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The Effect of Small Internal and External Damping on the Stability of Distributed Non-conservative Systems by O.N. Kirillov; A.O. Seyranian is a Engineering article available to read on EtoBox.

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The effect of small internal and external damping on the stability of distributed non-conservative systems is investigated. A theory is constructed for the qualitative and quantitative description of the "destabilization paradox" in these systems, one manifestation of which is an abrupt drop in the critical load and frequency when small dissipative forces are taken into account. The theory is base on an analysis of the bifurcations of multiple eigenvalues of non-self-adjoint differential operators that depend on parameters. Explicit formulae are obtained for the collapse of multiple eigenvalues with Keldysh chains of arbitrary length, for linear differential operators that depend analytically on a complex spectral parameter and are smooth functions of a vector of real parameters. It is shown that the "destabilization paradox" is related to the perturbation by small damping of a double eigenvalue of a circulatory system with a Keldysh chain of length 2, which is responsible for the formation of a singularity on the boundary of the stability domain. Formulae describing the behaviour of the eigenvalues of a non-conservative system when the load and dissipation parameters are varied ar

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Author

O.N. Kirillov; A.O. Seyranian

Publisher

Elsevier Science; Elsevier ; Elsevier Ltd.; Elsevier BV (ISSN 0021-8928)

Published

2005

Language

EN

Field

Engineering (Physical Sciences)