非线性电容RLC串联电路的1/2次亚谐共振分析

摘要

Aiming at the research object for RLC series circuit with nonlinear capacitance,using Lagrange method to establish the differential equations of the system,the first approximate solution of 1/2 subharmonic resonance of the nonlinear vibration system is obtained by means of the method of multiple scales for nonlinear oscillations. Numerical analyses on the influence of the parameters of inductance,capacitance and electromotive force( emf) on the amplitude frequency response curve are,as follows,that is,with the increasing of resistance,the amplitude and resonant region of the primary resonance decrease and with the increasing of electromotive force ( emf ) , the amplitude and resonant region of the primary resonance increase. With the increasing resistance,the current is abate,and than the nonlinearity will weaken. The system of RLC series circuit is simulated by using MATLAB Simulink tool.%以非线性电容RLC串联电路为研究对象，运用拉格朗日方法建立了系统的微分方程，应用多尺度法求得1/2次亚谐共振的一次近似解并进行数值计算。分析电阻、电感、电容和电动势对幅频响应曲线的影响。结果表明，电阻可以抑制振幅值，电动势可以增大振幅值。电阻增加后电流减弱，非线性也就变弱。运用MATLAB的Simulink工具，对RLC串联电路系统进行仿真。