Conjugate resonances and bifurcations in nonlinear systems under biharmonical excitationстатья
Статья опубликована в высокорейтинговом журнале
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Аннотация:Using a bistable oscillator described by a Duffing equation as an example, resonances caused by a biharmonical external force with two different frequencies (the so-called vibrational resonances) are considered. It is shown that, in the case of a weakly damped oscillator, these resonances are conjugate; they occur as either the low and high frequency is varied. In addition, the resonances occur as the amplitude of the high-frequency excitation is varied. It is also shown that the high-frequency action induces the change in the number of stable steady states; these bifurcations are also conjugate, and are the cause of the seeming resonance in an overdamped oscillator. (C) 2003 Elsevier Ltd. All rights reserved.