SUPERHARMONIC RESONANCES IN TWO-MASSES VIBRATING MACHINES

Abstract

Two masses vibrating machine with inertial exciter and polynomial characteristic of elastic ties is considered. Its mathematical model is constructed and the stationary motions in frequency zone located between two natural ones are studied. With use of complex form of harmonic balance method the analysis of its dynamics is reduced to the solving of complex system of algebraic equations. Its subsequent numerical solution under changing parameters of the system gives an opportunity to build the bifurcation curves and discover pure combination resonances of different orders. One of the most suitable among them from the practical point of view is the resonance of the order 2:1 which, by this reason, is the focus of the article. With the help of original software the oscillations of vibrating machine are analyzed, bifurcation curves and spectral properties are studied. There are established certain correlations between parameters, which are necessary for designing of such machines, one approach for projecting of nonlinear elastic ties is discussed.