Mixed Parametric and Auto-oscillations at Nonlinear Parametric Excitation

The development of the theory of oscillatory processes, taking into account the properties of the energy source, contributes to improving the accuracy of calculating real objects for various purposes, the optimal choice of the power of the energy source to save it. Mixed parametric and self-oscillations under nonlinear parametric excitation in the interaction of an oscillatory system with an energy source are considered. The solution of the equations of motion is constructed using the method of direct linearization of nonlinearity. The conditions of stability of stationary modes of motion are derived. To study the effect of nonlinear parametric excitation on the properties of vibrations, calculations were carried out, the results of which were compared with the results of linear excitation. The results obtained show the difference between the dynamics of systems with linear and nonlinear parametric excitations, which has a quantitative and qualitative character. At the same time, quantitative differences are more significant. © The Author(s).