A theory of the destabilization paradox in non-conservative systems

Kirillov, Oleg (2004) A theory of the destabilization paradox in non-conservative systems. Acta Mechanica, 174 (3-4). pp. 145-166. ISSN 0001-5970

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Official URL: http://dx.doi.org/10.1007/s00707-004-0194-y


In the present paper, a theory is developed qualitatively and quantitatively describing the paradoxical behavior of general non-conservative systems under the action of small dissipative and gyroscopic forces. The problem is investigated by the approach based on the sensitivity analysis of multiple eigenvalues. The movement of eigenvalues of the system in the complex plane is analytically described and interpreted. Approximations of the asymptotic stability domain in the space of the system parameters are obtained. An explicit asymptotic expression for the critical load as a function of dissipation and gyroscopic parameters allowing to calculate a jump in the critical load is derived. The classical Ziegler–Herrmann–Jong pendulum considered as a mechanical application demonstrates the efficiency of the theory.

Item Type: Article
Subjects: G100 Mathematics
H300 Mechanical Engineering
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User: Oleg Kirillov
Date Deposited: 23 Jan 2017 11:15
Last Modified: 12 Oct 2019 22:27
URI: http://nrl.northumbria.ac.uk/id/eprint/29309

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