Bifurcation of Eigenvalues of Nonselfadjoint Differential Operators in Nonconservative Stability Problems

Oleg Kirillov*, Alexander Seyranian

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

In the present paper eigenvalue problems for non-selfadjoint 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 m ultipleeigen value with Keldysh chain of arbitrary length is considered. Explicit expressions describing bifurcation of eigen-values are found. The obtained formulae 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 theory, sensitivity analysis and structural optimization. As a mechanical application the extended Beck's problem of stability of an elastic column under action of potertial force and tangential follower force is considered and discussed in detail.

Original languageEnglish
Title of host publication21st International Conference on Offshore Mechanics and Arctic Engineering, Volume 3
EditorsS K Chakrabarti
Place of PublicationNew York
PublisherAmerican Society of Mechanical Engineers
Pages31-37
Number of pages7
Volume3
ISBN (Print)0-7918-3613-4
DOIs
Publication statusPublished - 23 Jun 2002
EventASME 2002 21st International Conference on Offshore Mechanics and Arctic Engineering - Oslo, Norway
Duration: 23 Jun 2002 → …

Conference

ConferenceASME 2002 21st International Conference on Offshore Mechanics and Arctic Engineering
Period23/06/02 → …

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