The mixed parametric and self-oscillations: The effect of nonlinear parametric excitation and delays on them causing self-oscillations

In the paper, the mixed parametric and self-oscillations in the presence of a nonlinear parametric action and a delay in friction causing self-oscillations have been studied. For this purpose, a model of a frictional self-oscillating system interacting with an energy source of limited power was used. The solution of nonlinear differential equations of motion was constructed using the direct linearization method. The relations of nonstationary and stationary oscillation modes were obtained. By application of the Routh — Hurwitz criteria, the conditions for the stability of stationary oscillations were derived. The calculations were carried out in order to gain information about the dynamics of fluctuations. An analysis of the data showed that the amplitude-frequency dependence changed its behavior under the influence of the delay. The latter also led to the appearance of stability regions on the lower branches of the amplitude curves, and a dependence arose on the steepness of the energy source characteristic.