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


O. N. Kirillov




Paradoxical effect of small dissipative and gyroscopic forces on the stability of a linear non-conservative system, which manifests it-self through the unpredictable at first sight behavior of the critical non-conservative load, is studied. By means of the analysis of bi-furcation 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.