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

Kirillov, Oleg (2007) Bifurcation of the roots of the characteristic polynomial and destabilization paradox in friction induced oscillations. Theoretical and Applied Mechanics, 34 (2). pp. 87-109. ISSN 1450-5584

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Official URL: http://dx.doi.org/10.2298/TAM0702087K

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.

Item Type: Article
Uncontrolled Keywords: Friction-induced oscillations, circulatory system, destabilization paradox due to small damping, characteristic polynomial, multiple roots, bifurcation, stability domain, Whitney umbrella singularity
Subjects: G100 Mathematics
H300 Mechanical Engineering
Department: Faculties > Engineering and Environment > Mathematics and Information Sciences
Depositing User: Oleg Kirillov
Date Deposited: 02 May 2017 08:53
Last Modified: 10 May 2017 15:27
URI: http://nrl.northumbria.ac.uk/id/eprint/30650

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