Analysis on 1/3 subharmonic resonance of RLC circuit with indutance nonlinearity

In order to study on nonlinear vibration of RLC circuit, a mathematical model of RLC circuit with inductance nonlinearity and harmonic excitation is established by means of Lagrange-Maxwell equation. Based on the method of multiple scales for nonlinear vibration analysis, the first approximation solutions and corresponding to steady state solutions of the 1/3 subharmonic resonance system are obtained. Numerical analysis results show that the amplitude of the system increases with increasing of plate area and linear coefficient of inductance, while it decreases with increasing plate distance, voltage, and nonlinear inductance coefficient. It has also been found the nature frequency of the system increases with the increasing plate distance but it decreases when the plate area and linear inductance coefficient increase.