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

Author(s): Kirillov O.N.

Journal: Theoretical and Applied Mechanics
ISSN 1450-5584

Volume: 34;
Issue: 2;
Start page: 87;
Date: 2007;
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Keywords: friction-induced oscillations | circulatory system | destabilization paradox due to small damping | characteristic polynomial | multiple roots | bifurcation | stability domain | Whitney umbrella singularity

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.
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