THE INFLUENCE OF DELAYS IN ELASTICITY AND DAMPING ON AUTO-PARAMETRIC OSCILLATIONS

The interaction of self-oscillations and parametric oscillations under the influence of delayed elastic and damping forces in the presence of a limited power energy source in the system is considered. To construct solutions to a nonlinear system of equations, the direct linearization method was used, which contains the linearization accuracy parameter. Using this method, equations of non-stationary and stationary motions are obtained to determine the amplitude, phase of oscillations and the speed of the energy source. Based on the Routh-Hurwitz criteria, the stability of stationary modes of motion is considered and the stability conditions are derived. In order to obtain information about the effect of elastic delays and damping on the dynamics of the system, calculations were performed for various combinations of their values. The corresponding amplitude-frequency characteristics and a graph of the load on the energy source from the side of the oscillatory system are constructed.