Conjugate resonances in nonlinear systems under biharmonical action. Vibro-induced bifurcations

Abstract

Using a bistable oscillator described by a Duffing equation as an example, we consider resonances caused by a biharmonical external force with essentially different frequencies. We show that these resonances are conjugate; they appear when either the low or high frequency changes. The resonances take place also as the amplitude of the high-frequency action varies. Besides we show that the high-frequency action induces the bifurcation of the change in the number of stable steady states in the system; so the seeming resonance in an overdamped oscillator is caused just this bifurcation.