The interaction of mixed forced, parametric and self-excited oscillations at limited excitation and delays

On the basis of a dynamic model of a frictional self-oscillating system, the influence of delays in elasticity and friction causing self-oscillations on mixed forced, parametric and self-oscillations during the interaction of an oscillating system with an energy source has been considered. The solution of nonlinear differential equations of motion of an oscillatory system and an energy source was constructed using the method of direct linearization. The latter differs from the known methods for the analysis of nonlinear systems by many advantages, including ease of use. Based on the Routh – Hurwitz criteria, the stability conditions for the analysis of stationary motions were obtained. Calculations were carried out to obtain information on the influence of delays on the oscillation modes. This influence was established to be very significant. The stability of stationary oscillations depends both on the characteristics of the energy source and on the magnitude of the delay; a weak or very weak stability appears.