Title :
Double Resonances of Coupled RLC Circuit and Spring System with Internal Resonance Considering Inductance Nonlinearity
Author :
Zhian, Yang ; Yihui, Cui
Abstract :
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.
Keywords :
RLC circuits; circuit resonance; coupled circuits; inductance; nonlinear dynamical systems; nonlinear network analysis; springs (mechanical); Lagrange-Maxwell equation; coupled RLC circuit; double resonances; harmonic excitation; inductance nonlinearity; internal resonance; mathematical model; nonlinear resistance; nonlinear vibration analysis; spring system; Coupling circuits; Inductance; Lagrangian functions; Mathematical model; Nonlinear equations; Numerical analysis; RLC circuits; Resonance; Springs; Steady-state; RLC circuit; coupling; inductance nonlinearity; the method of multiple scales;
Conference_Titel :
Electronic Measurement and Instruments, 2007. ICEMI '07. 8th International Conference on
Conference_Location :
Xi´an
Print_ISBN :
978-1-4244-1136-8
Electronic_ISBN :
978-1-4244-1136-8
DOI :
10.1109/ICEMI.2007.4350438
