The asymptotic stability of the oscillations of a two-mass resonance sifter

The asymptotic stability of the periodic oscillations in a model of a two-mass resonance sifter with a unilateral limiter without a gap is proved, on the assumption that the linear generating system allows of oscillations with frequencies of ω and 2ω and the frequency of the external motor is identical with ω. This formulation corresponds to the widely used mode of operation of the sifter – resonance. The presence of a limiter leads to nondifferentiability along certain planes of the right-hand sides of the corresponding differential equations. The averaging principle, the applicability of which in the case considered has previously been justified, is employed. It is proved that the resonance mode of operation obtained is subharmonic.