The non-linear vibrations of parametrically self-excited system with two degrees of freedom

Non-linear vibrations of a system with two degrees of freedom with parametric and self-excited vibrations interaction were investigated in this paper. The analysis was carried out for the main parametric resonance in the neighbourhood of the first and second frequencies of free vibrations. The free vibrations amplitudes and the widths of the synchronization areas were calculated analytically. Stability of the obtained periodic solutions was examined as well. The analytical results were verified and supplemented with the analog and computer simulation.