Analysis on primary resonance of RLC circuit with inductance 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 multiple scales method for nonlinear vibration analysis, the first approximation solutions and corresponding to steady state solutions of the primary resonance system are obtained. Numerical analysis results show that the amplitude of the system increase with increasing voltage and plate area, while they decrease with increasing plate distance, resistance and nonlinear inductance coefficient. With the decreasing of resistance and plate distance, resonant regions of amplitude frequency response curves enlarge. 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.