Analysis and control of friction-induced oscillations in a continuous system

Abstract

We analyse and control friction-induced oscillations in a continuous system due to the drooping characteristics of the friction force. The model consists of a cantilever beam with an end mass that is in frictional contact with a rigid rotating disc. Time-delayed displacement feedback applied normal to the disc surface is used to control the vibrations. Linear stability analysis yields the stability boundary corresponding to the Hopf bifurcation point. Nonlinear analysis is performed to obtain conditions on the control parameters for which the nature of the bifurcation is subcritical such that these values can be avoided. The control parameters for effective quenching of the vibrations are obtained. An interesting regime of control parameters for which the system is stable for low and high velocities but unstable for intermediate velocities is also observed.