In this paper, the nonlinear resonances analysis of a RLC series circuit modeled by a modified Van der Pol oscillator is investigated. After establishing of a new general class of nonlinear ordinary differential equation, a forced Van der Pol oscillator subjected to an inertial nonlinearity is derived. From this equation the multiple scales method is used to find the various resonant states. As analytical results primary resonance, sub-harmonic resonance of order 1/3 and super-harmonic resonance of order 3 are obtained. The steady-state solutions and theirs stabilities are determined. Numerical simulations display bistability, hysteresis, jump and bifurcation phenomena. The effects of different parameters on the system behavior are investigated and results are presented graphically and discussed.
Comments: 20 pages
[v1] 2018-06-22 07:41:06
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