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

Full text not available from this repository. (Request a copy)
Official URL: http://dx.doi.org/10.1137/S0036139902414720

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: 23 Jan 2017 11:11
URI: http://nrl.northumbria.ac.uk/id/eprint/29312

Actions (login required)

View Item View Item

Downloads

Downloads per month over past year

View more statistics


Policies: NRL Policies | NRL University Deposit Policy | NRL Deposit Licence