Bifurcation of Eigenvalues of Nonselfadjoint Differential Operators in Nonconservative Stability Problems
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 multipleeigen value with Keldysh chain of arbitra...
Published in: | 21st International Conference on Offshore Mechanics and Arctic Engineering, Volume 3 |
---|---|
Main Authors: | , |
Format: | Book Part |
Language: | unknown |
Published: |
American Society of Mechanical Engineers
2002
|
Subjects: | |
Online Access: | https://nrl.northumbria.ac.uk/id/eprint/29495/ https://doi.org/10.1115/OMAE2002-28076 |
id |
ftunivnorthumb:oai:nrl.northumbria.ac.uk:29495 |
---|---|
record_format |
openpolar |
spelling |
ftunivnorthumb:oai:nrl.northumbria.ac.uk:29495 2023-05-15T14:25:07+02:00 Bifurcation of Eigenvalues of Nonselfadjoint Differential Operators in Nonconservative Stability Problems Kirillov, Oleg Seyranian, Alexander 2002-06-23 https://nrl.northumbria.ac.uk/id/eprint/29495/ https://doi.org/10.1115/OMAE2002-28076 unknown American Society of Mechanical Engineers Kirillov, Oleg and Seyranian, Alexander (2002) Bifurcation of Eigenvalues of Nonselfadjoint Differential Operators in Nonconservative Stability Problems. In: 21st International Conference on Offshore Mechanics and Arctic Engineering, Volume 3. American Society of Mechanical Engineers, New York, pp. 31-37. ISBN 0-7918-3613-4 H300 Mechanical Engineering Book Section PeerReviewed 2002 ftunivnorthumb https://doi.org/10.1115/OMAE2002-28076 2022-09-25T06:05:06Z 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 multipleeigen 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 potential force and tangential follower force is considered and discussed in detail. Book Part Arctic Northumbria University, Newcastle: Northumbria Research Link (NRL) 21st International Conference on Offshore Mechanics and Arctic Engineering, Volume 3 31 37 |
institution |
Open Polar |
collection |
Northumbria University, Newcastle: Northumbria Research Link (NRL) |
op_collection_id |
ftunivnorthumb |
language |
unknown |
topic |
H300 Mechanical Engineering |
spellingShingle |
H300 Mechanical Engineering Kirillov, Oleg Seyranian, Alexander Bifurcation of Eigenvalues of Nonselfadjoint Differential Operators in Nonconservative Stability Problems |
topic_facet |
H300 Mechanical Engineering |
description |
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 multipleeigen 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 potential force and tangential follower force is considered and discussed in detail. |
format |
Book Part |
author |
Kirillov, Oleg Seyranian, Alexander |
author_facet |
Kirillov, Oleg Seyranian, Alexander |
author_sort |
Kirillov, Oleg |
title |
Bifurcation of Eigenvalues of Nonselfadjoint Differential Operators in Nonconservative Stability Problems |
title_short |
Bifurcation of Eigenvalues of Nonselfadjoint Differential Operators in Nonconservative Stability Problems |
title_full |
Bifurcation of Eigenvalues of Nonselfadjoint Differential Operators in Nonconservative Stability Problems |
title_fullStr |
Bifurcation of Eigenvalues of Nonselfadjoint Differential Operators in Nonconservative Stability Problems |
title_full_unstemmed |
Bifurcation of Eigenvalues of Nonselfadjoint Differential Operators in Nonconservative Stability Problems |
title_sort |
bifurcation of eigenvalues of nonselfadjoint differential operators in nonconservative stability problems |
publisher |
American Society of Mechanical Engineers |
publishDate |
2002 |
url |
https://nrl.northumbria.ac.uk/id/eprint/29495/ https://doi.org/10.1115/OMAE2002-28076 |
genre |
Arctic |
genre_facet |
Arctic |
op_relation |
Kirillov, Oleg and Seyranian, Alexander (2002) Bifurcation of Eigenvalues of Nonselfadjoint Differential Operators in Nonconservative Stability Problems. In: 21st International Conference on Offshore Mechanics and Arctic Engineering, Volume 3. American Society of Mechanical Engineers, New York, pp. 31-37. ISBN 0-7918-3613-4 |
op_doi |
https://doi.org/10.1115/OMAE2002-28076 |
container_title |
21st International Conference on Offshore Mechanics and Arctic Engineering, Volume 3 |
container_start_page |
31 |
op_container_end_page |
37 |
_version_ |
1766297546493263872 |