非线性电容RLC串联电路的1/3亚谐共振
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摘要
以非线性电容RLC串联电路为研究对象,应用拉格朗日方法建立了非线性振动方程,基于多尺度法得到1/3次亚谐共振的一次近似解,数值计算分析可知电容、电感、电阻和电动势对亚谐共振幅频响应均有影响.结果表明:1/3次亚谐共振区域对电动势值敏感,电动势、电阻或电容大于一定值后,系统将不出现1/3次亚谐共振响应.运用Matlab的Simulink工具,对RLC串联电路系统进行仿真.
With RLC series circuit with nonlinear capacitance research object,the nonlinear vibration differential equation is derived by means of Lagrange equation,and the first approximate solution of primary resonance of the nonlinear vibration system is obtained by means of the method of multiple scales for nonlinear oscillations.Numerical analysis on the influence of resistance,inductance,capacitance and electromotive force(emf)parameters on amplitude frequency response curve are carried out.The numerical results show that the emf amplitude has significant impact on the 1/3subharmonic resonance region.The1/3subharmonic resonance of the RLC series circuit will not appear when the emf,the resistance or the capacitance of foundation is greater than a certain value.The system of RLC series circuit is simulated by using Matlab Simulink tool.
With RLC series circuit with nonlinear capacitance research object,the nonlinear vibration differential equation is derived by means of Lagrange equation,and the first approximate solution of primary resonance of the nonlinear vibration system is obtained by means of the method of multiple scales for nonlinear oscillations.Numerical analysis on the influence of resistance,inductance,capacitance and electromotive force(emf)parameters on amplitude frequency response curve are carried out.The numerical results show that the emf amplitude has significant impact on the 1/3subharmonic resonance region.The1/3subharmonic resonance of the RLC series circuit will not appear when the emf,the resistance or the capacitance of foundation is greater than a certain value.The system of RLC series circuit is simulated by using Matlab Simulink tool.
引文
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[10]OKSASOGLU A,VAVRIV D.Interaction of low and high frequency oscillation in a nonlinear RLC Circuit[J].IEEE Transaction on Circuit and Systems-I:Fundamental Theory and Application,1994,41(10):669-672.
[11]李高峰,杨志安.皮带驱动机构的1/3次亚谐共振分析[J].机械强度,2008,30(3):371-375.LI Gaofeng,YANG Zhian.Study on 1/3subharmonic resonant of the belt driver mechanism[J].Journal of Mechanical Strength,2008,30(3):371-375.
[12]李高峰.非线性电容RLC串联电路的主共振研究[J].计算物理,2014,31(3):351-356.LI Gaofeng.Primary resonance analysis of RLC series circuit with nonlinear capacitance[J].Chinese Journal of Computational Physics,2014,31(3):351-356.
[2]王小艳.非线性RLC电路特性的数字仿真研究[J].高压电器,2001,37(6):52-54.WANG Xiaoyan.Numerical simulation of nonlinear RLC electric circuit characteristics[J].High Voltage Apparatus,2001,37(6):52-54.
[3]杨志安,崔一辉.非线性电阻电感型RLC串联电路主共振分析[J].天津大学学报,2007,40(5):579-583.YANG Zhian,CUI Yihui.Primary resonance analysis of RLC series circuit with resistance and inductance nonlinearity[J].Journa l of Tianjin Un iversity,2007,40(5):579-583.
[4]杨志安,贾尚帅.RLC串联电路与微梁耦合系统1∶2内共振分析[J].应用力学学报,2010,27(1):80-85,225.YANG Zhian,JIA Shangshuai.Analysis of the 1∶2internal resonance coupled RLC circuit and microbeam system[J].CHINESE JOURNAL OF APPLIED MECHANICS,2010,27(1):80-85,225.
[5]杨庆怡,张卫平.RLC电路非线性现象产生机制的研究[J].广西大学学报:自然科学版,2013,38(06):1471-1475.YANG Qingyi,ZHANG Weiping.Quantunm effects of non-linear resistance mesoscopic circuit with infinitesimal variation of current[J].Journal of Guangxi University:Nat Sci Ed,2013,38(06):1471-1475.
[6]常秀芳,李高.RLC-振荡电路中的数学模型[J].山西大同大学学报:自然科学版,2009,25(1):71-73.CHANG Xiufang,LI Gao.RLC-Mathematical models in vibrating circuit[J].Journal of Shanxi Datong University:Natural Science,2009,25(1):71-73.
[7]HOMSUP N,HOMSUP W.Unconstrained optimization method for finding DC operating points of RLC Nonlinear Circuits[A].Modelling and Simulation(MS'99)[C].Philadelphia PA:IASTED,1999:606-607.
[8]BLANKENSTEIN G.Geometric modeling of nonlinear RLC circuits[J].IEEE transactions on circuits and systems[J].Regular Papers,2005,52(2):396-404.
[9]CHAKRAVARTHY S K.Nonlinear oscillations due to spurious energisation of transformers[J].EE Proc-Electr Power Appl,1998,145(6):585-592.
[10]OKSASOGLU A,VAVRIV D.Interaction of low and high frequency oscillation in a nonlinear RLC Circuit[J].IEEE Transaction on Circuit and Systems-I:Fundamental Theory and Application,1994,41(10):669-672.
[11]李高峰,杨志安.皮带驱动机构的1/3次亚谐共振分析[J].机械强度,2008,30(3):371-375.LI Gaofeng,YANG Zhian.Study on 1/3subharmonic resonant of the belt driver mechanism[J].Journal of Mechanical Strength,2008,30(3):371-375.
[12]李高峰.非线性电容RLC串联电路的主共振研究[J].计算物理,2014,31(3):351-356.LI Gaofeng.Primary resonance analysis of RLC series circuit with nonlinear capacitance[J].Chinese Journal of Computational Physics,2014,31(3):351-356.