Primary Resonance of Circuit-Spring System with Internal Resonance and Inductance Nonlinearity

Nonlinear phenomena are observed in coupled RLC (Resistance-Inductance-Capacitance) circuit and spring system; a new mathematical model is presented to adapt advanced research. Its dynamic equation considering inductance nonlinearity and harmonic excitation is established by Lagrange-Maxwell equation. Based on multiple scales method for nonlinear vibration analysis, the first approximation solutions and its steady state solutions of the doubled resonance system are obtained. Shown as the numerical analysis results, the two coupled modals are all excited and vibrated when the system meets the double resonances condition. Energy is transformed between two modals. With the changing of parameters of the system, vibration amplitude of certain modal can be changed more obviously. Changing the excitation, a similar saturation phenomenon can be found. In addition, nonlinear inductance can change the topology structure of response curves when the parameters and resonant conditions are equal.