基于Euler Bernoulli理论的压电系统集中参数模型修正
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摘要
针对压电俘能系统悬臂梁结构集中参数模型的局限性,引入Euler Bernoulli梁振动模型。通过分析两模型在振动时相对位移传递率发现,集中参数模型在基础激励情况下,传递率峰值存在较大偏差。理论分析Euler Bernoulli及集中参数模型在1阶模态附近位移传递率函数,对集中参数模型进行修正。仿真及有限元结果表明修正后的集中参数模型相对位移传递率峰值与Euler Bernoulli模型在低阶模态吻合良好。
The Euler-Bernoulli beam vibration model is introduced for the limitation of the lumped-parameter model of cantilever structures in piezoelectric energy capture systems. The relative displacement transfer rates of the Euler-Bernoulli beam model and the lumped-parameter model under base excitation are analyzed. The results show that the relative error of the transfer rate peak value resulted from the lumped-parameter model in predicting the relative motion at the tip of the beam is very large. Then, the displacement transfer functions near the first-order modal of the two models are analyzed theoretically. According to the results, the lumped-parameter model is modified. The simulation and finite element analysis results show that the peak value of the relative displacement transmissibility of the modified lumped-parameter model agrees well with the Euler Bernoulli model in low-order modes.
The Euler-Bernoulli beam vibration model is introduced for the limitation of the lumped-parameter model of cantilever structures in piezoelectric energy capture systems. The relative displacement transfer rates of the Euler-Bernoulli beam model and the lumped-parameter model under base excitation are analyzed. The results show that the relative error of the transfer rate peak value resulted from the lumped-parameter model in predicting the relative motion at the tip of the beam is very large. Then, the displacement transfer functions near the first-order modal of the two models are analyzed theoretically. According to the results, the lumped-parameter model is modified. The simulation and finite element analysis results show that the peak value of the relative displacement transmissibility of the modified lumped-parameter model agrees well with the Euler Bernoulli model in low-order modes.
引文
[1]刘海利,徐天柱,黄震宇,等.基于谐振器的多模态压电换能结构研究[J].振动工程学报,2011,24(5):491-497.
[2]袁江波,谢涛,陈维山,等.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.
[3]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].物理学报物理学报,2011,60(7):430-436.
[4]蒋树农,郭少华,李显.方单压电片悬臂梁式压电俘能器效能分析[J].振动与冲击振动与冲击,2012,19):90-94.
[5]ZHU YANG,ZU J W,GUO L.A Magneto-electric Generator for Energy Harvesting From the Vibration of Magnetic Levitation[J].IEEE Transactions on Magnetics,2012,48(11):3344-3347.
[6]李海涛,秦卫阳.双稳态压电能量获取系统的分岔混沌阈值[J].应用数学和力学应用数学和力学,2014,35(6):652-662
[7]ZHOU SHENG XI,CAO JUN YI,LIN JING.Theoretical analysis and experimental verification for improving energy harvesting performance of nonlinear monostable energy harvesters[J].Nonlinear Dynamics,2016,86(3):1599-1611.
[8]ROUNDY S,WRIGHT PK.A piezoelectric vibration based generator for wireless electronics[J].Smart Material Structures,2004,13(5):1131-1142(12).
[9]STEPHEN NG,On energy harvesting from ambient vibration[J].Journal of Sound&Vibration,2006,293(1):409-425.
[10]吴义鹏,季宏丽,裘进浩,等.共振频率可调式非线性压电振动能量收集器[J].振动与冲击动与冲击,2017,36(5):12-16.
[11]STRUTT J W(Lord Rayleigh).The Theory of Sound[M],Macmillan,London,1894.
[12]MEIROVITCH L.Fundamentals of Vibrations[M].Mc Graw-Hill,New York,2001.
[13]ALPER ERTURK,DANIEL J INMAN.Piezoelectric energy harvesting[M].A John Wiley and Sons,Ltd.,Publication,USA,2011.
[2]袁江波,谢涛,陈维山,等.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.
[3]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].物理学报物理学报,2011,60(7):430-436.
[4]蒋树农,郭少华,李显.方单压电片悬臂梁式压电俘能器效能分析[J].振动与冲击振动与冲击,2012,19):90-94.
[5]ZHU YANG,ZU J W,GUO L.A Magneto-electric Generator for Energy Harvesting From the Vibration of Magnetic Levitation[J].IEEE Transactions on Magnetics,2012,48(11):3344-3347.
[6]李海涛,秦卫阳.双稳态压电能量获取系统的分岔混沌阈值[J].应用数学和力学应用数学和力学,2014,35(6):652-662
[7]ZHOU SHENG XI,CAO JUN YI,LIN JING.Theoretical analysis and experimental verification for improving energy harvesting performance of nonlinear monostable energy harvesters[J].Nonlinear Dynamics,2016,86(3):1599-1611.
[8]ROUNDY S,WRIGHT PK.A piezoelectric vibration based generator for wireless electronics[J].Smart Material Structures,2004,13(5):1131-1142(12).
[9]STEPHEN NG,On energy harvesting from ambient vibration[J].Journal of Sound&Vibration,2006,293(1):409-425.
[10]吴义鹏,季宏丽,裘进浩,等.共振频率可调式非线性压电振动能量收集器[J].振动与冲击动与冲击,2017,36(5):12-16.
[11]STRUTT J W(Lord Rayleigh).The Theory of Sound[M],Macmillan,London,1894.
[12]MEIROVITCH L.Fundamentals of Vibrations[M].Mc Graw-Hill,New York,2001.
[13]ALPER ERTURK,DANIEL J INMAN.Piezoelectric energy harvesting[M].A John Wiley and Sons,Ltd.,Publication,USA,2011.
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