Instability of an oscillator moving along a thin ring on a viscoelastic foundation

Abstract

The stability of an oscillator uniformly moving along a thin ring that is connected to an immovable axis by a distributed viscoelastic foundation has been studied. The dynamic reaction of the ring to the oscillator is represented by a frequency and velocity dependent equivalent stiffness. The characteristic equation for the vibration of the oscillator is obtained. It is shown that this equation can have roots with a positive real part, which imply the exponential increase of the amplitude of the oscillator’s vibration in time, i.e. instability. The critical velocity after which instability can occur is determined. With the help of the D-decomposition method, the instability domains are found in the space of the system parameters. Parametric study of the stability domains is carried out.