Combination resonances and their bifurcations in the nonlinear vibromachines with a polynomial characteristic of restoring force and periodic excitation

Abstract

Much attention was given to the study of combination resonances of nonlinear systems in the 80 years of the last century. However, the use of in recent years in various technological processes of the vibromachines with polyharmonic vibrations of the working body, again makes topical the task of their further study. Mathematical models of the nonlinear machines of one mass schemes (screening, concentration tables, transporting machines) with polynomial characteristics of restoring and dissipative forces and periodic excitation are investigated. Their dynamics in the zones of sub- and superharmonic resonances of order 2:1 and 1:2 are studied. By numerical simulation and with use of original software the analysis of the spectral and phase composition of the oscillations is performed, the main types of bifurcations of the stationary regimes are allocated, the role of the biharmonic part of the excitation on the nature of the oscillations and their margin of stability are revealed. Conclusions concerning the practical relevance of these resonances based on research findings are formulated.