Double Resonances of Coupled RLC Circuit and Spring System with Internal Resonance Considering Inductance Nonlinearity

In order to study the nonlinear vibration of coupled RLC circuit and spring system, a mathematical model of coupled RLC circuit and spring system considering inductance nonlinearity and harmonic excitation is established combined with Lagrange-Maxwell equation. Based on multiple scales method for nonlinear vibration analysis, the first approximation solutions and corresponding to steady state solutions of the doubled resonances system are obtained. Numerical analysis results show that two coupled modals are all excited and vibrated when the system meets for double resonance condition. Energy is transformed between two modals. Amplitudes of two modals change with the parameters of the system and peak value of response curves change with the detuning parameter. It has also been found nonlinear resistance can control vibrations of the system when the parameters and resonant conditions are equal.