2ND SUPERHARMONIC RESONANCE OF COUPLED RLC CIRCUIT AND SPRING SYSTEM WITH RESISTANCE AND INDUCTANCE NONLINEARITY

In order to study nonlinear vibration of coupled RLC (Resistance-Inductance-Capacitance) circuit and spring system, a mathematical model of coupled RLC circuit and spring system with inductance and resistance nonlinearity and harmonic excitation is established in terms of Lagrange-Maxwell equation. Based on the multiple scales method for nonlinear vibration analysis, the first approximation solutions and its corresponding steady state solutions of the system are obtained. Numerical analysis results show that the amplitude and resonant region of the system increase with the increase of voltage, plate area and resistance R1, while they decrease with the increase of plate distance, resistance R0 and R2. It has also been found that the nature frequency of the system increases with the increase of plate distance but it decreases when the plate area and linear inductance coefficient increase.