Effect of time delay on the generation of oscillation in a single degree-of-freedom mass-spring-damper system by nonlinear velocity feedback

Abstract

The present paper investigates the effect of time delay in a particular type of single degree-of-freedom self-excited oscillator. The self-excited vibration is generated in the system by using linear velocity feedback (to destabilize the static equilibrium of the system) with a nonlinear Rayleigh type feedback (to limit the growth of the instability into a stable limit cycle). The general method of describing function is employed to study the dynamics with the presence of time delay. Also, the analytical results are verified with the simulation result. Without time delay, the control law can generate a stable limit cycle with the proper choice of control parameters. However, the presence of time delay introduces a globally unstable limit cycle in the system with a stable one. Though the amplitude of the stable limit cycle dies down with the increase of time delay and finally vanishes by stabilizing the static equilibrium of the system. The effect of control parameters is also studied.