On the effect of delays in self-oscillating system with external influence

Self-oscillating system that interacts with energy source of limited power is considered in the presence of external force and joint action of delays in damping and elasticity. On the basis of the direct linearisation method, the solution of non-linear equations of the system is obtained. The equations of non-stationary motion, relations for calculating the amplitude and phase of stationary oscillations, the speed of the energy source and the load on it on the side of the oscillatory system are derived. Stability conditions of stationary oscillations were obtained with the use of the Routh–Hurwitz criteria. Calculations were carried out to study the influence of delays on dynamics of the system. The results show the combined effect of delays in elasticity and damping on dynamics of oscillations. Delays change the shape of the amplitude-frequency curve, shift it up/down and shift it in the frequency range. Delays also affect the stability of oscillations. If in the case of no delay there is no resonant curve then various intensity resonant curve may appear if delay is present. The intensity of resonant curve depends on the amount of delay. Considering the influence of delays on dynamics of oscillations, it was assumed that other parameters of the system are unchanged.