摘要
为了研究非线性电阻电感型RLC串联电路的非线性振动,应用拉格朗日-麦克斯韦方程建立受简谐激励的具有电阻和电感非线性RLC电路的数学模型.根据非线性振动的多尺度法,得到系统满足主共振条件的一次近似解以及对应的定常解.对其进行数值计算,分析系统参数对响应曲线的影响.结果表明:增大极板面积,响应曲线的振幅和共振区变大;增大极板间距、电感非线性系数和电阻,响应曲线的振幅和共振区变小.非线性电感和电阻可以抑制电量的振动.系统的固有频率随极板间距增大而增大,随极板面积和电感线性系数的增大而减小.
In order to study the nonlinear vibration of RLC series circuit, a mathematical model of RLC circuit with inductance and resistance nonlinearity and harmonic excitation was established by means of Lagrange-Maxwell equation. Based on multiple scales method for nonlinear vibration analysis, the first approximation solutions and their corresponding steady state solutions to the primary resonance system were obtained. Numerical analysis results show that the amplitude and resonant region of the system increase with plate area increasing, while decrease with the increase of plate distance, resistance, and nonlinear coefficient of inductance. Nonlinear resistance and inductance can control the vibration of RLC circuit. It is also found that the natural frequency of the system increases when plate distance increases but decreases when the plate area and inductance linear coefficient increase.
出处
《天津大学学报》
EI
CAS
CSCD
北大核心
2007年第5期579-583,共5页
Journal of Tianjin University(Science and Technology)
关键词
RLC电路
非线性电阻
非线性电感
多尺度法
主共振
RLC circuit
nonlinear resistance
nonlinear inductance
multiple scales method
primary resonance
