The influence of nonlinear parametric excitation on the interaction of forced, parametric and self-oscillations

In order to reveal the effect of nonlinear (cubic) parametric excitation (NPE) on the interaction of forced, parametric, and self-oscillation with a limited-power energy source, a widely used computed model of a self-oscillating system receiving energy from such a source was used. Solutions of nonlinear differential equations of the model were constructed using the direct linearization method (DLM), which is distinguished from the known ones by its simplicity its simplicity and low time costs. The friction force characteristic causing self-oscillations was linearized by DLM. Equations for the amplitude, oscillation phase and the velocity of the energy source in nonstationary and stationary motion cases were derived. Using the Routh — Hurwitz criteria, the stability of stationary movements was considered. The influence of NPE on the interaction of forced, parametric and self-oscillations was investigated by calculations. The latter showed NPE to change the shape of the amplitude curves inherent in linear action and to have a significant impact on the motion stability.