Oscillations under a nonlinear parametric action and combinations of delays

The paper considers oscillations under nonlinear parametric action and combinations of delays in elasticity and damping. The model for the study is a rod with a spring, which is driven by an energy source of limited power. To solve nonlinear differential equations of motion of the system, the method of direct linearization of nonlinearity has been used. Equations were obtained for determining the nonstationary and stationary values of the amplitude and phase of oscillations, the speed of the energy source. Based on the Routh – Hurwitz criteria, the conditions for the stability of stationary motion modes were derived. To obtain information about the combined effect of delays on the dynamics of oscillations, the calculations were carried out for their various values, linear and nonlinear elastic forces. The graphs constructed based on the calculation results clearly show the combined effect of various delay values on the amplitude-frequency curves. The delays measure the amplitude curve, shift it to the right-left, up-down, and affect the stability of the oscillations.