Collapse of the Keldysh Chains and Stability of Continuous Nonconservative Systems

Seyranian, Alexander and Kirillov, Oleg (2004) Collapse of the Keldysh Chains and Stability of Continuous Nonconservative Systems. SIAM Journal on Applied Mathematics, 64 (4). pp. 1383-1407. ISSN 0036-1399

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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.

Item Type:	Article
Subjects:	G100 Mathematics
Department:	Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User:	Oleg Kirillov
Date Deposited:	23 Jan 2017 11:06
Last Modified:	12 Oct 2019 22:27
URI:	http://nrl.northumbria.ac.uk/id/eprint/29312

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