Metrikine A.V. and Popp K.


Instability of vibrations of an oscillator moving along a beam on an elastic half-space


European Journal of Mechanics A/Solids 18(2), 331-349, 1999



Summary. The stability of vertical vibrations of an oscillator moving uniformly along a beam on elastic half-space is investigated. Expressions for the equivalent stiffness of the beam are derived in the point of contact with the oscillator. It is shown that the imaginary part of the equivalent stiffness can have a sign, which is interpreted as so-called “negative viscosity”.  Frequency bands where the equivalent stiffness gives the “negative viscosity” are analyzed. Using the expressions for the equivalent stiffness the instability zones for the oscillator vibrations are found. The instability can take place when the velocity of the oscillator exceeds the minimum phase velocity of waves in the beam. The effect of a viscosity in the beam on the stability of the system is considered. It is shown that a small viscosity destabilizes the system.