Collapse of the Keldysh Chains and Stability of Continuous Nonconservative Systems

Alexander Seyranian, Oleg Kirillov

Research output: Contribution to journalArticlepeer-review

24 Citations (Scopus)

Abstract

In the present paper, eigenvalue problems for non-self-adjoint linear differential operators smoothly dependent on a vector of real parameters are considered. Bifurcation of eigenvalues along smooth curves in the parameter space is studied. The case of a multiple eigenvalue with the Keldysh chain of arbitrary length is investigated. Explicit expressions describing bifurcation of eigenvalues are found. The obtained formulas use eigenfunctions and associated functions of the adjoint eigenvalue problems as well as the derivatives of the differential operator taken at the initial point of the parameter space. These results are important for the stability problems and sensitivity analysis of nonconservative systems. As a mechanical application, the extended Beck problem of stability of an elastic column subjected to a partially tangential follower force is considered and discussed in detail.
Original languageEnglish
Pages (from-to)1383-1407
Number of pages25
JournalSIAM Journal on Applied Mathematics
Volume64
Issue number4
Early online date20 May 2004
DOIs
Publication statusE-pub ahead of print - 20 May 2004

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