Asymptotic stability of oscillations of two-bodies vibrating screen with   one-sided obstacle without clearances
  We prove asymptotic stability of periodic oscillations in two-bodies vibrating screen model under assumption that the frequencies w1 and w2 of the generating system (without obstacle and periodic driving) satisfy the assumption w1:w2=1:2. We also assume that the frequency of the external periodic driving equals to w1. These settings correspond to nonlinear resonance which is a well known phenomenon in industrial implementation of the vibrating screen. The justification is performed over nonsmooth analog of the second Bogolyubov's theorem proposed by the author in his previous papers. It is rigorously proven that the periodic oscillations obtained have two frequencies, in contrast with the case when the obtacle is absent. 
Oleg Makarenkov