Stability of a nonideally excited Duffing oscillator

Abstract This paper investigates the dynamics of a Duffing oscillator excited by an unbalanced motor. The interaction between motor and vibrating system is considered as nonideal, which means that excitation provided can be influenced response, case in general for real systems. constitutes important difference with respect to classical (ideally excited) oscillator, where amplitude frequency external forcing are assumed known priori. Starting from pre-resonant initial conditions, we investigate phenomena passage through resonance (the evolves towards post-resonant state after some transient near-resonant oscillations) resonant capture gets locked into stationary oscillation). stability solutions analytically studied detail averaging procedures, obtained results confirmed numerical simulations.