, Volume 4, Issue 1-2, pp 15-23

Frequency-locking in nonlinear forced oscillators near 3:1 and 4:1 resonances

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Abstract

In this paper, frequency-locking phenomenon in self-excited nonlinear oscillators subjected to harmonic excitation is investigated near the 3:1 and 4:1 subharmonic resonances. Analytical treatment based on perturbation techniques is performed to study the quasiperiodic modulation domain and the frequency-locking area in the vicinity of these resonances. It is shown that this analytical method, based on a double averaging procedure, is efficient to capture the modulation domain of the quasiperiodic response as well as the threshold of synchronization area near the considered subharmonic resonances.