Bifurcation of the roots of the characteristic polynomial and the destabilization paradox in friction induced oscillations

Abstract

Paradoxical effect of small dissipative and gyroscopic forces on the stability of a linear non-conservative system, which manifests itself through the unpredictable at first sight behavior of the critical non-conservative load, is studied. By means of the analysis of bifurcation of multiple roots of the characteristic polynomial of the non-conservative system, the analytical description of this phenomenon is obtained. As mechanical examples two systems possessing friction induced oscillations are considered: a mass sliding over a conveyor belt and a model of a disc brake describing the onset of squeal during the braking of a vehicle.

Keywords

• friction-induced oscillations
• circulatory system
• destabilization paradox due to small damping
• characteristic polynomial
• multiple roots
• bifurcation
• stability domain
• Whitney umbrella singularity