonlinear /
multi-frequency excitation /
magnetic levitation /
energy harvesting /
harmonic balance
{{custom_keyword}} /
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
参考文献
[1] 袁江波, 谢涛, 陈维山, 肖娜. 悬臂梁压电发电装置的实验研究[J]. 振动与冲击, 2009, 28(7): 69-72. [Yuan Jiang-bo, Xie Tao, Chen Wei-shan, Xiao Na. Experimential Study on Piezoelectric Generator with Cantilever [J]. Journal of Vibration and Shock, 2009, 28(7): 69-72. (in Chinese).]
[2] 陈仲生, 杨拥民. 悬臂梁压电振子宽带低频振动能量俘获的随机共振机理研究[J]. 物理学报, 2011, 60(7): 074301: 1-7. [Chen Zhong-Sheng, Yang Yong-Min. Stochastic resonance mechanism for wide band and low frequency vibration energy harvesting based on piezoelectric cantilever beams [J]. Acta Physica Sinica, 2011, 60(7): 074301 (in Chinese)]
[3] Roundy, S., Wright, P. K., and Rabaey, J, A Study of low level vibrations as a power source for wireless sensor nodes[J]. Computer Communications,2003, 26(11): 1131–1144.
[4] P. Mitcheson, E. Yeatman, G. Rao, A. Holmes,et al. Energy harvesting from human and machine motion for wireless electronic devices[J]. Proceedings of the IEEE,2008, 96 (9) : 1457-1486.
[5] S. Lam Po Tang, Recent developments in flexible wearable electronics for monitoring applications.[J] Transactions of the Institute of Measurement and Control,2007, 29(3-4) : 283-300.
[6] Jiang XZ, Wang J, Li YC, et al. Energy harvesting for powering wireless sensor networks in low-frequency and large-force environments[J]. Journal of Mechanical Engineering Science, 2015,229: 1953-1964.
[7] Jiang WA and Chen LQ Snap-through piezoelectric energy harvesting [J]. Journal of sound and Vibration 2014, 333: 4314-4325.
[8] 毕勤胜, 陈予恕, 吴志强. 多频激励Duffing 系统的分岔和混沌[J]. 应用数学和力学, 1998, 19(2): 113-120.(BI Qin-sheng, CHEN Yu-shu, WU Zhi-qiang. Bifurcation in nonlinear Duffing system with multi-frequency external periodic forces[J]. Applied Mathematics and Mechanics, 1998, 19(2): 113-120(in Chinese))
[9] AHN S. Yang, DT Mook. Combination resonances in the response of the Duffing oscillator to a three-frequency excitation [J]. Acta Mech.,1998, 131: 235–245
[10] Chen E.L., Yang S.P., Yuan X.R.. The subharmonic resonance in a multi-degree of freedom hysteretic no-nlinear system with multi-frequency excitation [C]. The International Conference on vibration Engineering. Shenyang: Northeastern university Press, 1998: 270-273
[11] 杨德森, 董雷, 时洁等. 多频激励Duffing系统振动状态研究[J]. 振动与冲击, 2011, 30(12): 19-21.(YANG De-sen, DONG Lei, SHI Jie, et al. Duffing system vibration behavior under multi-frequency excitation [J].Journal of Vibration and Shock, 2011, 30(12): 19-21(in Chinese))
[12] Zhou L., Chen F.. Chaotic motions of the duffing-van der pol oscillator with external and parametric excitations [J]. Shock and Vibration, 2014, 2014(5): 1-5.
[13] 王祖尧, 丁虎, 陈立群.两自由度磁力悬浮非线性振动能量采集研[J]. 振动与冲击, 2016, 35(16): 57-58. (WANG Zu-yao, DING Hu, CHEN Li-qun. Nonlinear oscillations of a two degree-of-freedom energy harvester of magnetic levitation [J].Journal of Vibration and Shock, 2016, 35 (16) : 57-58(in Chinese))
[14] Mann BP, Sims ND, Energy harvesting from the nonlinear oscillations of magnetic levitation [J]. Journal of Sound and Vibration, 2009, 319: 515–530.
{{custom_fnGroup.title_cn}}
脚注
{{custom_fn.content}}